Accurate van der Waals coefficients from density functional theory
Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn
2012-01-01
The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765
Towards a more accurate van der Waals density functional
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2014-03-01
The van der Waals density functional (vdW-DF) of Dion et al. [1] has attracted considerable attention, because the functional is able to describe intra- and intermolecular bondings with different natures, e.g., covalent and van der Waals bondings in a seamless fashion within the framework of density functional theory. However, the accuracy of the functional is yet to be improved for the applications to various systems. Here I propose an exchange functional for the second version of vdW-DF [2], which improves the accuracy of vdW-DF. The keys in the improved exchange are the matching to the gradient expansion approximation in the slowly varying limit and the large density gradient behavior set in Becke's exchange (B86b)[3]. Systematic study on gas phase molecules, solids, and molecular adsorption demonstrates the applicability of the proposed functional to a wide variety of materials.
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry.
Tao, Jianmin; Mo, Yuxiang
2016-08-12
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang
2016-08-01
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.
Brandenburg, Jan Gerit; Caldeweyher, Eike; Grimme, Stefan
2016-06-21
We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.
NASA Astrophysics Data System (ADS)
Janesko, Benjamin G.; Proynov, Emil
2017-02-01
Density functional approximations (DFAs) often suffer from self-repulsion and delocalization errors which are reduced by exact (Hartree-Fock-like) exchange admixture. Oyeyemi and co-workers recently showed that several DFAs with little exact exchange incorrectly predict bent alkynyl radical geometries, giving errors in ab initio composite methods using density functional theory geometries [V. B. Oyeyemi et al., J. Phys. Chem. Lett. 3, 289 (2012)]. We show that the simple Hartree-Fock-Slater and Xα DFAs, which have substantial delocalization error, predict linear alkynyl radical geometries without incorporating exact exchange. Our Rung 3.5 DFAs, and rescaled generalized gradient approximations, can give either linear σ, bent σ -π , or nearly linear π radicals, all without incorporating exact exchange. This highlights the complexity of delocalization error, the utility of accurate empirical DFA geometries for ab initio composite methods, and the insights to be gained from Rung 3.5 DFAs.
Brandenburg, Jan Gerit; Grimme, Stefan
2014-06-05
The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of <0.5 kcal/mol compared to DFT-D are obtained.
NASA Astrophysics Data System (ADS)
Buda, I. G.; Lane, C.; Barbiellini, B.; Ruzsinszky, A.; Sun, J.; Bansil, A.
2017-03-01
We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.
Buda, I. G.; Lane, C.; Barbiellini, B.; Ruzsinszky, A.; Sun, J.; Bansil, A.
2017-01-01
We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally. PMID:28333131
NASA Astrophysics Data System (ADS)
Sun, Jianwei
The accuracy and computational efficiency of the widely used Kohn-Sham density functional theory (DFT) are limited by the approximation to its exchange-correlation energy Exc. The earliest local density approximation (LDA) overestimates the strengths of all bonds near equilibrium (even the vdW bonds). By adding the electron density gradient to model Exc, generalized gradient approximations (GGAs) generally soften the bonds to give robust and overall more accurate descriptions, except for the vdW interaction which is largely lost. Further improvement for covalent, ionic, and hydrogen bonds can be obtained by the computationally more expensive hybrid GGAs, which mix GGAs with the nonlocal exact exchange. Meta-GGAs are still semilocal in computation and thus efficient. Compared to GGAs, they add the kinetic energy density that enables them to recognize and accordingly treat different bonds, which no LDA or GGA can. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and vdW bonds) at comparable efficiency. Often SCAN matches or improves upon the accuracy of a hybrid functional, at almost-GGA cost. This work has been supported by NSF under DMR-1305135 and CNS-09-58854, and by DOE BES EFRC CCDM under DE-SC0012575.
NASA Astrophysics Data System (ADS)
Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo; Sun, Zhaoru; Ruzsinszky, Adrienn; Peng, Haowei; Yang, Zenghui; Paul, Arpita; Waghmare, Umesh; Wu, Xifan; Klein, Michael L.; Perdew, John P.
2016-09-01
One atom or molecule binds to another through various types of bond, the strengths of which range from several meV to several eV. Although some computational methods can provide accurate descriptions of all bond types, those methods are not efficient enough for many studies (for example, large systems, ab initio molecular dynamics and high-throughput searches for functional materials). Here, we show that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) within the density functional theory framework predicts accurate geometries and energies of diversely bonded molecules and materials (including covalent, metallic, ionic, hydrogen and van der Waals bonds). This represents a significant improvement at comparable efficiency over its predecessors, the GGAs that currently dominate materials computation. Often, SCAN matches or improves on the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on chemistry and materials science.
Goodpaster, Jason D.; Barnes, Taylor A.; Miller, Thomas F.; Manby, Frederick R.
2014-05-14
We analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using wavefunction methods, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We test an MP2 correction for this term and demonstrate that the corrected embedding scheme accurately reproduces wavefunction calculations for a series of chemical reactions. Our projector-based embedding method uses localized occupied orbitals to partition the system; as with other local correlation methods, abrupt changes in the character of the localized orbitals along a reaction coordinate can lead to discontinuities in the embedded energy, but we show that these discontinuities are small and can be systematically reduced by increasing the size of the active region. Convergence of reaction energies with respect to the size of the active subsystem is shown to be rapid for all cases where the density functional treatment is able to capture the polarization of the environment, even in conjugated systems, and even when the partition cuts across a double bond.
Accurate ab Initio Spin Densities.
Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus
2012-06-12
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].
NASA Astrophysics Data System (ADS)
Powell, Jacob; Heider, Emily C.; Campiglia, Andres; Harper, James K.
2016-10-01
The ability of density functional theory (DFT) methods to predict accurate fluorescence spectra for polycyclic aromatic hydrocarbons (PAHs) is explored. Two methods, PBE0 and CAM-B3LYP, are evaluated both in the gas phase and in solution. Spectra for several of the most toxic PAHs are predicted and compared to experiment, including three isomers of C24H14 and a PAH containing heteroatoms. Unusually high-resolution experimental spectra are obtained for comparison by analyzing each PAH at 4.2 K in an n-alkane matrix. All theoretical spectra visually conform to the profiles of the experimental data but are systematically offset by a small amount. Specifically, when solvent is included the PBE0 functional overestimates peaks by 16.1 ± 6.6 nm while CAM-B3LYP underestimates the same transitions by 14.5 ± 7.6 nm. These calculated spectra can be empirically corrected to decrease the uncertainties to 6.5 ± 5.1 and 5.7 ± 5.1 nm for the PBE0 and CAM-B3LYP methods, respectively. A comparison of computed spectra in the gas phase indicates that the inclusion of n-octane shifts peaks by +11 nm on average and this change is roughly equivalent for PBE0 and CAM-B3LYP. An automated approach for comparing spectra is also described that minimizes residuals between a given theoretical spectrum and all available experimental spectra. This approach identifies the correct spectrum in all cases and excludes approximately 80% of the incorrect spectra, demonstrating that an automated search of theoretical libraries of spectra may eventually become feasible.
Mackie, Iain D; Dilabio, Gino A
2010-06-21
B971, PBE and PBE1 density functionals with 6-31G(d) basis sets are shown to accurately describe the binding in dispersion bound dimers. This is achieved through the use of dispersion-correcting potentials (DCPs) in conjunction with counterpoise corrections. DCPs resemble and are applied like conventional effective core potentials that can be used with most computational chemistry programs without code modification. Rather, DCPs are implemented by simple appendage to the input files for these types of programs. Binding energies are predicted to within ca. 11% and monomer separations to within ca. 0.06 A of high-level wavefunction data using B971/6-31G(d)-DCP. Similar results are obtained for PBE and PBE1 with the 6-31G(d) basis sets and DCPs. Although results found using the 3-21G(d) are not as impressive, they never-the-less show promise as a means of initial study for a wide variety of dimers, including those dominated by dispersion, hydrogen-bonding and a mixture of interactions. Notable improvement is found in comparison to M06-2X/6-31G(d) data, e.g., mean absolute deviations for the S22-set of dimers of ca. 13.6 and 16.5% for B971/6-31G(d)-DCP and M06-2X, respectively. However, it should be pointed out that the latter data were obtained using a larger integration grid size since a smaller grid results in different binding energies and geometries for simple dispersion-bound dimers such as methane and ethene.
NASA Astrophysics Data System (ADS)
Lutnæs, Ola B.; Teale, Andrew M.; Helgaker, Trygve; Tozer, David J.; Ruud, Kenneth; Gauss, Jürgen
2009-10-01
An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.
Matanovic, Ivana; Atanassov, Plamen; Kiefer, Boris; Garzon, Fernando; Henson, Neil J.
2014-10-05
The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized-gradient approximation (GGA), nonlocal correlation, meta-GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised-RPBE, vdW-DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW-DF and meta-GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of 22.62 and 21.1% for the NAN stretching and RhAH stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the RhAH and NAN stretching modes from the bulk phonons and by solving one- and two-dimensional Schr€odinger equation associated with the RhAH, RhAN, and NAN potential energy we calculated the anharmonic correction for NAN and RhAH stretching modes as 231 cm21 and 277 cm21 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments.
NASA Astrophysics Data System (ADS)
Ghosh, Swarnava; Suryanarayana, Phanish
2017-03-01
As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable 'egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.
Sun, Y Y; Kim, Yong-Hyun; Lee, Kyuho; Zhang, S B
2008-10-21
Density functional theory (DFT) in the commonly used local density or generalized gradient approximation fails to describe van der Waals (vdW) interactions that are vital to organic, biological, and other molecular systems. Here, we propose a simple, efficient, yet accurate local atomic potential (LAP) approach, named DFT+LAP, for including vdW interactions in the framework of DFT. The LAPs for H, C, N, and O are generated by fitting the DFT+LAP potential energy curves of small molecule dimers to those obtained from coupled cluster calculations with single, double, and perturbatively treated triple excitations, CCSD(T). Excellent transferability of the LAPs is demonstrated by remarkable agreement with the JSCH-2005 benchmark database [P. Jurecka et al. Phys. Chem. Chem. Phys. 8, 1985 (2006)], which provides the interaction energies of CCSD(T) quality for 165 vdW and hydrogen-bonded complexes. For over 100 vdW dominant complexes in this database, our DFT+LAP calculations give a mean absolute deviation from the benchmark results less than 0.5 kcal/mol. The DFT+LAP approach involves no extra computational cost other than standard DFT calculations and no modification of existing DFT codes, which enables straightforward quantum simulations, such as ab initio molecular dynamics, on biomolecular systems, as well as on other organic systems.
Hammond, J.; Govind, N.; Kowalski, K.; Autschbach, J.; Xantheas, S.; PNNL; Univ. of Buffalo
2009-12-07
The static dipole polarizabilities of water clusters (2 {le} N {le} 12) are determined at the coupled-cluster level of theory (CCSD). For the dipole polarizability of the water monomer it was determined that the role of the basis set is more important than that of electron correlation and that the basis set augmentation converges with two sets of diffuse functions. The CCSD results are used to benchmark a variety of density functionals while the performance of several families of basis sets (Dunning, Pople, and Sadlej) in producing accurate values for the polarizabilities was also examined. The Sadlej family of basis sets was found to produce accurate results when compared to the ones obtained with the much larger Dunning basis sets. It was furthermore determined that the PBE0 density functional with the aug-cc-pVDZ basis set produces overall remarkably accurate polarizabilities at a moderate computational cost.
NASA Astrophysics Data System (ADS)
Ihrig, Arvid Conrad; Wieferink, Jürgen; Zhang, Igor Ying; Ropo, Matti; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Blum, Volker
2015-09-01
A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant (‘RI-LVL’), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.
Gao, Ting; Sun, Shi-Ling; Shi, Li-Li; Li, Hui; Li, Hong-Zhi; Su, Zhong-Min; Lu, Ying-Hua
2009-05-14
Support vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce least-squares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LS-SVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LS-SVM approach reduces the root-mean-square deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the B3LYP/6-31G(d) calculation. Thus, the LS-SVM correction on top of B3LYP/6-31G(d) is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally.
Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Thygesen, Kristian S.
2014-05-01
We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent density-functional theory. The key ingredient is a renormalization scheme, which eliminates the divergence of the correlation hole characteristic of any local kernel. This new class of renormalized kernels gives a significantly better description of the short-range correlations in covalent bonds compared to the random phase approximation (RPA) and yields a fourfold improvement of RPA binding energies in both molecules and solids. We also consider examples of barrier heights in chemical reactions, molecular adsorption, and graphene interacting with metal surfaces, which are three examples where the RPA has been successful. In these cases, the renormalized kernel provides results that are of equal quality or even slightly better than the RPA, with a similar computational cost.
Barone, Veronica; Hod, Oded; Peralta, Juan E; Scuseria, Gustavo E
2011-04-19
Over the last several years, low-dimensional graphene derivatives, such as carbon nanotubes and graphene nanoribbons, have played a central role in the pursuit of a plausible carbon-based nanotechnology. Their electronic properties can be either metallic or semiconducting depending purely on morphology, but predicting their electronic behavior has proven challenging. The combination of experimental efforts with modeling of these nanometer-scale structures has been instrumental in gaining insight into their physical and chemical properties and the processes involved at these scales. Particularly, approximations based on density functional theory have emerged as a successful computational tool for predicting the electronic structure of these materials. In this Account, we review our efforts in modeling graphitic nanostructures from first principles with hybrid density functionals, namely the Heyd-Scuseria-Ernzerhof (HSE) screened exchange hybrid and the hybrid meta-generalized functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh). These functionals provide a powerful tool for quantitatively studying structure-property relations and the effects of external perturbations such as chemical substitutions, electric and magnetic fields, and mechanical deformations on the electronic and magnetic properties of these low-dimensional carbon materials. We show how HSE and TPSSh successfully predict the electronic properties of these materials, providing a good description of their band structure and density of states, their work function, and their magnetic ordering in the cases in which magnetism arises. Moreover, these approximations are capable of successfully predicting optical transitions (first and higher order) in both metallic and semiconducting single-walled carbon nanotubes of various chiralities and diameters with impressive accuracy. This versatility includes the correct prediction of the trigonal warping splitting in metallic nanotubes. The results predicted
NASA Astrophysics Data System (ADS)
Liu, Jie; Herbert, John M.
2015-07-01
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ˜40 times faster than traditional TDDFT calculations.
Liu, Jie; Herbert, John M
2015-07-21
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ∼40 times faster than traditional TDDFT calculations.
Teale, Andrew M; Lutnæs, Ola B; Helgaker, Trygve; Tozer, David J; Gauss, Jürgen
2013-01-14
Accurate sets of benchmark nuclear-magnetic-resonance shielding constants and spin-rotation constants are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the calculated coupled-cluster constants is established by a careful comparison with experimental data, taking into account zero-point vibrational corrections. Coupled-cluster basis-set convergence is analyzed and extrapolation techniques are employed to estimate basis-set-limit quantities, thereby establishing an accurate benchmark data set. Together with the set provided for rotational g-tensors and magnetizabilities in our previous work [O. B. Lutnæs, A. M. Teale, T. Helgaker, D. J. Tozer, K. Ruud, and J. Gauss, J. Chem. Phys. 131, 144104 (2009)], it provides a substantial source of consistently calculated high-accuracy data on second-order magnetic response properties. The utility of this benchmark data set is demonstrated by examining a wide variety of Kohn-Sham exchange-correlation functionals for the calculation of these properties. None of the existing approximate functionals provide an accuracy competitive with that provided by CCSD or CCSD(T) theory. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of Kohn-Sham calculations constrained to give the same electronic density. Routes to future improvements are discussed in light of this comparison.
NASA Astrophysics Data System (ADS)
Gloor, Guy J.; Jackson, George; Blas, Felipe J.; del Río, Elvira Martín; de Miguel, Enrique
2004-12-01
A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martı´n del Rı´o, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martı´n del Rı´o, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and
Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W; Castillo-Alvarado, F L
2009-07-14
A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic energy (T(c)) is computed using the density-functional theory virial relation. Based on our calculations, it is shown that the conventional approach where atomic energies are computed using only the noninteracting part of the kinetic energy might be in error by hundreds of kJ/mol.
Accurate Measurement of Bone Density with QCT
NASA Technical Reports Server (NTRS)
Cleek, Tammy M.; Beaupre, Gary S.; Matsubara, Miki; Whalen, Robert T.; Dalton, Bonnie P. (Technical Monitor)
2002-01-01
The objective of this study was to determine the accuracy of bone density measurement with a new OCT technology. A phantom was fabricated using two materials, a water-equivalent compound and hydroxyapatite (HA), combined in precise proportions (QRM GrnbH, Germany). The phantom was designed to have the approximate physical size and range in bone density as a human calcaneus, with regions of 0, 50, 100, 200, 400, and 800 mg/cc HA. The phantom was scanned at 80, 120 and 140 KVp with a GE CT/i HiSpeed Advantage scanner. A ring of highly attenuating material (polyvinyl chloride or teflon) was slipped over the phantom to alter the image by introducing non-axi-symmetric beam hardening. Images were corrected with a new OCT technology using an estimate of the effective X-ray beam spectrum to eliminate beam hardening artifacts. The algorithm computes the volume fraction of HA and water-equivalent matrix in each voxel. We found excellent agreement between expected and computed HA volume fractions. Results were insensitive to beam hardening ring material, HA concentration, and scan voltage settings. Data from all 3 voltages with a best fit linear regression are displays.
Mardirossian, Narbe; Head-Gordon, Martin
2016-09-13
The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. Overall, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). As an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.
Vargas, Alfredo; Krivokapic, Itana; Hauser, Andreas; Lawson Daku, Latévi Max
2013-03-21
We report a detailed DFT study of the energetic and structural properties of the spin-crossover Co(ii) complex [Co(tpy)(2)](2+) (tpy = 2,2':6',2''-terpyridine) in the low-spin (LS) and the high-spin (HS) states, using several generalized gradient approximation and hybrid functionals. In either spin-state, the results obtained with the functionals are consistent with one another and in good agreement with available experimental data. Although the different functionals correctly predict the LS state as the electronic ground state of [Co(tpy)(2)](2+), they give estimates of the HS-LS zero-point energy difference which strongly depend on the functional used. This dependency on the functional was also reported for the DFT estimates of the zero-point energy difference in the HS complex [Co(bpy)(3)](2+) (bpy = 2,2'-bipyridine) [A. Vargas, A. Hauser and L. M. Lawson Daku, J. Chem. Theory Comput., 2009, 5, 97]. The comparison of the and estimates showed that all functionals correctly predict an increase of the zero-point energy difference upon the bpy → tpy ligand substitution, which furthermore weakly depends on the functionals, amounting to . From these results and basic thermodynamic considerations, we establish that, despite their limitations, current DFT methods can be applied to the accurate determination of the spin-state energetics of complexes of a transition metal ion, or of these complexes in different environments, provided that the spin-state energetics is accurately known in one case. Thus, making use of the availability of a highly accurate ab initio estimate of the HS-LS energy difference in the complex [Co(NCH)(6)](2+) [L. M. Lawson Daku, F. Aquilante, T. W. Robinson and A. Hauser, J. Chem. Theory Comput., 2012, 8, 4216], we obtain for [Co(tpy)(2)](2+) and [Co(bpy)(3)](2+) best estimates of and , in good agreement with the known magnetic behaviour of the two complexes.
NASA Astrophysics Data System (ADS)
Hu, Ching-Han; Chong, Delano P.
1997-03-01
Density functional theory and the unrestricted generalized transition state (uGTS) model were applied to study the core-electron binding energies (CEBEs) of open-shell molecules. Basis set scaling based on Clementi and Raimondi's rules for atomic screening was used along with the cc-pVTZ basis set. The scaled pVTZ basis set is almost as good as the cc-pV5Z and complete basis set limit in predicting CEBEs. For small molecules (O 2, NO, NF 2 and NO 2) the average absolute deviation (aad) of our prediction (scaled pVTZ) is only 0.29 eV. For the larger molecule (CF 3) 2NO the aad is 0.56 eV, compared with experimental uncertainty of 0.5 eV. Theoretical predicted multiplet splittings for the small molecules agree quite well with experiment: the average deviation is -0.33 eV. For (CF 3) 2NO the calculated multiplet splittings are much smaller than the experimental ones. We also predict the CEBEs of PO, SN and SO, which have not been observed experimentally.
Chan, Bun; Radom, Leo
2016-08-09
In the present study, we have obtained geometries and frequency scale factors for a number of double-hybrid density functional theory (DH-DFT) procedures. We have evaluated their performance for obtaining thermochemical quantities [zero-point vibrational energies (ZPVE) and thermal corrections for 298 K enthalpies (ΔH298) and 298 K entropies (S298)] to be used within high-level composite protocols (using the W2X procedure as a probe). We find that, in comparison with the previously prescribed protocol for optimization and frequency calculations (B3-LYP/cc-pVTZ+d), the use of contemporary DH-DFT methods such as DuT-D3 and DSD-type procedures leads to a slight overall improved performance compared with B3-LYP. A major strength of this approach, however, lies in the better robustness of the DH-DFT methods in that the largest deviations are notably smaller than those for B3-LYP. In general, the specific choices of the DH-DFT procedure and the associated basis set do not drastically change the performance. Nonetheless, we find that the DSD-PBE-P86/aug'-cc-pVTZ+d combination has a very slight edge over the others that we have examined, and we recommend its general use for geometry optimization and vibrational frequency calculations, in particular within high-level composite methods such as the higher-level members of the WnX series of protocols. The scale factors determined for DSD-PBE-P86/aug'-cc-pVTZ+d are 0.9830 (ZPVE), 0.9876 (ΔH298), and 0.9923 (S298).
Partition Density Functional Theory
NASA Astrophysics Data System (ADS)
Wasserman, Adam
2012-02-01
Partition Density Functional Theory (PDFT) is a formally exact method for obtaining molecular properties from self-consistent calculations on isolated fragments [1,2]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that sum to the correct molecular density. I describe our progress understanding the behavior of the fragment energies as a function of fragment occupations, derivative discontinuities, practical implementation, and applications of PDFT to small molecules. I also discuss implications for ground-state Density Functional Theory, such as the promise of PDFT to circumvent the delocalization error of approximate density functionals. [4pt] [1] M.H. Cohen and A. Wasserman, J. Phys. Chem. A, 111, 2229(2007).[0pt] [2] P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010).
NASA Astrophysics Data System (ADS)
Kapil, V.; VandeVondele, J.; Ceriotti, M.
2016-02-01
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious approximations. Even though recent developments have significantly reduced the overhead for modeling the quantum nature of the nuclei, the cost is still prohibitive when combined with advanced electronic structure methods. Here we present how multiple time step integrators can be combined with ring-polymer contraction techniques (effectively, multiple time stepping in imaginary time) to reduce virtually to zero the overhead of modelling nuclear quantum effects, while describing inter-atomic forces at high levels of electronic structure theory. This is demonstrated for a combination of MP2 and semi-local DFT applied to the Zundel cation. The approach can be seamlessly combined with other methods to reduce the computational cost of path integral calculations, such as high-order factorizations of the Boltzmann operator or generalized Langevin equation thermostats.
Kapil, V.; Ceriotti, M.; VandeVondele, J.
2016-02-07
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious approximations. Even though recent developments have significantly reduced the overhead for modeling the quantum nature of the nuclei, the cost is still prohibitive when combined with advanced electronic structure methods. Here we present how multiple time step integrators can be combined with ring-polymer contraction techniques (effectively, multiple time stepping in imaginary time) to reduce virtually to zero the overhead of modelling nuclear quantum effects, while describing inter-atomic forces at high levels of electronic structure theory. This is demonstrated for a combination of MP2 and semi-local DFT applied to the Zundel cation. The approach can be seamlessly combined with other methods to reduce the computational cost of path integral calculations, such as high-order factorizations of the Boltzmann operator or generalized Langevin equation thermostats.
AN ACCURATE FLUX DENSITY SCALE FROM 1 TO 50 GHz
Perley, R. A.; Butler, B. J. E-mail: BButler@nrao.edu
2013-02-15
We develop an absolute flux density scale for centimeter-wavelength astronomy by combining accurate flux density ratios determined by the Very Large Array between the planet Mars and a set of potential calibrators with the Rudy thermophysical emission model of Mars, adjusted to the absolute scale established by the Wilkinson Microwave Anisotropy Probe. The radio sources 3C123, 3C196, 3C286, and 3C295 are found to be varying at a level of less than {approx}5% per century at all frequencies between 1 and 50 GHz, and hence are suitable as flux density standards. We present polynomial expressions for their spectral flux densities, valid from 1 to 50 GHz, with absolute accuracy estimated at 1%-3% depending on frequency. Of the four sources, 3C286 is the most compact and has the flattest spectral index, making it the most suitable object on which to establish the spectral flux density scale. The sources 3C48, 3C138, 3C147, NGC 7027, NGC 6542, and MWC 349 show significant variability on various timescales. Polynomial coefficients for the spectral flux density are developed for 3C48, 3C138, and 3C147 for each of the 17 observation dates, spanning 1983-2012. The planets Venus, Uranus, and Neptune are included in our observations, and we derive their brightness temperatures over the same frequency range.
Towards accurate and precise estimates of lion density.
Elliot, Nicholas B; Gopalaswamy, Arjun M
2016-12-13
Reliable estimates of animal density are fundamental to our understanding of ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation biology since wildlife authorities rely on these figures to make decisions. However, it is notoriously difficult to accurately estimate density for wide-ranging species such as carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores. African lions (Panthera leo) provide an excellent example as although abundance indices have been shown to produce poor inferences, they continue to be used to estimate lion density and inform management and policy. In this study we adapt a Bayesian spatially explicit capture-recapture model to estimate lion density in the Maasai Mara National Reserve (MMNR) and surrounding conservancies in Kenya. We utilize sightings data from a three-month survey period to produce statistically rigorous spatial density estimates. Overall posterior mean lion density was estimated to be 16.85 (posterior standard deviation = 1.30) lions over one year of age per 100km(2) with a sex ratio of 2.2♀:1♂. We argue that such methods should be developed, improved and favored over less reliable methods such as track and call-up surveys. We caution against trend analyses based on surveys of differing reliability and call for a unified framework to assess lion numbers across their range in order for better informed management and policy decisions to be made. This article is protected by copyright. All rights reserved.
Wave-function functionals for the density
Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht
2011-11-15
We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.
Does a pneumotach accurately characterize voice function?
NASA Astrophysics Data System (ADS)
Walters, Gage; Krane, Michael
2016-11-01
A study is presented which addresses how a pneumotach might adversely affect clinical measurements of voice function. A pneumotach is a device, typically a mask, worn over the mouth, in order to measure time-varying glottal volume flow. By measuring the time-varying difference in pressure across a known aerodynamic resistance element in the mask, the glottal volume flow waveform is estimated. Because it adds aerodynamic resistance to the vocal system, there is some concern that using a pneumotach may not accurately portray the behavior of the voice. To test this hypothesis, experiments were performed in a simplified airway model with the principal dimensions of an adult human upper airway. A compliant constriction, fabricated from silicone rubber, modeled the vocal folds. Variations of transglottal pressure, time-averaged volume flow, model vocal fold vibration amplitude, and radiated sound with subglottal pressure were performed, with and without the pneumotach in place, and differences noted. Acknowledge support of NIH Grant 2R01DC005642-10A1.
Karton, Amir; Tarnopolsky, Alex; Lamère, Jean-François; Schatz, George C; Martin, Jan M L
2008-12-18
We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we
Density-dependent covariant energy density functionals
Lalazissis, G. A.
2012-10-20
Relativistic nuclear energy density functionals are applied to the description of a variety of nuclear structure phenomena at and away fromstability line. Isoscalar monopole, isovector dipole and isoscalar quadrupole giant resonances are calculated using fully self-consistent relativistic quasiparticle randomphase approximation, based on the relativistic Hartree-Bogoliubovmodel. The impact of pairing correlations on the fission barriers in heavy and superheavy nuclei is examined. The role of pion in constructing desnity functionals is also investigated.
Density functional theory of complex transition densities.
Ernzerhof, Matthias
2006-09-28
We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.
Density functional theory: Foundations reviewed
NASA Astrophysics Data System (ADS)
Kryachko, Eugene S.; Ludeña, Eduardo V.
2014-11-01
-geared functionals. These problems are discussed by making reference to ab initio DFT as well as to the local-scaling-transformation version of DFT, LS-DFT. In addition, we examine the question of the accuracy of approximate exchange-correlation functionals in the light of their non-observance of the variational principle. Why do approximate functionals yield reasonable (and accurate) descriptions of many molecular and condensed matter properties? Are the conditions imposed on exchange and correlation functionals sufficiently adequate to produce accurate semi-empirical functionals? In this respect, we consider the question of whether the results reflect a true approach to chemical accuracy or are just the outcome of a virtuoso-like performance which cannot be systematically improved. We discuss the issue of the accuracy of the contemporary DFT results by contrasting them to those obtained by the alternative RDMT and NOFT. We discuss the possibility of improving DFT functionals by applying in a systematic way the N-representability conditions on the 2-RDM. In this respect, we emphasize the possibility of constructing 2-matrices in the context of the local scaling transformation version of DFT to which the N-representability condition of RDM theory may be applied. We end up our revision of HKS-DFT by considering some of the problems related to spin symmetry and discuss some current issues dealing with a proper treatment of open-shell systems. We are particularly concerned, as in the rest of this paper, mostly with foundational issues arising in the construction of functionals. We dedicate the whole Section 4 to the local-scaling transformation version of density functional theory, LS-DFT. The reason is that in this theory some of the fundamental problems that appear in HKS-DFT, have been solved. For example, in LS-DFT the functionals are, in principle, designed to fulfill v- and N-representability conditions from the outset. This is possible because LS-DFT is based on density
Accurate sperm morphology assessment predicts sperm function.
Abu Hassan Abu, D; Franken, D R; Hoffman, B; Henkel, R
2012-05-01
Sperm morphology has been associated with in vitro as well as in vivo fertilisation. The study aimed to evaluate the possible relation between the percentage of spermatozoa with normal morphology and the following sperm functional assays: (i) zona-induced acrosome reaction (ZIAR); (ii) DNA integrity; (iii) chromatin condensation; (iv) sperm apoptosis; and (v) fertilisation rates. Regression analysis was employed to calculate the association between morphology and different functional tests. Normal sperm morphology correlated significantly with the percentages of live acrosome-reacted spermatozoa in the ZIAR (r = 0.518; P < 0.0001; n = 92), DNA integrity (r = -0.515; P = 0.0018; n = 34), CMA(3) -positive spermatozoa (r = -0.745; P < 0.0001; n = 92), sperm apoptosis (r = -0.395; P = 0.0206; n = 34) and necrosis (r = -0.545; P = 0.0009; n = 34). Negative correlations existed between for the acrosome reaction, and DNA integrity, while negative associations were recorded with the percentages of CMA(3) -positive spermatozoa, apoptotic and necrotic spermatozoa. Sperm morphology is related to sperm dysfunction such as poor chromatin condensation, acrosome reaction and DNA integrity. Negative and significant correlations existed between normal sperm morphology and chromatin condensation, the percentage of spermatozoa with abnormal DNA and spermatozoa with apoptotic activity. The authors do not regard sperm morphology as the only test for the diagnosis of male fertility, but sperm morphology can serve as a valuable indicator of underlying dysfunction.
NASA Astrophysics Data System (ADS)
Challacombe, Matt; Cioslowski, Jerzy
When applied to electronic wavefunctions calculated with Gaussian-type basis functions, the Hiller-Sucher-Feinberg (HSF) identity improves the accuracy of the electron density at non-hydrogen nuclei by more than an order of magnitude, yielding approximate electron-nuclear cusps. However, the HSF electron densities at hydrogen nuclei bound to heavy atoms are greatly overestimated. This phenomenon is associated with the asymptotic behaviour of the HSF density, which incorrectly decreases to a constant when the sum of Hellmann-Feynman forces acting on nuclei is finite. A method for constraining variational wavefunctions to yield vanishing Hellmann-Feynman forces is described. Hartree-Fock calculations of the constrained HSF (CHSF) electron densities with the 6-31G, 6-31G**, and 6-311++G** basis sets are reported at the nuclei of various diatomic molecules, and are compared with their corresponding conventional, HSF, and Hartree-Fock limit values. These calculations show that differences between HSF and CHSF densities are minor at nonhydrogen nuclei. Importantly, the calculated HF/6-311++G** CHSF densities are on average three times more accurate than the conventional densities at hydrogen nuclei.
General performance of density functionals.
Sousa, Sérgio Filipe; Fernandes, Pedro Alexandrino; Ramos, Maria João
2007-10-25
The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
Maps of current density using density-functional methods
NASA Astrophysics Data System (ADS)
Soncini, A.; Teale, A. M.; Helgaker, T.; de Proft, F.; Tozer, D. J.
2008-08-01
The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered-namely, O3, CO, PN, and H2CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules.
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Density Functionals with Broad Applicability in Chemistry
Zhao, Yan; Truhlar, Donald G.
2008-02-01
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy “across-theboard” for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06- 2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate
NASA Astrophysics Data System (ADS)
Chong, Delano P.; Hu, Ching-Han; Duffy, Patrick
1996-02-01
A scaling procedure based on Clementi and Raimondi's rules for atomic screening was proposed for atomic orbital basis sets in the unrestricted generalized transition state (uGTS) model of density functional calculation of core-electron binding energies (CEBEs). The exchange-correlation potential is based on a combined functional of Becke's exchange (B88) and Perdew's correlation (P86). This proposal was tested on CEBEs of twelve small molecules, including F 2, N 2 and H 2O, and applied to the computation of CEBEs of three isomers of C 2H 4O 2: acetic acid (CH 3COOH), methyl formate (HCOOCH 3), and glycolic aldehyde (CH 2OHCHO). In all cases, the new scaled pVTZ basis performs almost as well as the much larger cc-pV5Z and the average absolute difference between the results from the scaled pVTZ and estimated complete basis set limits is 0.04 eV.
Accurate Electron Densities at Nuclei Using Small Ramp-Gaussian Basis Sets.
McKemmish, Laura K; Gilbert, Andrew T B
2015-08-11
Electron densities at nuclei are difficult to calculate accurately with all-Gaussian basis sets because they lack an electron-nuclear cusp. The newly developed mixed ramp-Gaussian basis sets, such as R-31G, possess electron-nuclear cusps due to the presence of ramp functions in the basis. The R-31G basis set is a general-purpose mixed ramp-Gaussian basis set modeled on the 6-31G basis set. The prediction of electron densities at nuclei using R-31G basis sets for Li-F outperforms Dunning, Pople, and Jensen general purpose all-Gaussian basis sets of triple-ζ quality or lower and the cc-pVQZ basis set. It is of similar quality to the specialized pcJ-0 basis set which was developed with partial decontraction of core functions and extra high exponent s-Gaussians to predict electron density at the nucleus. These results show significant advantages in the properties of mixed ramp-Gaussian basis sets compared to all-Gaussian basis sets.
Constrained density functional for noncollinear magnetism
NASA Astrophysics Data System (ADS)
Ma, Pui-Wai; Dudarev, S. L.
2015-02-01
Energies of arbitrary small- and large-angle noncollinear excited magnetic configurations are computed using a highly accurate constrained density functional theory approach. Numerical convergence and accuracy are controlled by the choice of Lagrange multipliers λI entering the constraining conditions. The penalty part Ep of the constrained energy functional at its minimum is shown to be inversely proportional to λI, enabling a simple, robust, and accurate iterative procedure to be followed to find a convergent solution. The method is implemented as a part of ab initio vasp package, and applied to the investigation of noncollinear B2-like and <001 > double-layer antiferromagnetic configurations of bcc iron, Fe2 dimer, and amorphous iron. Forces acting on atoms depend on the orientations of magnetic moments, and the proposed approach enables constrained self-consistent noncollinear magnetic and structural relaxation of large atomic systems to be carried out.
Studies in Density Functional Theory
NASA Astrophysics Data System (ADS)
Lee, Hsing
The first chapter begins with reviews of density -functional theory and Green's function method. The connections between these two theories are emphasized. Then we present an approximate model of kinetic energy functional and a possible form of the universal functional is given through an equality obeyed by true ground state densities. Chapter two is aimed at developing a general formulation of the response function in density-functional theory. We first give our definition of response functions in the context of functional derivative. The parameter-differentiation technique employed greatly reduces the efforts for computations. The advantage of this method is its numerical simplicity. It is also the aim of this chapter to elucidate the connections between exchange-correlation potential and the response functions. We show that the computations of response functions in the Kohn-Sham formulation will be exact if the so-called uniqueness assumption we present here is true. Various integral formulas for nonlinear response functions are derived here for the first time. In the third chapter we demonstrate that the exchange -correlation functional given in the form of Pade approximation to gradient expansion approximation, yields excellent results when applied to atoms. The coefficients for the Pade approximation are derived by numerical fits to the exchange and exchange -correlation energies of the atoms He through Ar. The fitted non-local gradient corrections are used in the minimization of the Kohn-Sham functional to solve for the exchange and exchange-correlation total energies. The resulting standard deviations in the calculated total energies are 0.0043 for exchange only and 0.0014 for exchange-correlation. The conjoint relation of kinetic and exchange energy functionals is proposed in the fourth chapter. Supportive evidence is given numerically and theoretically. Test cases are the second-row atoms and a group of small molecules with Becke equivalent form, and
Efficient and accurate computation of the incomplete Airy functions
NASA Technical Reports Server (NTRS)
Constantinides, E. D.; Marhefka, R. J.
1993-01-01
The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
Density functionals from deep learning
NASA Astrophysics Data System (ADS)
McMahon, Jeffrey
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional (DF) are necessary. Machine learning has recently been proposed as a novel approach to discover such a DF (or components of it). Conventional machine learning algorithms, however, are limited in their ability to process data in their raw form, leading to invariance and/or sensitivity issues. In this presentation, an alternative approach based on deep learning will be demonstrated. Deep learning allows computational models that are capable of discovering intricate structure in large and/or high-dimensional data sets with multiple levels of abstraction, and do not suffer from the aforementioned issues. Results from the application of this approach to the prediction of the kinetic-energy DF of noninteracting electrons will be presented. Using theoretical results from computer science, a connection between the underlying model and the theorems of Hohenberg and Kohn will also be suggested.
Accurate perception of negative emotions predicts functional capacity in schizophrenia.
Abram, Samantha V; Karpouzian, Tatiana M; Reilly, James L; Derntl, Birgit; Habel, Ute; Smith, Matthew J
2014-04-30
Several studies suggest facial affect perception (FAP) deficits in schizophrenia are linked to poorer social functioning. However, whether reduced functioning is associated with inaccurate perception of specific emotional valence or a global FAP impairment remains unclear. The present study examined whether impairment in the perception of specific emotional valences (positive, negative) and neutrality were uniquely associated with social functioning, using a multimodal social functioning battery. A sample of 59 individuals with schizophrenia and 41 controls completed a computerized FAP task, and measures of functional capacity, social competence, and social attainment. Participants also underwent neuropsychological testing and symptom assessment. Regression analyses revealed that only accurately perceiving negative emotions explained significant variance (7.9%) in functional capacity after accounting for neurocognitive function and symptoms. Partial correlations indicated that accurately perceiving anger, in particular, was positively correlated with functional capacity. FAP for positive, negative, or neutral emotions were not related to social competence or social attainment. Our findings were consistent with prior literature suggesting negative emotions are related to functional capacity in schizophrenia. Furthermore, the observed relationship between perceiving anger and performance of everyday living skills is novel and warrants further exploration.
Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Chemistry by Way of Density Functional Theory
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Partridge, Harry; Langohff, Stephen R.; Arnold, James O. (Technical Monitor)
1996-01-01
In this work we demonstrate that density functional theory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.
Accurate Computation of Divided Differences of the Exponential Function,
1983-06-01
differences are not for arbitrary smooth functions f but for well known analytic functions such as exp. sin and cos. Thus we can exploit their properties in...have a bad name in practice. However in a number of applications the functional form of f is known (e.g. exp) and can be exploited to obtain accurate...n do X =s(1) s(1)=d(i) For j=2.....-1 do11=t, (j) z=Y next j next i SS7 . (Shift back and stop.] ,-tt+77. d(i).-e"d(i), s(i-1)’e~ s(i-i) for i=2
Gedanken densities and exact constraints in density functional theory
Perdew, John P.; Ruzsinszky, Adrienn; Sun, Jianwei; Burke, Kieron
2014-05-14
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA’s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.
Sokkar, T Z N; El-Farahaty, K A; El-Bakary, M A; Omar, E Z; Hamza, A A
2016-05-01
A modified method was suggested to improve the performance of the Pluta microscope in its nonduplicated mode in the calculation of the areal craze density especially, for relatively low draw ratio (low areal craze density). This method decreases the error that is resulted from the similarity between the formed crazes and the dark fringes of the interference pattern. Furthermore, an accurate method to calculate the birefringence and the orientation function of the drawn fibers via nonduplicated Pluta polarizing interference microscope for high areal craze density (high draw ratio) was suggested. The advantage of the suggested method is to relate the optomechanical properties of the tested fiber with the areal craze density, for the same region of the fiber material.
Accurate estimators of correlation functions in Fourier space
NASA Astrophysics Data System (ADS)
Sefusatti, E.; Crocce, M.; Scoccimarro, R.; Couchman, H. M. P.
2016-08-01
Efficient estimators of Fourier-space statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved small-scale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher order interpolation kernels than the standard Cloud-In-Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01 per cent all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological data sets.
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
NASA Astrophysics Data System (ADS)
Pribram-Jones, Aurora
Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the
Accurate bulk density determination of irregularly shaped translucent and opaque aerogels
NASA Astrophysics Data System (ADS)
Petkov, M. P.; Jones, S. M.
2016-05-01
We present a volumetric method for accurate determination of bulk density of aerogels, calculated from extrapolated weight of the dry pure solid and volume estimates based on the Archimedes' principle of volume displacement, using packed 100 μm-sized monodispersed glass spheres as a "quasi-fluid" media. Hard particle packing theory is invoked to demonstrate the reproducibility of the apparent density of the quasi-fluid. Accuracy rivaling that of the refractive index method is demonstrated for both translucent and opaque aerogels with different absorptive properties, as well as for aerogels with regular and irregular shapes.
Combining heterogeneous data sources for accurate functional annotation of proteins
2013-01-01
Combining heterogeneous sources of data is essential for accurate prediction of protein function. The task is complicated by the fact that while sequence-based features can be readily compared across species, most other data are species-specific. In this paper, we present a multi-view extension to GOstruct, a structured-output framework for function annotation of proteins. The extended framework can learn from disparate data sources, with each data source provided to the framework in the form of a kernel. Our empirical results demonstrate that the multi-view framework is able to utilize all available information, yielding better performance than sequence-based models trained across species and models trained from collections of data within a given species. This version of GOstruct participated in the recent Critical Assessment of Functional Annotations (CAFA) challenge; since then we have significantly improved the natural language processing component of the method, which now provides performance that is on par with that provided by sequence information. The GOstruct framework is available for download at http://strut.sourceforge.net. PMID:23514123
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe2O3, Fe3O4, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
NASA Astrophysics Data System (ADS)
Challacombe, Matt; Cioslowski, Jerzy
1994-01-01
A new, highly optimized implementation of the Hiller-Sucher-Feinberg (HSF) identity is presented. The HSF identity, when applied to molecular wave functions calculated with Gaussian-type basis functions, not only improves the overall accuracy of the electron density by more than an order of magnitude, but also yields approximate cusps at nuclei. The three classes of molecular integrals, L, U, and V, which are encountered in the calculation of the HSF density, are derived in compact form. Efficient algorithms for the accurate evaluation of these integrals are detailed, including a novel approach to the necessary numerical quadratures and the thresholding of two-electron V integrals. Hartree-Fock (HF) electron densities calculated with both the conventional definition and from the HSF identity are compared to their respective HF limits for a variety of diatomic molecules and basis sets. The average error in the calculated HSF electron densities at non-hydrogen nuclei equals 0.17%, which constitutes a marked improvement over an error of 5.77% in the conventional densities.
Density Functional O(N) Calculations
NASA Astrophysics Data System (ADS)
Ordejón, Pablo
1998-03-01
We have developed a scheme for performing Density Functional Theory calculations with O(N) scaling.(P. Ordejón, E. Artacho and J. M. Soler, Phys. Rev. B, 53), 10441 (1996) The method uses arbitrarily flexible and complete Atomic Orbitals (AO) basis sets. This gives a wide range of choice, from extremely fast calculations with minimal basis sets, to greatly accurate calculations with complete sets. The size-efficiency of AO bases, together with the O(N) scaling of the algorithm, allow the application of the method to systems with many hundreds of atoms, in single processor workstations. I will present the SIESTA code,(D. Sanchez-Portal, P. Ordejón, E. Artacho and J. M. Soler, Int. J. Quantum Chem., 65), 453 (1997) in which the method is implemented, with several LDA, LSD and GGA functionals available, and using norm-conserving, non-local pseudopotentials (in the Kleinman-Bylander form) to eliminate the core electrons. The calculation of static properties such as energies, forces, pressure, stress and magnetic moments, as well as molecular dynamics (MD) simulations capabilities (including variable cell shape, constant temperature and constant pressure MD) are fully implemented. I will also show examples of the accuracy of the method, and applications to large-scale materials and biomolecular systems.
Building a Universal Nuclear Energy Density Functional
Carlson, Joe A.; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Universal Nuclear Energy Density Functional
Carlson, Joseph; Furnstahl, Richard; Horoi, Mihai; Lusk, Rusty; Nazarewicz, Witold; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-01
An understanding of the properties of atomic nuclei is crucial for a complete nuclear theory, for element formation, for properties of stars, and for present and future energy and defense applications. During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. Until recently such an undertaking was hard to imagine, and even at the present time such an ambitious endeavor would be far beyond what a single researcher or a traditional research group could carry out.
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Spin Density Matrices for Nuclear Density Functionals with Parity Violation
NASA Astrophysics Data System (ADS)
Barrett, Bruce; Giraud, Bertrand
2010-11-01
Within the context of the radial density functional [1], we apply the spin density matrix (SDM) used in atomic and molecular physics [2] to nuclear physics. The vector part of the SDM defines a ``hedgehog'' situation, which exists only if nuclear states contain some amount of parity violation. Thus, looking for the vector profile of the SDM could be used as a test for parity violation in nuclei. The difference between the scalar profile and the vector profile of the SDM will be illustrated by a toy model. [4pt] [1] B. G. Giraud, Phys. Rev. C 78, 014307 (2008).[0pt] [2] A. Goerling, Phys. Rev. A 47, 2783 (1993).
Nagy, A.
2011-09-15
A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).
Density Scaling of Noninteracting Kinetic Energy Functionals.
Borgoo, Alex; Tozer, David J
2013-05-14
The influence of imposing an approximate density scaling condition on a noninteracting kinetic energy functional is investigated. A simple generalized gradient approximation (GGA) is presented, which satisfies both the density scaling condition and the usual coordinate scaling condition; the remaining multiplicative constant is determined from an energy criterion. In post-Kohn-Sham calculations, noninteracting kinetic energies of the closed-shell molecules of the G1 set determined using the GGA are a modest improvement over those determined using the corresponding local functional, which does not satisfy the density scaling condition. Potential energy curves of CO, F2, and P2 exhibit binding with the GGA, compared to purely repulsive curves with the local functional. Adjusting the exponent in the GGA form in order to optimize energy accuracy violates the density scaling condition, and two of the diatomics no longer exhibit binding. Results are compared with those from other local/GGA functionals in the literature.
Improved association in a classical density functional theory for water
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment.
Density functionals for the strong-interaction limit
NASA Astrophysics Data System (ADS)
Seidl, Michael; Perdew, John P.; Kurth, Stefan
2000-07-01
The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation of DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model for that limit, and its gradient expansion. The exchange-correlation (xc) energy Exc[ρ]≡∫10dαWα[ρ] follows from the xc potential energies Wα at different interaction strengths α>=0 [but at fixed density ρ(r)]. For small α~0, the integrand Wα is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large α. For that purpose, we present density functionals for the coefficients in the asymptotic expansion Wα-->W∞+W'∞α-1/2 for α-->∞ in the PC model. WPC∞ arises from strict correlation, and W'PC∞ from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W∞ and W'∞ agree with those from a self-correlation-free meta-generalized gradient approximation, both for atoms and for atomization energies of molecules. We also (i) explain the difference between the PC cell and the exchange-correlation hole, (ii) present a density-functional measure of correlation strength, (iii) describe the electron localization and spin polarization energy in a highly stretched H2 molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Range Separation and Local Hybridization in Density Functional Theory†
Henderson, Thomas M.; Janesko, Benjamin G.; Scuseria, Gustavo E.
2016-01-01
Kohn–Sham density functional theory has become a standard method for modeling energetic, spectroscopic, and chemical reactivity properties of large molecules and solids. Density functional theory provides a rigorous theoretical framework for modeling the many-body exchange-correlation effects that dominate the computational cost of traditional wave function approaches. The advent of hybrid exchange-correlation functionals which incorporate a fraction of nonlocal exact exchange has solidified the prominence of density functional theory within computational chemistry. Hybrids provide accurate treatments of properties such as thermochemistry and molecular geometry. But they also exhibit some rather spectacular failures, and often contain multiple empirical parameters. This article reviews our work on developing novel exchange-correlation functionals that build upon the successes of global hybrids. We focus on more flexible functional forms, including local and range-separated hybrid functionals, constructed to obey known exact constraints and (ideally) to incorporate a minimum of empirical parametrization. The article places our work within the context of some other new approximate density functionals and discusses prospects for future work. PMID:19006280
Whitenack, Daniel L; Wasserman, Adam
2012-04-28
Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.
The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
Bakosi, Jozsef; Ristorcelli, Raymond J
2010-01-01
Probability density function (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.
Nonlocal kinetic-energy-density functionals
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-04-01
In this paper we present nonlocal kinetic-energy functionals {ital T}[{ital n}] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. {copyright} {ital 1996 The American Physical Society.}
Prediction of Dislocation Cores in Aluminum from Density Functional Theory
NASA Astrophysics Data System (ADS)
Woodward, C.; Trinkle, D. R.; Hector, L. G., Jr.; Olmsted, D. L.
2008-02-01
The strain field of isolated screw and edge dislocation cores in aluminum are calculated using density-functional theory and a flexible boundary condition method. Nye tensor density contours and differential displacement fields are used to accurately bound Shockley partial separation distances. Our results of 5 7.5 Å (screw) and 7.0 9.5 Å (edge) eliminate uncertainties resulting from the wide range of previous results based on Peierls-Nabarro and atomistic methods. Favorable agreement of the predicted cores with limited experimental measurements demonstrates the need for quantum mechanical treatment of dislocation cores.
A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
Periodic subsystem density-functional theory
Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide
2014-11-07
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Van der Waals density functional: An appropriate exchange functional
NASA Astrophysics Data System (ADS)
Cooper, Valentino R.
2010-04-01
In this Rapid Communication, an exchange functional which is compatible with the nonlocal Rutgers-Chalmers correlation functional [van der Waals density functional (vdW-DF)] is presented. This functional, when employed with vdW-DF, demonstrates remarkable improvements on intermolecular separation distances while further improving the accuracy of vdW-DF interaction energies. The key to the success of this three-parameter functional is its reduction in short-range exchange repulsion through matching to the gradient expansion approximation in the slowly varying/high-density limit while recovering the large reduced gradient, s , limit set in the revised Perdew-Burke-Ernzerhof (revPBE) exchange functional. This augmented exchange functional could be a solution to long-standing issues of vdW-DF lending to further applicability of density-functional theory to the study of relatively large, dispersion bound (van der Waals) complexes.
Efficient Diffuse Basis Sets for Density Functional Theory.
Papajak, Ewa; Truhlar, Donald G
2010-03-09
Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for density functional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for density functional calculations, but the computational cost savings are a factor of about two to seven.
Error analysis in nuclear density functional theory
NASA Astrophysics Data System (ADS)
Schunck, Nicolas; McDonnell, Jordan D.; Sarich, Jason; Wild, Stefan M.; Higdon, Dave
2015-03-01
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the Universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
Koopmans' condition for density-functional theory
Dabo, Ismaila; Ferretti, Andrea; Poilvert, Nicolas; Marzari, Nicola; Li, Yanli; Cococcioni, Matteo
2010-09-15
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition - that identifies orbital energies as opposite total electron removal energies - to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data - with an accuracy comparable to that of GW many-body perturbation theory - while providing an explicit total energy functional that preserves or improves on the description of established structural properties.
A correction to a highly accurate voight function algorithm
NASA Technical Reports Server (NTRS)
Shippony, Z.; Read, W. G.
2002-01-01
An algorithm for rapidly computing the complex Voigt function was published by Shippony and Read. Its claimed accuracy was 1 part in 10^8. It was brought to our attention by Wells that Shippony and Read was not meeting its claimed accuracy for extremely small but non zero y values. Although true, the fix to the code is so trivial to warrant this note for those who use this algorithm.
Density functional calculation of intermolecular potentials.
Nyeland, Carl
2011-06-30
Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.
Radiative Strength Functions and Level Densities
Schiller, A; Becker, J A; Bernstein, L A; Voinov, A; Guttormsen, M; Hjorth-Jensen, M; Rekstad, J; Siem, S; Mitchell, G E; Tavukcu, E
2002-08-28
Radiative strength functions and level densities have been extracted from primary {gamma}-ray spectra for {sup 27,28}Si, {sup 56,57}Fe, {sup 96,97}Mo, and several rare earth nuclei. An unexpectedly strong ({approx} 1 mb MeV) resonance at 3 MeV in the radiative strength function has been observed for well-deformed rare earth nuclei. The physical origin of this resonance and its connection to the scissors mode is discussed.
Density functional theory studies of etoricoxib
NASA Astrophysics Data System (ADS)
Sachdeva, Ritika; Kaur, Prabhjot; Singh, V. P.; Saini, G. S. S.
2016-05-01
Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of density functional theory calculations using 6-311++ g (d, p) basis set and B3LYP functional.
Density functional theory: Fixing Jacob's ladder
NASA Astrophysics Data System (ADS)
Car, Roberto
2016-09-01
Density functional theory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.
Uncertainty Quantification for Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
McDonnell, Jordan; Schunck, Nicolas; Nazarewicz, Witold; Higdon, Dave; Sarich, Jason; Wild, Stefan
2014-09-01
Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. This work was supported by the US Department of Energy under Contracts No. DE-SC0008499 and No. DE-AC52-07NA27344.
Determination of accurate, mean bond lengths from radial distribution functions
NASA Astrophysics Data System (ADS)
Sukhomlinov, Sergey V.; Müser, Martin H.
2017-01-01
The mean bond length d between a central atom and its nearest neighbors can be estimated from the position of the first peak in the radial distribution function g(r). However, as we demonstrate here, this estimate does not allow one to deduce temperature-induced changes in d. Instead, skewness has to be included into the analysis, which can be achieved, for example, via the skew normal distribution (SND). Fits to the first peak using the SND give bond length in good agreement with direct measurements of nearest-neighbor distribution functions in crystals as well as with a Voronoi-tessellation based detection of nearest-neighbors in liquids. While the location of the first peak in g(r) may shift to smaller values with increasing temperature for three studied liquids—argon, copper, and the bulk-metallic-glass (BMG) forming alloy Zr60Cu30Al10—we find our improved estimates of d to systematically increase with temperature in all cases. Recent conclusions on temperature-induced bond contractions in simple metallic or BMG-forming liquids may therefore have arisen from the neglect of skewness effects.
Advances in time-dependent current-density functional theory
NASA Astrophysics Data System (ADS)
Berger, Arjan
In this work we solve the problem of the gauge dependence of molecular magnetic properties (magnetizabilities, circular dichroism) using time-dependent current-density functional theory [1]. We also present a new functional that accurately describes the optical absorption spectra of insulators, semiconductors and metals [2] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger Phys. Rev. Lett. 114, 066404 (2015) J.A. Berger, Phys. Rev. Lett. 115, 137402 (2015) This study has been partially supported through the Grant NEXT No. ANR-10-LABX-0037 in the framework of the Programme des Investissements d'Avenir.
A Scalable Implementation of Van der Waals Density Functionals
NASA Astrophysics Data System (ADS)
Wu, Jun; Gygi, Francois
2010-03-01
Recently developed Van der Waals density functionals[1] offer the promise to account for weak intermolecular interactions that are not described accurately by local exchange-correlation density functionals. In spite of recent progress [2], the computational cost of such calculations remains high. We present a scalable parallel implementation of the functional proposed by Dion et al.[1]. The method is implemented in the Qbox first-principles simulation code (http://eslab.ucdavis.edu/software/qbox). Application to large molecular systems will be presented. [4pt] [1] M. Dion et al. Phys. Rev. Lett. 92, 246401 (2004).[0pt] [2] G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
Implementing an Inexpensive and Accurate Introductory Gas Density Activity with High School Students
ERIC Educational Resources Information Center
Cunningham, W. Patrick; Joseph, Christopher; Morey, Samantha; Santos Romo, Ana; Shope, Cullen; Strang, Jonathan; Yang, Kevin
2015-01-01
A simplified activity examined gas density while employing cost-efficient syringes in place of traditional glass bulbs. The exercise measured the density of methane, with very good accuracy and precision, in both first-year high school and AP chemistry settings. The participating students were tasked with finding the density of a gas. The…
Vieira, Vasco M. N. C. S.; Engelen, Aschwin H.; Huanel, Oscar R.; Guillemin, Marie-Laure
2016-01-01
Survival is a fundamental demographic component and the importance of its accurate estimation goes beyond the traditional estimation of life expectancy. The evolutionary stability of isomorphic biphasic life-cycles and the occurrence of its different ploidy phases at uneven abundances are hypothesized to be driven by differences in survival rates between haploids and diploids. We monitored Gracilaria chilensis, a commercially exploited red alga with an isomorphic biphasic life-cycle, having found density-dependent survival with competition and Allee effects. While estimating the linear-in-the-parameters survival function, all model I regression methods (i.e, vertical least squares) provided biased line-fits rendering them inappropriate for studies about ecology, evolution or population management. Hence, we developed an iterative two-step non-linear model II regression (i.e, oblique least squares), which provided improved line-fits and estimates of survival function parameters, while robust to the data aspects that usually turn the regression methods numerically unstable. PMID:27936048
NASA Astrophysics Data System (ADS)
Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron
2014-03-01
Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).
Optimization of a van der Waals Density Functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernandez-Serra, Marivi; Soler, Jose M.
2015-03-01
In particularly delicate systems, like liquid water, ab initio exchange and correlation functionals are simply not accurate enough for many practical applications. In these cases, fitting the functional to reference data is a sensible alternative to empirical interatomic potentials. However, a global optimization requires functional forms that depend on many parameters and the usual trial and error strategy becomes cumbersome and suboptimal. We present a general and powerful optimization scheme called data projection onto parameter space (DPPS). In an arbitrarily large parameter space, DPPS expands the vector of unknown parameters in vectors of known data. Poorly sampled subspaces are determined by the physically-motivated functional shape of ab initio functionals, using Bayes' theory to combine this prior information with reference energies and electron densities of monomers, clusters, and condensed phases of water. We aknowledge support from FIS2012-37549 (MF and JMS) and DOE Early Career Award No. DE-SC0003871 (M.-V.F.-S.)
Implementation Strategies for Orbital-dependent Density Functionals
NASA Astrophysics Data System (ADS)
Bento, Marsal E.; Vieira, Daniel
2016-12-01
The development of density functional theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems. Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.
Accurate and robust methods for variable density incompressible flows with discontinuities
Rider, W.J.; Kothe, D.B.; Puckett, E.G.
1996-09-01
We are interested in the solution of incompressible flows which are characterized by large density variations, interfacial physics, arbitrary material topologies and strong vortical content. The issues present in constant density incompressible flow are exacerbated by the presence of density discontinuities. A much greater premium requirement is placed the positivity of computed quantities The mechanism of baroclinc vorticity generation exists ({gradient}p x {gradient}p) to further complicate the physics.
Accurate quantification of width and density of bone structures by computed tomography
Hangartner, Thomas N.; Short, David F.
2007-10-15
In computed tomography (CT), the representation of edges between objects of different densities is influenced by the limited spatial resolution of the scanner. This results in the misrepresentation of density of narrow objects, leading to errors of up to 70% and more. Our interest is in the imaging and measurement of narrow bone structures, and the issues are the same for imaging with clinical CT scanners, peripheral quantitative CT scanners or micro CT scanners. Mathematical models, phantoms and tests with patient data led to the following procedures: (i) extract density profiles at one-degree increments from the CT images at right angles to the bone boundary; (ii) consider the outer and inner edge of each profile separately due to different adjacent soft tissues; (iii) measure the width of each profile based on a threshold at fixed percentage of the difference between the soft-tissue value and a first approximated bone value; (iv) correct the underlying material density of bone for each profile based on the measured width with the help of the density-versus-width curve obtained from computer simulations and phantom measurements. This latter curve is specific to a certain scanner and is not dependent on the densities of the tissues within the range seen in patients. This procedure allows the calculation of the material density of bone. Based on phantom measurements, we estimate the density error to be below 2% relative to the density of normal bone and the bone-width error about one tenth of a pixel size.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Exact probability-density function for phase-measurement interferometry
NASA Astrophysics Data System (ADS)
Ho, Keang-Po; Kahn, Joseph M.
1995-09-01
Conventional analyses of the accuracy of phase-measurement interferometry derive a figure of merit that is either a variance or a signal-to-noise ratio. We derive the probability-density function of the phase-measurement output, so that the measurement confidence interval can be determined. We include both laser phase noise and additive Gaussian noise, and we consider both unmodulated interferometers and those employing phase or frequency modulation. For both unmodulated and modulated interferometers the confidence interval can be obtained by numerical integration of the probability-density function. For the modulated interferometer we derive a series summation for the confidence interval. For both unmodulated and modulated interferometers we derive approximate analytical expressions for the confidence interval, which we show to be extremely accurate at high signal-to-noise ratios.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Burke, Kieron; Yang, Zeng-hui; Ullrich, Carsten A.; Trail, John R.; Needs, Richard J.
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Nonequilibrium Anderson model made simple with density functional theory
NASA Astrophysics Data System (ADS)
Kurth, S.; Stefanucci, G.
2016-12-01
The single-impurity Anderson model is studied within the i-DFT framework, a recently proposed extension of density functional theory (DFT) for the description of electron transport in the steady state. i-DFT is designed to give both the steady current and density at the impurity, and it requires the knowledge of the exchange-correlation (xc) bias and on-site potential (gate). In this work we construct an approximation for both quantities which is accurate in a wide range of temperatures, gates, and biases, thus providing a simple and unifying framework to calculate the differential conductance at negligible computational cost in different regimes. Our results mark a substantial advance for DFT and may inform the construction of functionals applicable to other correlated systems.
Computing dispersion interactions in density functional theory
NASA Astrophysics Data System (ADS)
Cooper, V. R.; Kong, L.; Langreth, D. C.
2010-02-01
In this article techniques for including dispersion interactions within density functional theory are examined. In particular comparisons are made between four popular methods: dispersion corrected DFT, pseudopotential correction schemes, symmetry adapted perturbation theory, and a non-local density functional - the so called Rutgers-Chalmers van der Waals density functional (vdW-DF). The S22 benchmark data set is used to evaluate the relative accuracy of these methods and factors such as scalability and transferability are also discussed. We demonstrate that vdW-DF presents an excellent compromise between computational speed and accuracy and lends most easily to full scale application in solid materials. This claim is supported through a brief discussion of a recent large scale application to H2 in a prototype metal organic framework material (MOF), Zn2BDC2TED. The vdW-DF shows overwhelming promise for first-principles studies of physisorbed molecules in porous extended systems; thereby having broad applicability for studies as diverse as molecular adsorption and storage, battery technology, catalysis and gas separations.
Semilocal density functional obeying a strongly tightened bound for exchange
Sun, Jianwei; Perdew, John P.; Ruzsinszky, Adrienn
2015-01-01
Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules. PMID:25561554
Many-body theory and Energy Density Functionals
NASA Astrophysics Data System (ADS)
Baldo, M.
2016-07-01
In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-06-01
Sodium azide is being investigated as a potential precursor to a high-nitrogen content energetic material. Changes in the experimentally measured raman spectra under compression and high temperature indicate that a structural change may have taken place. Accurate mode assignments of new peaks arising in the raman spectra have been inconclusive. In this work, the first order raman spectra of sodium azide's alpha and beta phases are calculated using Density Function Pertubation Theory (DFPT) under compression and expansion. Normal mode assignments are made and compared to experiment. In addition, the equation of state of both phases is obtained up to 90 GPa.
Density functional theory for atomic Fermi gases
NASA Astrophysics Data System (ADS)
Ma, Ping Nang; Pilati, Sebastiano; Troyer, Matthias; Dai, Xi
2012-08-01
The interplay between interaction and inhomogeneity for electrons in solids generates many interesting phenomena, including insulating and metallic behaviour, magnetism, superconductivity, quantum criticality and more exotic phases. Many of the same phenomena appear in ultracold fermionic atoms in optical lattices, which provide clean, controlled and tunable `quantum simulators' to explore the intriguing physics of fermionic systems. Although density functional theory (DFT) is widely used to calculate material properties, it has not yet been applied to cold atomic gases in optical lattices. Here we present a new density functional for short-range interactions (as opposed to Coulomb interactions of electrons), which renders DFT suitable for atomic Fermi gases. This grants us access to an extensive toolset, previously developed for materials simulations, to calculate the static and dynamic properties of atomic Fermi gases in optical lattices and external potentials. Ultracold atom quantum simulators can in turn be used to explore limitations of DFT functionals, and to further improve hybrid functionals, thus forming a bridge between materials simulations and atomic physics.
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Machine-learned approximations to Density Functional Theory Hamiltonians
NASA Astrophysics Data System (ADS)
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Machine-learned approximations to Density Functional Theory Hamiltonians.
Hegde, Ganesh; Bowen, R Chris
2017-02-15
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Self-consistent polarization density functional theory: Application to Argon
Maerzke, Katie A.; Murdachaew, Garold; Mundy, Christopher J.; Schenter, Gregory K.; Siepmann, J. I.
2009-03-12
We present a comprehensive set of results for argon, a case study in weak interactions, using the selfconsistent polarization density functional theory (SCP-DFT). With minimal parameterization, SCPDFT is found is give excellent results for the dimer interaction energy, the second virial coefficient, the liquid structure, and the lattice constant and cohesion energy of the face-centered cubic (fcc) crystal compared to both accurate theoretical and experimental benchmarks. Thus, SCP-DFT holds promise as a fast, efficient, and accurate method for performing ab initio dynamics that include additional polarization and dispersion interactions for large, complex systems involving solvation and bond breaking. This work was supported by the U.S. Department of Energy's (DOE) Office of Basic Energy Sciences, Chemical Sciences program. The Pacific Northwest National Laboratory is operated by Battelle for DOE.
Density functional theory for inhomogeneous associating chain fluids.
Bryk, P; Sokołowski, S; Pizio, O
2006-07-14
We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Recent progress in density functional theory
NASA Astrophysics Data System (ADS)
Truhlar, Donald
2014-03-01
Ongoing work involves several areas of density functional theory: new methods for computing electronic excitation energies, including a new way to remove spin contamination in the spin-flip Tamm-Dancoff approximation and a configuration-interaction-corrected Tamm-Dancoff Approximation for treating conical intersections; new ways to treat open-shell states, including a reinterpreted broken-symmetry method and multi-configuration Kohn-Sham theory; a new exchange-correlation functional; new tests of density functional theory against databases for electronic transition energies and molecules and solids containing metal atoms; and applications. A selection of results will be presented. I am grateful to the following collaborators for contributions to the ongoing work: Boris Averkiev, Rebecca Carlson, Laura Fernandez, Laura Gagliardi, Chad Hoyer, Francesc Illas, Miho Isegawa, Shaohong Li, Giovanni Li Manni, Sijie Luo, Dongxia Ma, Remi Maurice, Rubén Means-Pañeda, Roberto Peverati, Nora Planas, Prasenjit Seal, Pragya Verma, Bo Wang, Xuefei Xu, Ke R. Yang, Haoyu Yu, Wenjing Zhang, and Jingjing Zheng. Supported in part by the AFOSR and U.S. DOE.
Optimization of constrained density functional theory
NASA Astrophysics Data System (ADS)
O'Regan, David D.; Teobaldi, Gilberto
2016-07-01
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.
Fast and accurate probability density estimation in large high dimensional astronomical datasets
NASA Astrophysics Data System (ADS)
Gupta, Pramod; Connolly, Andrew J.; Gardner, Jeffrey P.
2015-01-01
Astronomical surveys will generate measurements of hundreds of attributes (e.g. color, size, shape) on hundreds of millions of sources. Analyzing these large, high dimensional data sets will require efficient algorithms for data analysis. An example of this is probability density estimation that is at the heart of many classification problems such as the separation of stars and quasars based on their colors. Popular density estimation techniques use binning or kernel density estimation. Kernel density estimation has a small memory footprint but often requires large computational resources. Binning has small computational requirements but usually binning is implemented with multi-dimensional arrays which leads to memory requirements which scale exponentially with the number of dimensions. Hence both techniques do not scale well to large data sets in high dimensions. We present an alternative approach of binning implemented with hash tables (BASH tables). This approach uses the sparseness of data in the high dimensional space to ensure that the memory requirements are small. However hashing requires some extra computation so a priori it is not clear if the reduction in memory requirements will lead to increased computational requirements. Through an implementation of BASH tables in C++ we show that the additional computational requirements of hashing are negligible. Hence this approach has small memory and computational requirements. We apply our density estimation technique to photometric selection of quasars using non-parametric Bayesian classification and show that the accuracy of the classification is same as the accuracy of earlier approaches. Since the BASH table approach is one to three orders of magnitude faster than the earlier approaches it may be useful in various other applications of density estimation in astrostatistics.
Insight and progress in density functional theory
NASA Astrophysics Data System (ADS)
Yang, Weitao; Mori-Sanchez, Paula; Cohen, Aron J.
2012-12-01
Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties. The errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These errors can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently.
Modulation Based on Probability Density Functions
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Probability density functions in turbulent channel flow
NASA Technical Reports Server (NTRS)
Dinavahi, Surya P. G.
1992-01-01
The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-05
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.
Seeking: Accurate Measurement Techniques for Deep-Bone Density and Structure
NASA Technical Reports Server (NTRS)
Sibonga, Jean
2009-01-01
We are seeking a clinically-useful technology with enough sensitivity to assess the microstructure of "spongy" bone that is found in the marrow cavities of whole bones. However, this technology must be for skeletal sites surrounded by layers of soft tissues, such as the spine and the hip. Soft tissue interferes with conventional imaging and using a more accessible area -- for example, the wrist or the ankle of limbs-- as a proxy for the less accessible skeletal regions, will not be accurate. A non-radioactive technology is strongly preferred.
Band terminations in density functional theory
Afanasjev, A. V.
2008-11-15
The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its maximum exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields provided that other effects can be reliably isolated. Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion [H. Zdunczuk, W. Satula, and R. A. Wyss, Phys. Rev. C 71, 024305 (2005)] that the relative energies of the terminating states in the N{ne}Z,A{approx}44 mass region given by {delta}E provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction in density functional theories has been reanalyzed. The current investigation shows that the {delta}E value is affected also by the relative placement of the states with different orbital angular momentum l, namely, the placement of the d (l=2) and f (l=3) states. This indicates the dependence of the {delta}E value on the properties of the central potential.
Nitrogenase structure and function relationships by density functional theory.
Harris, Travis V; Szilagyi, Robert K
2011-01-01
Modern density functional theory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic density functional theory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.
Study of time-accurate integration of the variable-density Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Lu, Xiaoyi; Pantano, Carlos
2015-11-01
We present several theoretical elements that affect time-consistent integration of the low-Mach number approximation of variable-density Navier-Stokes equations. The goal is for velocity, pressure, density, and scalars to achieve uniform order of accuracy, consistent with the time integrator being used. We show examples of second-order (using Crank-Nicolson and Adams-Bashforth) and third-order (using additive semi-implicit Runge-Kutta) uniform convergence with the proposed conceptual framework. Furthermore, the consistent approach can be extended to other time integrators. In addition, the method is formulated using approximate/incomplete factorization methods for easy incorporation in existing solvers. One of the observed benefits of the proposed approach is improved stability, even for large density difference, in comparison with other existing formulations. A linearized stability analysis is also carried out for some test problems to better understand the behavior of the approach. This work was supported in part by the Department of Energy, National Nuclear Security Administration, under award no. DE-NA0002382 and the California Institute of Technology.
Dispersion interactions in Density Functional Theory
NASA Astrophysics Data System (ADS)
Andrinopoulos, Lampros; Hine, Nicholas; Mostofi, Arash
2012-02-01
Semilocal functionals in Density Functional Theory (DFT) achieve high accuracy simulating a wide range of systems, but miss the effect of dispersion (vdW) interactions, important in weakly bound systems. We study two different methods to include vdW in DFT: First, we investigate a recent approach [1] to evaluate the vdW contribution to the total energy using maximally-localized Wannier functions. Using a set of simple dimers, we show that it has a number of shortcomings that hamper its predictive power; we then develop and implement a series of improvements [2] and obtain binding energies and equilibrium geometries in closer agreement to quantum-chemical coupled-cluster calculations. Second, we implement the vdW-DF functional [3], using Soler's method [4], within ONETEP [5], a linear-scaling DFT code, and apply it to a range of systems. This method within a linear-scaling DFT code allows the simulation of weakly bound systems of larger scale, such as organic/inorganic interfaces, biological systems and implicit solvation models. [1] P. Silvestrelli, JPC A 113, 5224 (2009). [2] L. Andrinopoulos et al, JCP 135, 154105 (2011). [3] M. Dion et al, PRL 92, 246401 (2004). [4] G. Rom'an-P'erez, J.M. Soler, PRL 103, 096102 (2009). [5] C. Skylaris et al, JCP 122, 084119 (2005).
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
NASA Astrophysics Data System (ADS)
Öz, E.; Batsch, F.; Muggli, P.
2016-09-01
A method to accurately measure the density of Rb vapor is described. We plan on using this method for the Advanced Wakefield (AWAKE) (Assmann et al., 2014 [1]) project at CERN , which will be the world's first proton driven plasma wakefield experiment. The method is similar to the hook (Marlow, 1967 [2]) method and has been described in great detail in the work by Hill et al. (1986) [3]. In this method a cosine fit is applied to the interferogram to obtain a relative accuracy on the order of 1% for the vapor density-length product. A single-mode, fiber-based, Mach-Zenhder interferometer will be built and used near the ends of the 10 meter-long AWAKE plasma source to be able to make accurate relative density measurement between these two locations. This can then be used to infer the vapor density gradient along the AWAKE plasma source and also change it to the value desired for the plasma wakefield experiment. Here we describe the plan in detail and show preliminary results obtained using a prototype 8 cm long novel Rb vapor cell.
An affordable and accurate conductivity probe for density measurements in stratified flows
NASA Astrophysics Data System (ADS)
Carminati, Marco; Luzzatto-Fegiz, Paolo
2015-11-01
In stratified flow experiments, conductivity (combined with temperature) is often used to measure density. The probes typically used can provide very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost conductivity probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB cables as the actual conductivity sensors. By removing the metallic shield from a micro-B connector, 5 gold-plated microelectrodes are exposed and available for 4-wire measurements. These have a cell constant ~550m-1, an intrinsic thermal noise of at most 30pA/Hz1/2, as well as sub-millisecond time response, making them highly suitable for many stratified flow measurements. In addition, we present the design of a custom electronic board (Arduino-based and Matlab-controlled) for simultaneous acquisition from 4 sensors, with resolution (in conductivity, and resulting density) exceeding the performance of typical existing probes. We illustrate the use of our conductivity-measuring system through stratified flow experiments, and describe plans to release simple instructions to construct our complete system for around 200.
Density functional theory with fractional orbital occupations.
Chai, Jeng-Da
2012-04-21
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.
Phases of Polonium via Density Functional Theory
NASA Astrophysics Data System (ADS)
Verstraete, Matthieu J.
2010-01-01
The thermodynamical properties of the main phases of metallic polonium are examined using density functional theory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.
Modeling NMR lineshapes using logspline density functions.
Raz, J; Fernandez, E J; Gillespie, J
1997-08-01
Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An algorithm for fitting the model is described, the performance of the model and algorithm is investigated in applications to real and simulated data sets, and the logspline approach is compared to a previous Hermitian spline approach and to the Lorentzian model. The logspline model is more parsimonious than the Hermitian spline model, provides a better fit to real data, and is much less biased than the Lorentzian model.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2006-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2004-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Density-functional study of paramagnetic iron
NASA Astrophysics Data System (ADS)
Zhang, Hualei; Johansson, Börje; Vitos, Levente
2011-10-01
By using density-functional theory in combination with the coherent-potential approximation and the disordered local magnetic moment picture, we demonstrate that the competing high-temperature cubic phases of paramagnetic Fe correspond to two distinct total energy minima in the tetragonal (Bain) configurational space. Both the face-centered-cubic (fcc) and the body-centered-cubic (bcc) lattices are dynamically stable, and at static conditions the fcc structure is found to be the thermodynamically stable phase. The theoretical bcc and fcc bulk parameters are in agreement with the experimental data. Due to the shallow energy minimum around the bcc structure, increasing temperature is predicted to stabilize the bcc (δ) phase against the fcc (γ) one.
Towards the island of stability with relativistic energy density functionals
Prassa, V.; Niksic, T.; Lalazissis, G. A.; Vretenar, D.
2012-10-20
Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. Modern semi-empirical functionals, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, are applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison to empirical masses, quadrupole deformations, and energy barriers of actinide nuclei. The model is used in a self-consistent mean-field calculation of spherical, axial and triaxial shapes of superheavy nuclei, alpha-decay energies and lifetimes. The effect of explicit treatment of collective correlations is analyzed in calculations that consistently use a collective Hamiltonian model based on REDFs.
NASA Astrophysics Data System (ADS)
Lipparini, Enrico; Pederiva, Francesco
2016-08-01
The time dependent local isospin density approximation (TDLIDA) has been extended to the study of the transverse isospin response function in nuclear matter with an arbitrary neutron-proton asymmetry parameter ξ . The energy density functional has been chosen in order to fit existing accurate quantum Monte Carlo calculations with a density dependent potential. The evolution of the response with ξ in the Δ Tz=±1 channels is quite different. While the strength of the Δ Tz=+1 channel disappears rather quickly by increasing the asymmetry, the Δ Tz=-1 channel develops a stronger and stronger collective mode that in the regime typical of neutron star matter at β equilibrium almost completely exhausts the excitation spectrum of the system. The neutrino mean free paths obtained from the TDLIDA responses are strongly dependent on ξ and on the presence of collective modes, leading to a sizable difference with respect to the prediction of the Fermi gas model.
Internal density functional theory of molecular systems
NASA Astrophysics Data System (ADS)
Nalewajski, Roman F.
1984-08-01
A thermodynamiclike theory of internal equilibrium and constrained equilibrium states of individual molecular systems is formulated, based on the Legendre transformed density functional theory (LT DFT). The molecular system (nonrelativistic, field free, Born-Oppenheimer or non-Born-Oppenheimer) is treated as the closed composite thermodynamic system, consisting of very small, rigid (open) subsystems (simple systems) containing a multi-(m)-component charged fluid in the presence of an external field. The generalized Levy constrained search construction of various ``thermodynamic'' potentials of LT DFT is given and the local Maxwell relations are derived. The reduction of various second-order partial functional derivatives (system sensitivities) in terms of few independent, basic kernels is described, using the Jacobian determinants technique. The qualitative implications for the basic kernels of the theory, from the Maxwell relations and stability criteria (generalized Le Châtelier and Le Châtelier-Braun principles) are systematically examined. Finally, possible applications of the general formalism in the thermodynamic analysis of the chemical bond, molecular stability, and chemical reactivity are identified.
Accurate thickness/density measurements of organic light-emitting diodes
Maree, C.H.; Weller, R.A.; Feldman, L.C.; Pakbaz, K.; Lee, H.W.
1998-10-01
We report on the use of Rutherford backscattering spectroscopy for thickness analysis of organic light-emitting diode structures (OLEDs) with subnanometer resolution and a spatial resolution {lt}1thinspmm. A careful study of ion beam induced effects revealed some organic film degradation, but not so severe as to inhibit meaningful measurements. The method is independent of the substrate and is still applicable if the organic film is capped with a metal cathode. Common OLED materials have been the subject of this study: poly(2-methoxy,5-(2{sup {prime}}-ethylhexoxy)-1,4-phenylene-vinylene) (MEH-PPV), N{sup {prime}},N{sup {prime}}-diphenyl-N, N{sup {prime}}-bis(3-methylphenyl)-1,1{sup {prime}} biphenyl-4,4{sup {prime}}-diamine (TPD), and tris-(8-hydroxyquinoline) aluminum (Alq{sub 3}). The densities of thin films of evaporated TPD ({rho}=1.22{plus_minus}0.05thinspg/cm{sup 3}) and Alq{sub 3} ({rho}=1.51{plus_minus}0.03thinspg/cm{sup 3}) have been established. {copyright} {ital 1998 American Institute of Physics.}
Density functional theory in the solid state.
Hasnip, Philip J; Refson, Keith; Probert, Matt I J; Yates, Jonathan R; Clark, Stewart J; Pickard, Chris J
2014-03-13
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.
Density functional theory in the solid state
Hasnip, Philip J.; Refson, Keith; Probert, Matt I. J.; Yates, Jonathan R.; Clark, Stewart J.; Pickard, Chris J.
2014-01-01
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure–property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program. PMID:24516184
Dynamical density functional theory for microswimmers.
Menzel, Andreas M; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-14
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Dynamical density functional theory for microswimmers
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-01
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Bone mineral density, adiposity, and cognitive functions
Sohrabi, Hamid R.; Bates, Kristyn A.; Weinborn, Michael; Bucks, Romola S.; Rainey-Smith, Stephanie R.; Rodrigues, Mark A.; Bird, Sabine M.; Brown, Belinda M.; Beilby, John; Howard, Matthew; Criddle, Arthur; Wraith, Megan; Taddei, Kevin; Martins, Georgia; Paton, Athena; Shah, Tejal; Dhaliwal, Satvinder S.; Mehta, Pankaj D.; Foster, Jonathan K.; Martins, Ian J.; Lautenschlager, Nicola T.; Mastaglia, Francis; Laws, Simon M.; Martins, Ralph N.
2015-01-01
Cognitive decline and dementia due to Alzheimer's disease (AD) have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD) and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34–87 years old (62.78 ± 9.27), were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after 3 years. Blood samples were collected for apolipoprotein E (APOE) genotyping and dual energy x-ray absorptiometry (DXA) was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status, and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms. PMID:25741279
Accurate calculation of Green functions on the d-dimensional hypercubic lattice
NASA Astrophysics Data System (ADS)
Loh, Yen Lee
2011-07-01
We write the Green function of the d-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The smoothness of the integrand allows both real and imaginary parts of the Green function to be computed quickly and accurately for any dimension d and any real frequency, and the computational time scales only linearly with d.
Partitioned density functional approach for a Lennard-Jones fluid.
Zhou, Shiqi
2003-12-01
The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature T(*)=1.35 and a density point for reduced temperature T(*)=1. The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
Molecular acidity: A quantitative conceptual density functional theory description.
Liu, Shubin; Schauer, Cynthia K; Pedersen, Lee G
2009-10-28
Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.
Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints
NASA Astrophysics Data System (ADS)
Woodward, Clifford E.; Forsman, Jan
2008-08-01
We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of ``site functions'' for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.
More accurate fitting of {sup 125}I and {sup 103}Pd radial dose functions
Taylor, R. E. P.; Rogers, D. W. O.
2008-09-15
In this study an improved functional form for fitting the radial dose functions, g(r), of {sup 125}I and {sup 103}Pd brachytherapy seeds is presented. The new function is capable of accurately fitting radial dose functions over ranges as large as 0.05 cm{<=}r{<=}10 cm for {sup 125}I seeds and 0.10 cm{<=}r{<=}10 cm for {sup 103}Pd seeds. The average discrepancies between fit and calculated data are less than 0.5% over the full range of fit and maximum discrepancies are 2% or less. The fitting function is also capable of accounting for the sharp increase in g(r) (upturn) seen for some sources for r<0.1 cm. This upturn has previously been attributed to the breakdown of the approximation of the sources as a line, however, in this study we demonstrate that another contributing factor is the 4.5 keV characteristic x-rays emitted from the Ti seed casing. Radial dose functions are calculated for 18 {sup 125}I seeds and 9 {sup 103}Pd seeds using the EGSnrc Monte Carlo user-code BrachyDose. Fitting coefficients of the new function are tabulated for all 27 seeds. Extrapolation characteristics of the function are also investigated. The new functional form is an improvement over currently used fitting functions with its main strength being the ability to accurately fit the rapidly varying radial dose function at small distances. The new function is an excellent candidate for fitting the radial dose function of all {sup 103}Pd and {sup 125}I brachytherapy seeds and will increase the accuracy of dose distributions calculated around brachytherapy seeds using the TG-43 protocol over a wider range of data. More accurate values of g(r) for r<0.5 cm may be particularly important in the treatment of ocular melanoma.
Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism.
Vydrov, Oleg A; Van Voorhis, Troy
2009-03-14
The nonlocal van der Waals density functional (vdW-DF) captures the essential physics of the dispersion interaction not only in the asymptotic regime but also for a general case of overlapping fragment densities. A balanced treatment of other energetic contributions, such as exchange, is crucial if we aim for accurate description of various properties of weakly bound systems. In this paper, the vdW-DF correlation functional is modified to make it better compatible with accurate exchange functionals. We suggest a slightly simplified construction of the nonlocal correlation, yielding more accurate asymptotic C(6) coefficients. We also derive a gradient correction, containing a parameter that can be adjusted to suit an exchange functional of choice. We devise a particularly apt combination of exchange and correlation terms, which satisfies many important constraints and performs well for our benchmark tests.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
Accurate measurement method of Fabry-Perot cavity parameters via optical transfer function
Bondu, Francois; Debieu, Olivier
2007-05-10
It is shown how the transfer function from frequency noise to a Pound-Drever-Hall signal for a Fabry-Perot cavity can be used to accurately measure cavity length, cavity linewidth, mirror curvature, misalignments, laser beam shape mismatching with resonant beam shape, and cavity impedance mismatching with respect to vacuum.
A half century of density functional theory
Zangwill, Andrew
2015-07-15
Today’s most popular method for calculating the electronic structure of atoms, molecules, liquids, solids, and plasmas began as a bold hypothesis: The electron density distribution completely characterizes the ground state of a many-electron system.
Validation of density-functional versus density-functional+U approaches for oxide ultrathin films
NASA Astrophysics Data System (ADS)
Barcaro, Giovanni; Thomas, Iorwerth Owain; Fortunelli, Alessandro
2010-03-01
A comparison between available experimental information and the predictions of density-functional and density-functional+U approaches is presented for oxide ultrathin films grown on single-crystal metal surfaces. Prototypical examples of monolayer phases of an ionic oxide (ZnO), a late transition metal oxide (NiO), and an early transition metal oxide (TiO2) are considered. The aim is to validate the theoretical approaches, focusing on the prediction of structural features and the reproduction of scanning tunneling microscopy images, rationalized in terms of the local density of states of the systems. It is found that it is possible to reasonably estimate the optimal lattice constant of ultrathin supported films and that the inclusion of the Hubbard U term appreciably improves the accuracy of theoretical predictions, especially in the case of nonpolar ultrathin phases of a transition metal oxide. Moreover, the optimal value of U for the oxide layer at the interface with the metal support is found to differ from that appropriate for the bulk oxide, as a consequence of the intermixing of oxide and support electronic states and screening effects.
NASA Astrophysics Data System (ADS)
Mattsson, Ann E.; Wills, John M.
2013-03-01
The inability to computationally describe the physics governing the properties of actinides and their alloys is the poster child of failure of existing Density Functional Theory exchange-correlation functionals. The intricate competition between localization and delocalization of the electrons, present in these materials, exposes the limitations of functionals only designed to properly describe one or the other situation. We will discuss the manifestation of this competition in real materials and propositions on how to construct a functional able to accurately describe properties of these materials. I addition we will discuss both the importance of using the Dirac equation to describe the relativistic effects in these materials, and the connection to the physics of transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
NASA Astrophysics Data System (ADS)
Zhang, Zhisen; Wu, Tao; Wang, Qi; Pan, Haihua; Tang, Ruikang
2014-01-01
The interactions between proteins/peptides and materials are crucial to research and development in many biomedical engineering fields. The energetics of such interactions are key in the evaluation of new proteins/peptides and materials. Much research has recently focused on the quality of free energy profiles by Jarzynski's equality, a widely used equation in biosystems. In the present work, considerable discrepancies were observed between the results obtained by Jarzynski's equality and those derived by umbrella sampling in biomaterial-water model systems. Detailed analyses confirm that such discrepancies turn up only when the target molecule moves in the high-density water layer on a material surface. Then a hybrid scheme was adopted based on this observation. The agreement between the results of the hybrid scheme and umbrella sampling confirms the former observation, which indicates an approach to a fast and accurate estimation of adsorption free energy for large biomaterial interfacial systems.
Waldrop, Jonathan M; Song, Bo; Patkowski, Konrad; Wang, Xiaopo
2015-05-28
A new highly accurate potential energy curve for the krypton dimer was constructed using coupled-cluster calculations up to the singles, doubles, triples, and perturbative quadruples level, including corrections for core-core and core-valence correlation and for relativistic effects. The ab initio data points were fitted to an analytic potential which was used to compute the most important transport properties of the krypton gas. The viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor were calculated by the kinetic theory at low density and temperatures from 116 to 5000 K. The comparisons with literature experimental data as well as with values from other pair potentials indicate that our new potential is superior to all previous ones. The transport property values computed in this work are recommended as standard values over the complete temperature range.
A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies
2014-01-01
We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys.1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design. PMID:24634616
Building A Universal Nuclear Energy Density Functional (UNEDF)
Joe Carlson; Dick Furnstahl; Mihai Horoi; Rusty Lusk; Witek Nazarewicz; Esmond Ng; Ian Thompson; James Vary
2012-09-30
During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.
Density functional theory for comprehensive orbital energy calculations.
Nakata, Ayako; Tsuneda, Takao
2013-08-14
This study reveals the reason core 1s orbital energies and the highest occupied molecular orbital (HOMO) energies of hydrogen and rare gas atoms are underestimated by long-range corrected (LC) density functional theory (DFT), which quantitatively reproduces the HOMO energies of other systems and the lowest unoccupied molecular orbital (LUMO) energies. Applying the pseudospectral regional (PR) self-interaction correction (SIC) drastically improved the underestimated orbital energies in LC-DFT calculations, while maintaining or improving the accuracies in the calculated valence HOMO and LUMO energies. This indicates that the self-interaction error in exchange functionals causes the underestimations of core 1s orbital energies and the HOMO energies of hydrogen and rare gas atoms in LC-DFT calculations. To clarify the reason for the improvement, the fractional occupation dependences of total electronic energies and orbital energies were examined. The calculated results clearly showed that the LC-PR functional gives almost linear dependences of total electronic energies for a slight decrease in the occupation number of core 1s orbitals, although this linear dependence disappears for significant decrease due to the shrinking of exchange self-interaction regions. It was also clarified that the PRSIC hardly affects the occupation number dependences of the total electronic energies and orbital energies for the fractional occupations of HOMOs and LUMOs. As a result, it was concluded that core orbital energies are obtained accurately by combining LC-DFT with PRSIC.
a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.
NASA Astrophysics Data System (ADS)
Cowan, Mark Timothy
The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.
NASA Astrophysics Data System (ADS)
Ye, Zhencheng; Cai, Jun; Liu, Honglai; Hu, Ying
2005-11-01
Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.
Molecular dynamics simulation of liquid water: Hybrid density functionals
Todorova, T; Seitsonen, A; Hutter, J; Kuo, W; Mundy, C
2005-09-12
The structure, dynamical and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta functional, four gradient corrected functionals, the local density and Hartree-Fock approximation. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and under-structured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller averaged numbers of hydrogen bonds and similar hydrogen bond populations as pure density functionals. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than from the corresponding pure density functionals.
Pure density functional for strong correlation and the thermodynamic limit from machine learning
NASA Astrophysics Data System (ADS)
Li, Li; Baker, Thomas E.; White, Steven R.; Burke, Kieron
2016-12-01
We use the density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to F [n ] , the universal part of the electronic density functional, to within quantum chemical accuracy. We also develop a data-driven, atom-centered basis set for densities which greatly reduces the computational cost and accurately represents the physical information in the machine-learning calculation. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly stretched bonds without any specific difficulty (unlike all standard DFT approximations), and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.
Double-hybrid density-functional theory with meta-generalized-gradient approximations
Souvi, Sidi M. O. Sharkas, Kamal; Toulouse, Julien
2014-02-28
We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.
Introduction to Classical Density Functional Theory by a Computational Experiment
ERIC Educational Resources Information Center
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Weighted density-functional theory for simple fluids: Prewetting of a Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Sweatman, M. B.
2002-01-01
The prewetting of a Lennard-Jones fluid is studied using weighted density-functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. An accurate functional for hard spheres is used for the repulsive functional and a weighted density-functional method is used for the attractive part. The results for this theory are compared against mean-field density-functional theory, the theory of Velasco and Tarazona [E. Velasco and P. Tarazona, J. Chem. Phys. 91, 7916 (1989)] and grand canonical ensemble simulation results. The results demonstrate that the weighted density functional for attractive forces may offer a significant increase in accuracy over the other theories. The density-functional and simulation results also indicate that a previous estimate of the wetting temperature for a model of the interaction of argon with solid carbon dioxide, obtained from simulations [J. E. Finn and P. A. Monson, Phys. Rev. A, 39, 6402 (1989)], is incorrect. The weighted density-functional method indicates that triple-point prewetting is observed for this model potential.
Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J
2013-09-14
fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory.
Error estimates for density-functional theory predictions of surface energy and work function
NASA Astrophysics Data System (ADS)
De Waele, Sam; Lejaeghere, Kurt; Sluydts, Michael; Cottenier, Stefaan
2016-12-01
Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.
NASA Astrophysics Data System (ADS)
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-07
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The
Schlüns, Danny; Franchini, Mirko; Götz, Andreas W; Neugebauer, Johannes; Jacob, Christoph R; Visscher, Lucas
2017-02-05
We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc.
Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics.
Copan, Andreas V; Sokolov, Alexander Yu; Schaefer, Henry F
2014-06-10
We present an extensive benchmark study of density cumulant functional theory (DCFT) for thermochemistry and kinetics of closed- and open-shell molecules. The performance of DCFT methods (DC-06, DC-12, ODC-06, and ODC-12) is compared to that of coupled-electron pair methods (CEPA0 and OCEPA0) and coupled-cluster theory (CCSD and CCSD(T)) for the description of noncovalent interactions (A24 database), barrier heights of hydrogen-transfer reactions (HTBH38), radical stabilization energies (RSE30), adiabatic ionization energies (AIE), and covalent bond stretching in diatomic molecules. Our results indicate that out of four DCFT methods the ODC-12 method is the most reliable and accurate DCFT formulation to date. Compared to CCSD, ODC-12 shows superior results for all benchmark tests employed in our study. With respect to coupled-pair theories, ODC-12 outperforms CEPA0 and shows similar accuracy to the orbital-optimized CEPA0 variant (OCEPA0) for systems at equilibrium geometries. For covalent bond stretching, ODC-12 is found to be more reliable than OCEPA0. For the RSE30 and AIE data sets, ODC-12 shows competitive performance with CCSD(T). In addition to benchmark results, we report new reference values for the RSE30 data set computed using coupled cluster theory with up to perturbative quadruple excitations.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K_{1 }values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO_{2}^{2+} complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K_{1} values are significantly overestimated. Accurate predictions of the absolute log K_{1} values (root mean square deviation from experiment < 1.0 for log K_{1} values ranging from 0 to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K1 values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO22+ complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K1 values are significantly overestimated. Accurate predictions of the absolute log K1 values (root mean square deviation from experiment < 1.0 for log K1 values ranging from 0more » to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.« less
An accurate solution of elastodynamic problems by numerical local Green's functions
NASA Astrophysics Data System (ADS)
Loureiro, F. S.; Silva, J. E. A.; Mansur, W. J.
2015-09-01
Green's function based methodologies for elastodynamics in both time and frequency domains, which can be either numerical or analytical, appear in many branches of physics and engineering. Thus, the development of exact expressions for Green's functions is of great importance. Unfortunately, such expressions are known only for relatively few kinds of geometry, medium and boundary conditions. In this way, due to the difficulty in finding exact Green's functions, specially in the time domain, the present paper presents a solution of the transient elastodynamic equations by a time-stepping technique based on the Explicit Green's Approach method written in terms of the Green's and Step response functions, both being computed numerically by the finite element method. The major feature is the computation of these functions separately by the central difference time integration scheme and locally owing to the principle of causality. More precisely, Green's functions are computed only at t = Δt adopting two time substeps while Step response functions are computed directly without substeps. The proposed time-stepping method shows to be quite accurate with distinct numerical properties not presented in the standard central difference scheme as addressed in the numerical example.
NASA Astrophysics Data System (ADS)
Mighell, K. J.
2004-12-01
I describe the key features of my MATPHOT algorithm for accurate and precise stellar photometry and astrometry using discrete Point Spread Functions. A discrete Point Spread Function (PSF) is a sampled version of a continuous two-dimensional PSF. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or a FITS image file. The MATPHOT algorithm shifts discrete PSFs within an observational model using a 21-pixel-wide damped sinc function and position partial derivatives are computed using a five-point numerical differentiation formula. The MATPHOT algorithm achieves accurate and precise stellar photometry and astrometry of undersampled CCD observations by using supersampled discrete PSFs that are sampled 2, 3, or more times more finely than the observational data. I have written a C-language computer program called MPD which is based on the current implementation of the MATPHOT algorithm; all source code and documentation for MPD and support software is freely available at the following website: http://www.noao.edu/staff/mighell/matphot . I demonstrate the use of MPD and present a detailed MATPHOT analysis of simulated James Webb Space Telescope observations which demonstrates that millipixel relative astrometry and millimag photometric accuracy is achievable with very complicated space-based discrete PSFs. This work was supported by a grant from the National Aeronautics and Space Administration (NASA), Interagency Order No. S-13811-G, which was awarded by the Applied Information Systems Research (AISR) Program of NASA's Science Mission Directorate.
Do Bond Functions Help for the Calculation of Accurate Bond Energies?
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Arnold, James (Technical Monitor)
1998-01-01
The bond energies of 8 chemically bound diatomics are computed using several basis sets with and without bond functions (BF). The bond energies obtained using the aug-pVnZ+BF basis sets (with a correction for basis set superposition error, BSSE) tend to be slightly smaller that the results obtained using the aug-pV(n+I)Z basis sets, but slightly larger than the BSSE corrected aug-pV(n+I)Z results. The aug-cc-pVDZ+BF and aug-cc-pVTZ+BF basis sets yield reasonable estimates of bond energies, but, in most cases, these results cannot be considered highly accurate. Extrapolation of the results obtained with basis sets including bond functions appears to be inferior to the results obtained by extrapolation using atom-centered basis sets. Therefore bond functions do not appear to offer a path for obtaining highly accurate results for chemically bound systems at a lower computational cost than atom centered basis sets.
Screened hybrid density functionals for solid-state chemistry and physics.
Janesko, Benjamin G; Henderson, Thomas M; Scuseria, Gustavo E
2009-01-21
Density functional theory incorporating hybrid exchange-correlation functionals has been extraordinarily successful in providing accurate, computationally tractable treatments of molecular properties. However, conventional hybrid functionals can be problematic for solids. Their nonlocal, Hartree-Fock-like exchange term decays slowly and incorporates unphysical features in metals and narrow-bandgap semiconductors. This article provides an overview of our group's work on designing hybrid functionals for solids. We focus on the Heyd-Scuseria-Ernzerhof screened hybrid functional [J. Chem. Phys. 2003, 118, 8207], its applications to the chemistry and physics of solids and surfaces, and our efforts to build upon its successes.
Density functional calculations on hydrocarbon isodesmic reactions
NASA Astrophysics Data System (ADS)
Fortunelli, Alessandro; Selmi, Massimo
1994-06-01
Hartree—Fock, Hartree—Fock-plus-correlation and self-consistent Kohn—Sham calculations are performed on a set of hydrocarbon isodesmic reactions, i.e. reactions among hydrocarbons in which the number and type of carbon—carbon and carbon—hydrogen bonds is conserved. It is found that neither Hartree—Fock nor Kohn—Sham methods correctly predict standard enthalpies, Δ Hr(298 K), of these reactions, even though — for reactions involving molecules containing strained double bonds — the agreement between the theoretical estimates and the experimental values of Δ Hr seems to be improved by the self-consistent solution of the Kohn—Sham equations. The remaining discrepancies are attributed to intramolecular dispersion effects, that are not described by ordinary exchange—correlation functionals, and are eliminated by introducing corrections based on a simple semi-empirical model.
A perturbative density functional theory for square-well fluids.
Jin, Zhehui; Tang, Yiping; Wu, Jianzhong
2011-05-07
We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.
Testing for parity violation in nuclei using spin density matrices for nuclear density functionals
NASA Astrophysics Data System (ADS)
Barrett, B. R.; Giraud, B. G.
2015-06-01
The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a ‘hedgehog’ situation, which exists only if nuclear states contain some amount of parity violation. A toy model is given as an illustrative example.
McKechnie, Scott; Booth, George H.; Cohen, Aron J.; Cole, Jacqueline M.
2015-05-21
The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.
Postfragmentation density function for bacterial aggregates in laminar flow
NASA Astrophysics Data System (ADS)
Byrne, Erin; Bortz, David M.; Dzul, Steve; Solomon, Michael; Younger, John
2011-04-01
The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation.
Advanced Density Functional Theory Methods for Materials Science
NASA Astrophysics Data System (ADS)
Demers, Steven
In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description. Zinc Phosphide (Zn3P2) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn3P2 and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems. Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via 'classical' molecular
Verdict: Time-Dependent Density Functional Theory "Not Guilty" of Large Errors for Cyanines.
Jacquemin, Denis; Zhao, Yan; Valero, Rosendo; Adamo, Carlo; Ciofini, Ilaria; Truhlar, Donald G
2012-04-10
We assess the accuracy of eight Minnesota density functionals (M05 through M08-SO) and two others (PBE and PBE0) for the prediction of electronic excitation energies of a family of four cyanine dyes. We find that time-dependent density functional theory (TDDFT) with the five most recent of these functionals (from M06-HF through M08-SO) is able to predict excitation energies for cyanine dyes within 0.10-0.36 eV accuracy with respect to the most accurate available Quantum Monte Carlo calculations, providing a comparable accuracy to the latest generation of CASPT2 calculations, which have errors of 0.16-0.34 eV. Therefore previous conclusions that TDDFT cannot treat cyanine dyes reasonably accurately must be revised.
Density functional theory for field emission from carbon nano-structures.
Li, Zhibing
2015-12-01
Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on density functional theory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission.
Pérez-Jiménez, Angel J; Pérez-Jordá, José M; Illas, Francesc
2004-01-01
A new method to improve the excess spin density obtained from unrestricted Hartree-Fock wave functions in terms of natural orbitals is proposed. Using this modified excess spin density to evaluate the correlation energy by means of density functionals leads to large improvements in the computed magnetic coupling constants of several materials without need to modify the exchange contribution. This is important because it reconciles the density functional theory description with the one provided by multi-determinant wave functions. Using the present approach, the leading contribution to the magnetic coupling constant arises from electron correlation effects. The performance of the new method is illustrated on various materials including high-critical-temperature superconductors parent compounds.
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Dateo, Christopher E.; Schwenke, David W.; Chaban, Galina M.
2005-01-01
Accurate quartic force fields have been determined for the CCH- and NH2- molecular anions using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). Very large one-particle basis sets have been used including diffuse functions and up through g-type functions. Correlation of the nitrogen and carbon core electrons has been included, as well as other "small" effects, such as the diagonal Born-Oppenheimer correction, and basis set extrapolation, and corrections for higher-order correlation effects and scalar relativistic effects. Fundamental vibrational frequencies have been computed using standard second-order perturbation theory as well as variational methods. Comparison with the available experimental data is presented and discussed. The implications of our research for the astronomical observation of molecular anions will be discussed.
Applications and validations of the Minnesota density functionals
NASA Astrophysics Data System (ADS)
Zhao, Yan; Truhlar, Donald G.
2011-01-01
We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.
Improved description of soft layered materials with van der Waals density functional theory.
Graziano, Gabriella; Klimeš, Jiří; Fernandez-Alonso, Felix; Michaelides, Angelos
2012-10-24
The accurate description of van der Waals forces within density functional theory is currently one of the most active areas of research in computational physics and chemistry. Here we report results on the structural and energetic properties of graphite and hexagonal boron nitride, two layered materials where interlayer binding is dominated by van der Waals forces. Results from several density functionals are reported, including the optimized Becke88 van der Waals (optB88-vdW) and the optimized PBE van der Waals (optPBE-vdW) (Klimeš et al 2010 J. Phys.: Condens. Matter 22 022201) functionals. Where comparison to experiment and higher-level theory is possible, the results obtained from the two new van der Waals density functionals are in good agreement. An analysis of the physical nature of the interlayer binding in both graphite and hexagonal boron nitride is also reported.
Density Functional Calculations for the Neutron Star Matter at Subnormal Density
NASA Astrophysics Data System (ADS)
Kashiwaba, Yu; Nakatsukasa, Takashi
The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (\\bar{ρ },Yp), varying the lattice constant of the unit cell. For small Yp values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.
Preface: Special Topic on Advances in Density Functional Theory
Yang, Weitao
2014-05-14
This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering.
Reflection-Asymmetric Nuclear Deformations within the Density Functional Theory
Olsen, E; Erler, J; Nazarewicz, W.; Stoitsov, M
2012-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection- asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver axialhfb that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even- even isotopes of radium and thorium.
Gutzwiller density functional theory for correlated electron systems
Ho, K. M.; Schmalian, J.; Wang, C. Z.
2008-02-04
We develop a density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wave function which exactly obeys the Gutzwiller approximation for all one-particle operators. The solution of the many-electron problem is mapped onto the self-consistent solution of a set of single-particle Schroedinger equations, analogously to standard DFT-local density approximation calculations.
Density Functional Theory with Dissipation: Transport through Single Molecules
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
Conditional Probability Density Functions Arising in Bearing Estimation
1994-05-01
and a better known performance measure: the Cramer-Rao bound . 14. SUMECT TEm IL5 NUlMN OF PAMES Probability Density Function, bearing angle estimation...results obtained using the calculated density functions and a better known performance measure: the Cramer-Rao bound . The major results obtained are as...48 15. Sampling Inteval , Propagation Delay, and Covariance Singularities ....... 52 viii List of Figures (continued
Density functional study of the electric double layer formed by a high density electrolyte.
Henderson, Douglas; Lamperski, Stanisław; Jin, Zhehui; Wu, Jianzhong
2011-11-10
We use a classical density functional theory (DFT) to study the electric double layer formed by charged hard spheres near a planar charged surface. The DFT predictions are found to be in good agreement with recent computer simulation results. We study the capacitance of the charged hard-sphere system at a range of densities and surface charges and find that the capacitance exhibits a local minimum at low ionic densities and small electrode charge. Although this charging behavior is typical for an aqueous electrolyte solution, the local minimum gradually turns into a maximum as the density of the hard spheres increases. Charged hard spheres at high density provide a reasonable first approximation for ionic liquids. In agreement with experiment, the capacitance of this model ionic liquid double layer has a maximum at small electrode charge density.
Schütt, Heiko H; Harmeling, Stefan; Macke, Jakob H; Wichmann, Felix A
2016-05-01
The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available.
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-01-01
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access to precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. The SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded. PMID:25979264
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-05-15
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access to precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. Lastly, the SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded.
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-05-15
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access tomore » precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. Lastly, the SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded.« less
Density functional theory for polymeric systems in 2D.
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-22
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.
Cooling Function in Wide Range of Density and Metallicity
NASA Astrophysics Data System (ADS)
Wang, Ye; Ferland, G. J.
2013-06-01
This work focuses on how the plasma cooling function changes with density and metallicity over a wide range of temperature (104 K
Linear response of homogeneous nuclear matter with energy density functionals
NASA Astrophysics Data System (ADS)
Pastore, A.; Davesne, D.; Navarro, J.
2015-03-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
Excitons in solids with time-dependent density-functional theory: the bootstrap kernel and beyond
NASA Astrophysics Data System (ADS)
Byun, Young-Moo; Yang, Zeng-Hui; Ullrich, Carsten
Time-dependent density-functional theory (TDDFT) is an efficient method to describe the optical properties of solids. Lately, a series of bootstrap-type exchange-correlation (xc) kernels have been reported to produce accurate excitons in solids, but different bootstrap-type kernels exist in the literature, with mixed results. In this presentation, we reveal the origin of the confusion and show a new empirical TDDFT xc kernel to compute excitonic properties of semiconductors and insulators efficiently and accurately. Our method can be used for high-throughput screening calculations and large unit cell calculations. Work supported by NSF Grant DMR-1408904.
Filtered density function approach for reactive transport in groundwater
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Shells of charge: a density functional theory for charged hard spheres
NASA Astrophysics Data System (ADS)
Roth, Roland; Gillespie, Dirk
2016-06-01
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect ‘functionalizes’ the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences.
Conjugate-gradient optimization method for orbital-free density functional calculations.
Jiang, Hong; Yang, Weitao
2004-08-01
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient.
Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; ...
2016-01-19
An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based rst principles methods have the potential to provide the accuracy and computational e ciency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quanti cation of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures atmore » thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by di erent density functionals. We nd that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative di erences exhibited by the major classes of functionals, and estimate the magnitudes of these e ects when possible.« less
Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Maguel A.
2016-01-19
An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based rst principles methods have the potential to provide the accuracy and computational e ciency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quanti cation of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by di erent density functionals. We nd that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative di erences exhibited by the major classes of functionals, and estimate the magnitudes of these e ects when possible.
Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals.
Janthon, Patanachai; Luo, Sijie Andy; Kozlov, Sergey M; Viñes, Francesc; Limtrakul, Jumras; Truhlar, Donald G; Illas, Francesc
2014-09-09
Systematic evaluation of the accuracy of exchange-correlation functionals is essential to guide scientists in their choice of an optimal method for a given problem when using density functional theory. In this work, accuracy of one Generalized Gradient Approximation (GGA) functional, three meta-GGA functionals, one Nonseparable Gradient Approximation (NGA) functional, one meta-NGA, and three hybrid GGA functionals was evaluated for calculations of the closest interatomic distances, cohesive energies, and bulk moduli of all 3d, 4d, and 5d bulk transition metals that have face centered cubic (fcc), hexagonal closed packed (hcp), or body centered cubic (bcc) structures (a total of 27 cases). Our results show that including the extra elements of kinetic energy density and Hartree-Fock exchange energy density into gradient approximation density functionals does not usually improve them. Nevertheless, the accuracies of the Tao-Perdew-Staroverov-Scuseria (TPSS) and M06-L meta-GGAs and the MN12-L meta-NGA approach the accuracy of the Perdew-Burke-Ernzerhof (PBE) GGA, so usage of these functionals may be advisable for systems containing both solid-state transition metals and molecular species. The N12 NGA functional is also shown to be almost as accurate as PBE for bulk transition metals, and thus it could be a good choice for studies of catalysis given its proven good performance for molecular species.
Optimization of an exchange-correlation density functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M.
2016-06-01
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.
Basis convergence of range-separated density-functional theory
Franck, Odile Mussard, Bastien; Luppi, Eleonora Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Basis convergence of range-separated density-functional theory.
Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Density Functional Theory for General Hard-Core Lattice Gases
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2004-09-01
We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.
Force Density Function Relationships in 2-D Granular Media
NASA Technical Reports Server (NTRS)
Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.
2004-01-01
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
NASA Astrophysics Data System (ADS)
Friis, J.; Madsen, G. K. H.; Larsen, F. K.; Jiang, B.; Marthinsen, K.; Holmestad, R.
2003-12-01
Accurate experimental structure factors for Mg have been measured and compared with density functional theory (DFT) to test some commonly used functionals and self-interaction correction (SIC) schemes. Low order structure factors, free of extinction and on absolute scale, were measured accurately by quantitative convergent beam electron diffraction. In addition, a complete set of structure factors up to sin θ/λ=1.6 Å-1 was measured by x-ray diffraction at 10 K. The DFT calculations were performed using the full potential linearized augmented plane wave method. It was found that the agreement with experiment increases when going from the local density approximation (LDA) to the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhofer and further to the GGA of Engel and Vosko. Applying the SIC of Perdew and Zunger to the core states for LDA does not improve the agreement with theory, while applying the SIC of Lundin and Eriksson results in a significantly improved agreement. This implies that the main source of error in the LDA functional comes from the description of the core densities. Using the functional which agrees best with experiment, a non-nuclear maximum is established in the calculated electron density of beryllium but not of magnesium.
Methane dissociation on Pt(111): Searching for a specific reaction parameter density functional
Nattino, Francesco Migliorini, Davide; Kroes, Geert-Jan; Bonfanti, Matteo
2016-01-28
The theoretical description of methane dissociating on metal surfaces is a current frontier in the field of gas-surface dynamics. Dynamical models that aim at achieving a highly accurate description of this reaction rely on potential energy surfaces based on density functional theory calculations at the generalized gradient approximation. We focus here on the effect that the exchange-correlation functional has on the reactivity of methane on a metal surface, using CHD{sub 3} + Pt(111) as a test case. We present new ab initio molecular dynamics calculations performed with various density functionals, looking also at functionals that account for the van der Waals (vdW) interaction. While searching for a semi-empirical specific reaction parameter density functional for this system, we find that the use of a weighted average of the PBE and the RPBE exchange functionals together with a vdW-corrected correlation functional leads to an improved agreement with quantum state-resolved experimental data for the sticking probability, compared to previous PBE calculations. With this semi-empirical density functional, we have also investigated the surface temperature dependence of the methane dissociation reaction and the influence of the rotational alignment on the reactivity, and compared our results with experiments.
Cluster abundance in chameleon f(R) gravity I: toward an accurate halo mass function prediction
NASA Astrophysics Data System (ADS)
Cataneo, Matteo; Rapetti, David; Lombriser, Lucas; Li, Baojiu
2016-12-01
We refine the mass and environment dependent spherical collapse model of chameleon f(R) gravity by calibrating a phenomenological correction inspired by the parameterized post-Friedmann framework against high-resolution N-body simulations. We employ our method to predict the corresponding modified halo mass function, and provide fitting formulas to calculate the enhancement of the f(R) halo abundance with respect to that of General Relativity (GR) within a precision of lesssim 5% from the results obtained in the simulations. Similar accuracy can be achieved for the full f(R) mass function on the condition that the modeling of the reference GR abundance of halos is accurate at the percent level. We use our fits to forecast constraints on the additional scalar degree of freedom of the theory, finding that upper bounds competitive with current Solar System tests are within reach of cluster number count analyses from ongoing and upcoming surveys at much larger scales. Importantly, the flexibility of our method allows also for this to be applied to other scalar-tensor theories characterized by a mass and environment dependent spherical collapse.
New link between conceptual density functional theory and electron delocalization.
Matito, Eduard; Putz, Mihai V
2011-11-17
In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.
Density functional calculations of spin-wave dispersion curves.
NASA Astrophysics Data System (ADS)
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
Density functionals that recognize covalent, metallic, and weak bonds.
Sun, Jianwei; Xiao, Bing; Fang, Yuan; Haunschild, Robin; Hao, Pan; Ruzsinszky, Adrienn; Csonka, Gábor I; Scuseria, Gustavo E; Perdew, John P
2013-09-06
Computationally efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.
Perspective: Kohn-Sham density functional theory descending a staircase
NASA Astrophysics Data System (ADS)
Yu, Haoyu S.; Li, Shaohong L.; Truhlar, Donald G.
2016-10-01
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and—like Marcel Duchamp—we hope to convey progress in a stimulating way.
Perspective: Kohn-Sham density functional theory descending a staircase.
Yu, Haoyu S; Li, Shaohong L; Truhlar, Donald G
2016-10-07
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and-like Marcel Duchamp-we hope to convey progress in a stimulating way.
Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.
Gagliardi, Laura; Truhlar, Donald G; Li Manni, Giovanni; Carlson, Rebecca K; Hoyer, Chad E; Bao, Junwei Lucas
2017-01-17
The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than
van der Waals Density Functional Theory vdW-DFq for Semihard Materials
NASA Astrophysics Data System (ADS)
Peng, Qing; de, Suvranu
There are a large number of materials with mild stiffness, which are not as soft as tissues and not as strong as metals. These semihard materials includes energetic materials, molecular crystals, layered materials, and van der Waals crystals. The integrity and mechanical stability are mainly determined by the interactions between instantaneously induced dipoles, the so called London dispersion force or van der Waals force. It is challenging to accurately model the structural and mechanical properties of these semihard materials in the frame of density functional theory where the non-local correlation functionals are not well known. Here we propose a van der Waals density functional named vdW-DFq to accurately model the density and geometry of semihard materials. Using β-cyclotetramethylene tetranitramine as a prototype, we adjust the enhancement factor of the exchange energy functional with generalized gradient approximations. We find this method to be simple and robust over a wide tuning range when calibrating the functional on-demand with experimental data. With a calibrated value q = 1 . 05 , the proposed vdW-DFq method shows good performance in predicting the geometries of 11 common energetic material molecular crystals and 3 typical layered van der Waals crystals. The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # HDTRA1-13-1-0025.
Hatt, Mathieu; Cheze le Rest, Catherine; Descourt, Patrice; Dekker, Andre; De Ruysscher, Dirk; Oellers, Michel; Lambin, Philippe; Pradier, Olivier; Visvikis, Dimitris
2010-05-01
Purpose: Accurate contouring of positron emission tomography (PET) functional volumes is now considered crucial in image-guided radiotherapy and other oncology applications because the use of functional imaging allows for biological target definition. In addition, the definition of variable uptake regions within the tumor itself may facilitate dose painting for dosimetry optimization. Methods and Materials: Current state-of-the-art algorithms for functional volume segmentation use adaptive thresholding. We developed an approach called fuzzy locally adaptive Bayesian (FLAB), validated on homogeneous objects, and then improved it by allowing the use of up to three tumor classes for the delineation of inhomogeneous tumors (3-FLAB). Simulated and real tumors with histology data containing homogeneous and heterogeneous activity distributions were used to assess the algorithm's accuracy. Results: The new 3-FLAB algorithm is able to extract the overall tumor from the background tissues and delineate variable uptake regions within the tumors, with higher accuracy and robustness compared with adaptive threshold (T{sub bckg}) and fuzzy C-means (FCM). 3-FLAB performed with a mean classification error of less than 9% +- 8% on the simulated tumors, whereas binary-only implementation led to errors of 15% +- 11%. T{sub bckg} and FCM led to mean errors of 20% +- 12% and 17% +- 14%, respectively. 3-FLAB also led to more robust estimation of the maximum diameters of tumors with histology measurements, with <6% standard deviation, whereas binary FLAB, T{sub bckg} and FCM lead to 10%, 12%, and 13%, respectively. Conclusion: These encouraging results warrant further investigation in future studies that will investigate the impact of 3-FLAB in radiotherapy treatment planning, diagnosis, and therapy response evaluation.
Energy density functional for nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Erler, J.; Horowitz, C. J.; Nazarewicz, W.; Rafalski, M.; Reinhard, P.-G.
2013-04-01
Background: Recent observational data on neutron star masses and radii provide stringent constraints on the equation of state of neutron rich matter [Annu. Rev. Nucl. Part. Sci.ARPSDF0163-899810.1146/annurev-nucl-102711-095018 62, 485 (2012)].Purpose: We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars.Methods: We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals—a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties—are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one.Results: The new functional TOV-min yields results for nuclear bulk properties (energy, rms radius, diffraction radius, and surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When comparing SV-min and TOV-min, isoscalar nuclear matter indicators vary slightly while isovector properties are changed considerably. We discuss neutron skins, dipole polarizability, separation energies of the heaviest elements, and proton and neutron drip lines. We confirm a correlation between the neutron skin of 208Pb and the neutron star radius.Conclusions: We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass, and that predictions can only be made within an extremely broad uncertainty band. For atomic nuclei, the new functional TOV-min performs at least as well as the standard nuclear functionals, but
Kinetic-energy density functional: Atoms and shell structure
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-09-01
We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. {copyright} {ital 1996 The American Physical Society.}
Exploration of a modified density dependence in the Skyrme functional
Erler, J.; Reinhard, P.-G.; Kluepfel, P.
2010-10-15
A variant of the basic Skyrme-Hartree-Fock functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, superheavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g., for projection) and more flexibility in the regime of high densities.
SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters
NASA Astrophysics Data System (ADS)
Hui, Kerwin; Chai, Jeng-Da
2016-01-01
By incorporating the nonempirical strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] in the underlying expression of four existing hybrid and double-hybrid models, we propose one hybrid (SCAN0) and three double-hybrid (SCAN0-DH, SCAN-QIDH, and SCAN0-2) density functionals, which are free from any fitted parameters. The SCAN-based double-hybrid functionals consistently outperform their parent SCAN semilocal functional for self-interaction problems and noncovalent interactions. In particular, SCAN0-2, which includes about 79% of Hartree-Fock exchange and 50% of second-order Møller-Plesset correlation, is shown to be reliably accurate for a very diverse range of applications, such as thermochemistry, kinetics, noncovalent interactions, and self-interaction problems.
Energetics of H2 clusters from density functional and coupled cluster theories
NASA Astrophysics Data System (ADS)
Trail, J. R.; López Ríos, P.; Needs, R. J.
2017-03-01
We use coupled-cluster quantum chemical methods to calculate the energetics of molecular clusters cut out of periodic molecular hydrogen structures that model observed phases of solid hydrogen. The hydrogen structures are obtained from Kohn-Sham density functional theory (DFT) calculations at pressures of 150, 250, and 350 GPa, which are within the pressure range in which phases II, III, and IV are found to be stable. The calculated deviations in the DFT energies from the coupled-cluster data are reported for different functionals, and optimized functionals are generated which provide reduced errors. We give recommendations for semilocal and hybrid density functionals that are expected to provide an accurate description of hydrogen at high pressures.
On the evolution of the density probability density function in strongly self-gravitating systems
Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P{sub V} (ρ)∝ρ{sup –1.54} for the (volume-weighted) PDF and P{sub M} (ρ)∝ρ{sup –0.54} for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
On the Evolution of the Density Probability Density Function in Strongly Self-gravitating Systems
NASA Astrophysics Data System (ADS)
Girichidis, Philipp; Konstandin, Lukas; Whitworth, Anthony P.; Klessen, Ralf S.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form PV (ρ)vpropρ-1.54 for the (volume-weighted) PDF and PM (ρ)vpropρ-0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
The behavior of fluids near solutes: A density functional theory and computer simulation study
NASA Astrophysics Data System (ADS)
Reddy, Govardhan; Yethiraj, Arun
2004-09-01
The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.
NASA Astrophysics Data System (ADS)
Nocera, A.; Alvarez, G.
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Assessment of density functional methods for calculating thermochemistries of Si-H-Cl compounds
Hay, P.J.
1996-01-04
The performance of the gradient-corrected BLYP density functional and the hybrid B3LYP functional has been studied in calculations of bond energies of Si-H-Cl containing molecules involved in thermal chemical vapor deposition processes of silicon. Calculated atomization energies using the BLYP and B3LYP functionals are in better agreement with experiment (typically within 10 kcal/mol) compared to more computationally demanding methods such as MP4. Comparisons are also made with more accurate theoretical methods including corrected MP4 approaches. While predictions of thermochemical properties for second-row compounds from BLYP approaches are slightly less accurate than for first-row compounds, these techniques still represent a promising approach of obtaining theoretical estimates for thermochemical properties. 37 refs., 6 tabs.
Hammer, Rubi; Cooke, Gillian E.; Stein, Mark A.; Booth, James R.
2015-01-01
Finding neurobiological markers for neurodevelopmental disorders, such as attention deficit and hyperactivity disorder (ADHD), is a major objective of clinicians and neuroscientists. We examined if functional Magnetic Resonance Imaging (fMRI) data from a few distinct visuospatial working memory (VSWM) tasks enables accurately detecting cases with ADHD. We tested 20 boys with ADHD combined type and 20 typically developed (TD) boys in four VSWM tasks that differed in feedback availability (feedback, no-feedback) and reward size (large, small). We used a multimodal analysis based on brain activity in 16 regions of interest, significantly activated or deactivated in the four VSWM tasks (based on the entire participants' sample). Dimensionality of the data was reduced into 10 principal components that were used as the input variables to a logistic regression classifier. fMRI data from the four VSWM tasks enabled a classification accuracy of 92.5%, with high predicted ADHD probability values for most clinical cases, and low predicted ADHD probabilities for most TDs. This accuracy level was higher than those achieved by using the fMRI data of any single task, or the respective behavioral data. This indicates that task-based fMRI data acquired while participants perform a few distinct VSWM tasks enables improved detection of clinical cases. PMID:26509111
Accurate Astrometry and Photometry of Saturated and Coronagraphic Point Spread Functions
Marois, C; Lafreniere, D; Macintosh, B; Doyon, R
2006-02-07
For ground-based adaptive optics point source imaging, differential atmospheric refraction and flexure introduce a small drift of the point spread function (PSF) with time, and seeing and sky transmission variations modify the PSF flux. These effects need to be corrected to properly combine the images and obtain optimal signal-to-noise ratios, accurate relative astrometry and photometry of detected companions as well as precise detection limits. Usually, one can easily correct for these effects by using the PSF core, but this is impossible when high dynamic range observing techniques are used, like coronagraphy with a non-transmissive occulting mask, or if the stellar PSF core is saturated. We present a new technique that can solve these issues by using off-axis satellite PSFs produced by a periodic amplitude or phase mask conjugated to a pupil plane. It will be shown that these satellite PSFs track precisely the PSF position, its Strehl ratio and its intensity and can thus be used to register and to flux normalize the PSF. This approach can be easily implemented in existing adaptive optics instruments and should be considered for future extreme adaptive optics coronagraph instruments and in high-contrast imaging space observatories.
"Sloppy" nuclear energy density functionals: Effective model reduction
NASA Astrophysics Data System (ADS)
Nikšić, Tamara; Vretenar, Dario
2016-08-01
Concepts from information geometry are used to analyze parameter sensitivity for a nuclear energy density functional, representative of a class of semiempirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are "sloppy," namely, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, sloppy functionals exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the range of parameter sensitivity. Using the manifold boundary approximation method, we illustrate how to systematically construct effective nuclear density functionals of successively lower dimension in parameter space until sloppiness is eventually eliminated and the resulting functional contains only stiff combinations of parameters.
Dynamics of localized particles from density functional theory
NASA Astrophysics Data System (ADS)
Reinhardt, J.; Brader, J. M.
2012-01-01
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.
Nuclear energy density functional and the nuclear α decay
NASA Astrophysics Data System (ADS)
Lim, Yeunhwan; Oh, Yongseok
2017-03-01
The nuclear α decay of heavy nuclei is investigated based on the nuclear energy density functional, which leads to the α potential inside the parent nucleus in terms of the proton and neutron density profiles of the daughter nucleus. We use the Skyrme force model, Gogny force model, and relativistic mean-field model to get the nucleon density profiles inside heavy nuclei. Once the nucleon density profiles are determined, the parameters of the nuclear α potential are fitted to the observed α decay half-lives of heavy nuclei. This approach is then applied to predict unknown α decay half-lives of heavy nuclei. To estimate the Q values of unobserved α decays, we make use of the liquid droplet model.
Density functional theory is straying from the path toward the exact functional.
Medvedev, Michael G; Bushmarinov, Ivan S; Sun, Jianwei; Perdew, John P; Lyssenko, Konstantin A
2017-01-06
The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
NASA Astrophysics Data System (ADS)
Glossman, M. D.; Balbás, L. C.; Alonso, J. A.
1995-07-01
The radial electron density obtained for all the atoms of the main groups of the Periodic Table through the solution of the Euler equation associated with the nonlocal weighted density approximation (WDA) for the exchange and kinetic energy density functionals shows an incipient shell structure which is absent in other calculations using kinetic energy functionals based on the electronic density. The WDA radial density reveals two local maxima and the position of the first maximum correlates with the position of the maximum for the 1s orbital in the Hartree-Fock approximation. The cusp condition at the nucleus is fulfilled accurately. Also we study the density-based electron localization function (DELF) as a complementary procedure for the visualization of shells.
Tao, Jianmin; Perdew, John P; Staroverov, Viktor N; Scuseria, Gustavo E
2008-01-01
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known exact constraints
Excitons in solids with non-empirical hybrid time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Ullrich, Carsten; Yang, Zeng-Hui; Sottile, Francesco
2015-03-01
The Bethe-Salpeter equation (BSE) accurately describes the optical properties of solids, but is computationally expensive. Time-dependent density-functional theory (TDDFT) is more efficient, but standard functionals do not produce excitons in extended systems. We present a new, non-empirical hybrid TDDFT approach whose computational cost is much less than BSE, while the accuracy for both bound excitons and the continuum spectra is comparable to that of the BSE. Good performance is observed for both small-gap semiconductors and large-gap insulators. Work supported by NSF Grant DMR-1408904.
Charge transfer in time-dependent density-functional theory via spin-symmetry breaking
Fuks, Johanna I.; Maitra, Neepa T.
2011-04-15
Long-range charge-transfer excitations pose a major challenge for time-dependent density-functional approximations. We show that spin-symmetry breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and on the real LiH molecule within the pseudopotential approximation to demonstrate our results.
Sang, Xiahan; Kulovits, Andreas; Wang, Guofeng; Wiezorek, Jörg
2013-02-28
Accurate low-order structure factors (Fg) measured by quantitative convergent beam electron diffraction (QCBED) were used for validation of different density functional theory (DFT) approximations. Twenty-three low-order Fg were measured for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal based intermetallic phases γ-TiAl, β-NiAl, and γ1-FePd using a multi-beam off-zone axis QCBED method and then compared with Fg calculated by ab initio DFT using the local density approximation (LDA) and LDA + U, and different generalized gradient approximations (GGA) functionals. Different functionals perform very differently for different materials and crystal structures regarding prediction of low-order Fg. All the GGA functionals tested in the paper except for EV93 achieve good overall agreement with the experimentally determined low-order Fg for BCC Cr and Fe, while EV93 performs the best for FCC Ni and Cu. The LDA and GGA functional fail to predict accurately the low-order Fg for β-NiAl and γ1-FePd. The LDA + U approach, through tuning of U, can achieve excellent matches with the experimentally measured Fg for all the metallic systems investigated in this paper. The use of experimentally accessible low order Fg as an additional set of metrics in approaches of validation of DFT calculations is discussed and has potential to assist in and to stimulate development of improved functionals.
NASA Astrophysics Data System (ADS)
Sang, Xiahan; Kulovits, Andreas; Wang, Guofeng; Wiezorek, Jörg
2013-02-01
Accurate low-order structure factors (Fg) measured by quantitative convergent beam electron diffraction (QCBED) were used for validation of different density functional theory (DFT) approximations. Twenty-three low-order Fg were measured for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal based intermetallic phases γ-TiAl, β-NiAl, and γ1-FePd using a multi-beam off-zone axis QCBED method and then compared with Fg calculated by ab initio DFT using the local density approximation (LDA) and LDA + U, and different generalized gradient approximations (GGA) functionals. Different functionals perform very differently for different materials and crystal structures regarding prediction of low-order Fg. All the GGA functionals tested in the paper except for EV93 achieve good overall agreement with the experimentally determined low-order Fg for BCC Cr and Fe, while EV93 performs the best for FCC Ni and Cu. The LDA and GGA functional fail to predict accurately the low-order Fg for β-NiAl and γ1-FePd. The LDA + U approach, through tuning of U, can achieve excellent matches with the experimentally measured Fg for all the metallic systems investigated in this paper. The use of experimentally accessible low order Fg as an additional set of metrics in approaches of validation of DFT calculations is discussed and has potential to assist in and to stimulate development of improved functionals.
Hubert, Mickaël; Hedegård, Erik D; Jensen, Hans Jørgen Aa
2016-05-10
Computational methods that can accurately and effectively predict all types of electronic excitations for any molecular system are missing in the toolbox of the computational chemist. Although various Kohn-Sham density-functional methods (KS-DFT) fulfill this aim in some cases, they become inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functional theory-MC-srDFT-as a new tool in the toolbox. While initial applications for systems with multireference character and double excitations have been promising, it is nevertheless important that the accuracy of MC-srDFT is at least comparable to the best KS-DFT methods also for organic molecules that are typically of single-reference character. In this paper we therefore systematically investigate the performance of MC-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2, NEVPT2, and the coupled cluster based CC2 and CC3.
NASA Astrophysics Data System (ADS)
Tian, Li-Yun; Levämäki, Henrik; Ropo, Matti; Kokko, Kalevi; Nagy, Ágnes; Vitos, Levente
2016-08-01
Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; Nicholson, D. M.
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; ...
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of themore » density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.« less
Density Functional Study of Perovskite Superconductor MgCNi3
NASA Astrophysics Data System (ADS)
Kumar, Jagdish; Sharma, Devina; Kumar, Ranjan; Awana, V. P. S.; Ahluwalia, P. K.
2011-12-01
We here report the first principle density functional study of MgCNi3 which crystallize in cubic perovskite structure having critical transition temperature of 8 K. The interesting aspect of this compound is that in normal state it is non magnetic in nature despite conduction electrons in it are derived from partially filled Ni d states, which typically lead to ferromagnetism in metallic Ni and many Ni-based binary alloys. To investigate the detailed microscopic origin of the non magnetic nature we have done density functional based calculations on this compound. The lattice constant is calculated using minimum energy criteria from total energy versus lattice constant plot. By taking the calculated values of lattice constant we have done the precise calculations on the compound using Full Potential Linear Augmented Plane Wave (FP-LAPW) method implemented in ELK code. The electronic density of states is found spin degenerate that corresponds to a non-magnetic ground state. The density of states (DOS) at Fermi level, N(EF) is dominated by Ni-d states. The sharp peak observed just below Fermi level corresponds to van Hove singularity (vHs). The projected density of states (PDOS) suggests a strong hybridization of Ni-3d and C-2p states which is responsible for the observed non magnetic nature of MgCNi3.
Oyeyemi, Victor B; Keith, John A; Carter, Emily A
2014-09-04
Accurate bond dissociation energies (BDEs) are important for characterizing combustion chemistry, particularly the initial stages of pyrolysis. Here we contribute to evaluating the thermochemistry of biodiesel methyl ester molecules using ab initio BDEs derived from a multireference averaged coupled-pair functional (MRACPF2)-based scheme. Having previously validated this approach for hydrocarbons and a variety of oxygenates, herein we provide further validation for bonds within carboxylic acids and methyl esters, finding our scheme predicts BDEs within chemical accuracy (i.e., within 1 kcal/mol) for these molecules. Insights into BDE trends with ester size are then analyzed for methyl formate through methyl crotonate. We find that the carbonyl group in the ester moiety has only a local effect on BDEs. C═C double bonds in ester alkyl chains are found to increase the strengths of bonds adjacent to the double bond. An important exception are bonds beta to C═C or C═O bonds, which produce allylic-like radicals upon dissociation. The observed trends arise from different degrees of geometric relaxation and resonance stabilization in the radicals produced. We also compute BDEs in various small alkanes and alkenes as models for the long hydrocarbon chain of actual biodiesel methyl esters. We again show that allylic bonds in the alkenes are much weaker than those in the small methyl esters, indicating that hydrogen abstractions are more likely at the allylic site and even more likely at bis-allylic sites of alkyl chains due to more electrons involved in π-resonance in the latter. Lastly, we use the BDEs in small surrogates to estimate heretofore unknown BDEs in large methyl esters of biodiesel fuels.
Chen, Qiang; Yang, Bicheng
2016-01-01
By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions are also considered.
Relations among several nuclear and electronic density functional reactivity indexes
NASA Astrophysics Data System (ADS)
Torrent-Sucarrat, Miquel; Luis, Josep M.; Duran, Miquel; Toro-Labbé, Alejandro; Solà, Miquel
2003-11-01
An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the "Quantum Chemical le Chatelier Principle." Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.
Dispersion corrections to density functionals for water aromatic interactions.
Zimmerli, Urs; Parrinello, Michele; Koumoutsakos, Petros
2004-02-08
We investigate recently published methods for extending density functional theory to the description of long-range dispersive interactions. In all schemes an empirical correction consisting of a C6r(-6) term is introduced that is damped at short range. The coefficient C6 is calculated either from average molecular or atomic polarizabilities. We calculate geometry-dependent interaction energy profiles for the water benzene cluster and compare the results with second-order Møller-Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.
Density differences for near-Hartree-Fock atomic wave functions
NASA Astrophysics Data System (ADS)
Schmider, Hartmut; Sagar, Robin P.; Smith, Vedene H., Jr.
1994-05-01
The widely used near-Hartree-Fock functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer functions of Bunge et al. [At. Data Nucl. Tables 53, 113 (1993)] by means of different measures of functional distance on the charge density ρ for the atoms He to Xe. The results are correlated with the energy improvement, and an empriical relation between the linear deviation in the first derivative of ρ and the total energy is reported.
Perspective: Fundamental aspects of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Numerical Density-to-Potential Inversions in Time-dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Jensen, Daniel; Inchaustegui, Jean Pierre; Wasserman, Adam
2014-03-01
Time-dependent Density Functional Theory (TDDFT) is a formally exact method for solving the quantum many-body problem. In Kohn-Sham TDDFT, a fictitious noninteracting system is defined that exactly reproduces the time-dependent density of the interacting system. The potential that determines this noninteracting system (the time-dependent Kohn-Sham potential) has been proven to exist under certain restrictions, but finding the exact Kohn-Sham potential for a given density remains challenging. We show that this ill-posed inverse problem requires some form of regularization to produce realistic Kohn-Sham potentials. We explore various forms of regularization and illustrate how they work on simple one-dimensional model systems. We also show how our method can be applied to problems with both particle-in-a-box and periodic boundary conditions subject to oscillating electric fields.
NASA Astrophysics Data System (ADS)
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Multiphase aluminum equations of state via density functional theory
NASA Astrophysics Data System (ADS)
Sjostrom, Travis; Crockett, Scott; Rudin, Sven
2016-10-01
We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.
Towards improved local hybrid functionals by calibration of exchange-energy densities
Arbuznikov, Alexei V. E-mail: martin.kaupp@tu-berlin.de; Kaupp, Martin E-mail: martin.kaupp@tu-berlin.de
2014-11-28
A new approach for the calibration of (semi-)local and exact exchange-energy densities in the context of local hybrid functionals is reported. The calibration functions are derived from only the electron density and its spatial derivatives, avoiding spatial derivatives of the exact-exchange energy density or other computationally unfavorable contributions. The calibration functions fulfill the seven more important out of nine known exact constraints. It is shown that calibration improves substantially the definition of a non-dynamical correlation energy term for generalized gradient approximation (GGA)-based local hybrids. Moreover, gauge artifacts in the potential-energy curves of noble-gas dimers may be corrected by calibration. The developed calibration functions are then evaluated for a large range of energy-related properties (atomization energies, reaction barriers, ionization potentials, electron affinities, and total atomic energies) of three sets of local hybrids, using a simple one-parameter local-mixing. The functionals are based on (a) local spin-density approximation (LSDA) or (b) Perdew-Burke-Ernzerhof (PBE) exchange and correlation, and on (c) Becke-88 (B88) exchange and Lee-Yang-Parr (LYP) correlation. While the uncalibrated GGA-based functionals usually provide very poor thermochemical data, calibration allows a dramatic improvement, accompanied by only a small deterioration of reaction barriers. In particular, an optimized BLYP-based local-hybrid functional has been found that is a substantial improvement over the underlying global hybrids, as well as over previously reported LSDA-based local hybrids. It is expected that the present calibration approach will pave the way towards new generations of more accurate hyper-GGA functionals based on a local mixing of exchange-energy densities.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-09
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
Differentiable but exact formulation of density-functional theory.
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M; Helgaker, Trygve
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Density-functional theory for polar fluids at functionalized surfaces. I. Fluid-wall association
NASA Astrophysics Data System (ADS)
Tripathi, Sandeep; Chapman, Walter G.
2003-12-01
We present a novel perturbation density-functional theory (DFT) to describe adsorption of associating fluids on surfaces activated with polar sites to which fluid molecules can bond or associate, such as water adsorbing on activated carbon, silica, clay minerals, etc. Association is modeled within the framework of first order thermodynamic perturbation theory (TPT1). In this first of two papers, we explore in detail the changes brought about in a system due to fluid-wall (FW) association. Hence fluid-fluid association is not considered here. However, the theory can be coupled with existing DF theories of associating fluids to study the interplay between the wall-fluid and fluid-fluid association as is shown in a future paper by S. Tripathi. The proposed theory, in excellent agreement with simulations, shows that FW association significantly changes the fluid structure and adsorption behavior. The theory accurately predicts the distribution of bonded and nonbonded species away from the surface, adsorption characteristics and surface coverage over a range of conditions commonly found in several real systems. The most striking feature of the theory is that in addition to properties away from the wall, it also estimates the distribution of the fluid along the surface, or the three-dimensional (3D) structure, despite being one-dimensional (1D) in form.
Density versus spin-density functional in DFT+U and DFT+DMFT
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew; Marianetti, Chris
2015-03-01
The construction of multi-variable effective action theories such as DFT+U and DFT+DMFT requires the choice of a local subspace of correlated orbitals and an additional variable being either the charge density or spin density. This talk examines the differences between using charge-only and spin-dependent exchange-correlation functionals with the aim of providing guidance for constructing more sophisticated beyond-density functional theories. The widely used spin-dependent approximations to the exchange-correlation functional are found to lead to a large and in some cases unphysical effective exchange coupling within the correlated subspace. Additionally, the differences between Wannier and Projector based definitions of the correlated orbitals are examined, and only small differences are found provided that the orbitals are orthonormal and strongly localized. These results are documented in the context of the rare earth nickelates. This work is supported under the Grant DOE-ER-046169 and under the FAME grant, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.
Functional responses: a question of alternative prey and predator density.
Tschanz, Britta; Bersier, Louis-Felix; Bacher, Sven
2007-05-01
Throughout the study of ecology, there has been a growing realization that indirect effects among species cause complexity in food webs. Understanding and predicting the behavior of ecosystems consequently depends on our ability to identify indirect effects and their mechanisms. The present study experimentally investigates indirect interactions arising between two prey species that share a common predator. In a natural field experiment, we introduced different densities of mealworms (Tenebrio molitor), an alternative prey, to a previously studied predator-prey system in which paper wasps (Polistes dominulus) preyed on shield beetle larvae (Cassida rubiginosa). We tested if alternative prey affects predation on the first prey (i.e., the predator-dependent functional response of paper wasps) by modifying either interference among predators or the effective number of predators foraging on shield beetles. Presence of mealworms significantly reduced the effective number of predators, whereas predator interference was not affected. In this way, the experimentally introduced alternative prey altered the wasps' functional response and thereby indirectly influenced C. rubiginosa density. In all prey-density combinations offered, paper wasps constantly preferred T. molitor. This led to an asymmetrical, indirect interaction between both prey species: an increase in mealworm density significantly relaxed predation on C. rubiginosa, whereas an increase in C. rubiginosa density intensified predation on mealworms. Such asymmetrical outcomes of a fixed food preference can significantly affect the population dynamics of the species involved. In spite of the repeated finding of a Type III functional response in this system, our experiment did not reveal switching behavior in paper wasps. The variety of mechanisms underlying direct and indirect interactions within our study system exemplifies the importance of incorporating alternative prey when investigating the impact of a
Predator density and the functional responses of coral reef fish
NASA Astrophysics Data System (ADS)
Stier, A. C.; White, J. W.
2014-03-01
Predation is a key process driving coral reef fish population dynamics, with higher per capita prey mortality rates on reefs with more predators. Reef predators often forage together, and at high densities, they may either cooperate or antagonize one another, thereby causing prey mortality rates to be substantially higher or lower than one would expect if predators did not interact. However, we have a limited mechanistic understanding of how prey mortality rates change with predator densities. We re-analyzed a previously published observational dataset to investigate how the foraging response of the coney grouper ( Cephalopholis fulva) feeding on the bluehead wrasse ( Thalassoma bifasciatum) changed with shifts in predator and prey densities. Using a model-selection approach, we found that per-predator feeding rates were most consistent with a functional response that declines as predator density increases, suggesting either antagonistic interactions among predators or a shared antipredator behavioral response by the prey. Our findings suggest that variation in predator density (natural or anthropogenic) may have substantial consequences for coral reef fish population dynamics.
Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions
Liu, Shuanglong; Nurbawono, Argo; Zhang, Chun
2015-01-01
We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case. PMID:26472080
Averkiev, Boris B; Zhao, Yan; Truhlar, Donald G
2010-06-01
The structures of Pd(PH₃)₂ and Pt(PH₃)₂ complexes with ethene and conjugated CnH_{n+2} systems (n=4, 6, 8, and 10) were studied. Their binding energies were calculated using both wave function theory (WFT) and density functional theory (DFT). Previously it was reported that the binding energy of the alkene to the transition metal does not depend strongly on the size of the conjugated C_{n}H_{n+2} ligand, but that DFT methods systematically underestimate the binding energy more and more significantly as the size of the conjugated system is increased. Our results show that recently developed density functionals predict the binding energy for these systems much more accurately. New benchmark calculations carried out by the coupled cluster method based on Brueckner orbitals with double excitations and a quasiperturbative treatment of connected triple excitations (BCCD(T)) with a very large basis set agree even better with the DFT predictions than do the previous best estimates. The mean unsigned error in absolute and relative binding energies of the alkene ligands to Pd(PH₃)₂ is 2.5 kcal/mol for the ωB97 and M06 density functionals and 2.9 kcal/mol for the M06-L functional. Adding molecular mechanical damped dispersion yields even smaller mean unsigned errors: 1.3 kcal/mol for the M06-D functional, 1.5 kcal/mol for M06- L-D, and 1.8 kcal/mol for B97-D and ωB97X-D. The new functionals also lead to improved accuracy for the analogous Pt complexes. These results show that recently developed density functionals may be very useful for studying catalytic systems involving Pd d¹º centers and alkenes.
What Density Functional Theory could do for Quantum Information
NASA Astrophysics Data System (ADS)
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Covariant density functional theory: The role of the pion
Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.
2009-10-15
We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the {sigma} meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
Association between lung function and airway wall density
NASA Astrophysics Data System (ADS)
Leader, J. Ken; Zheng, Bin; Fuhrman, Carl R.; Tedrow, John; Park, Sang C.; Tan, Jun; Pu, Jiantao; Drescher, John M.; Gur, David; Sciurba, Frank C.
2009-02-01
Computed tomography (CT) examination is often used to quantify the relation between lung function and airway remodeling in chronic obstructive pulmonary disease (COPD). In this preliminary study, we examined the association between lung function and airway wall computed attenuation ("density") in 200 COPD screening subjects. Percent predicted FVC (FVC%), percent predicted FEV1 (FEV1%), and the ratio of FEV1 to FVC as a percentage (FEV1/FVC%) were measured post-bronchodilator. The apical bronchus of the right upper lobe was manually selected from CT examinations for evaluation. Total airway area, lumen area, wall area, lumen perimeter and wall area as fraction of the total airway area were computed. Mean HU (meanHU) and maximum HU (maxHU) values were computed across pixels assigned membership in the wall and with a HU value greater than -550. The Pearson correlation coefficients (PCC) between FVC%, FEV1%, and FEV1/FVC% and meanHU were -0.221 (p = 0.002), -0.175 (p = 0.014), and -0.110 (p = 0.123), respectively. The PCCs for maxHU were only significant for FVC%. The correlations between lung function and the airway morphometry parameters were slightly stronger compared to airway wall density. MeanHU was significantly correlated with wall area (PCC = 0.720), airway area (0.498) and wall area percent (0.611). This preliminary work demonstrates that airway wall density is associated with lung function. Although the correlations in our study were weaker than a recent study, airway wall density initially appears to be an important parameter in quantitative CT analysis of COPD.
Autoionization in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Kapoor, V.
2016-06-01
We compute the exact exchange-correlation potential of the time-dependent density-functional theory (TDDFT) for the correlated process of autoionization. The potential develops barriers which regulate the autoionization rate. TDDFT employing known and practicable exchange-correlation potentials does not capture any autoionization dynamics. Approximate exchange-correlation potentials capturing such dynamics would necessarily require memory effects and are unlikely to be developed, as will be illustrated.
Excitons in Time-Dependent Density-Functional Theory.
Ullrich, Carsten A; Yang, Zeng-hui
2016-01-01
This chapter gives an overview of the description of the optical and dielectric properties of bulk insulators and semiconductors in time-dependent density-functional theory (TDDFT), with an emphasis on excitons. We review the linear-response formalism for periodic solids, discuss excitonic exchange-correlation kernels, calculate exciton binding energies for various materials, and compare the treatment of excitons with TDDFT and with the Bethe-Salpeter equation.
Density functional theory across chemistry, physics and biology.
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-03-13
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.
Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory.
Ess, Daniel H; Johnson, Erin R; Hu, Xiangqian; Yang, Weitao
2011-01-13
Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.
Singlet-Triplet Energy Gaps for Diradicals from Fractional-Spin Density-Functional Theory
Ess, Daniel H.; Johnson, E. R.; Hu, Xiangqian; Yang, W. T.
2010-12-09
Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S2 operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.
Density functional theory studies of core-shell semiconductor nanoparticle quantum dots
NASA Astrophysics Data System (ADS)
Walker, Brent; Hendy, Shaun; Tilley, Richard
2008-03-01
In going from the macroscale to the nanoscale, quantum-mechanical effects become increasingly important and may mean that nanostructures of a material exhibit very different properties from the corresponding bulk. This is especially noticeable in the case of the optical properties of semiconductor nanoparticles (or quantum dots), which display a number of remarkable features (including very distinct peaks, and tunability across a broad range of wavelengths), due to quantum confinement. Our work involves modeling Si-Ge core-shell nanoparticles using large-scale computer simulations based on the density functional and time-dependent density functional theories. These simulations in particular provide us with predictions of the geometric structures and optical absorption spectra of nanoparticles in an accurate and computationally efficient way, and allow us to study the systematic trends in these properties as the composition and size of the nanoparticle change.
Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter
NASA Astrophysics Data System (ADS)
Militzer, Burkhard; Driver, Kevin
2011-10-01
We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied, demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results.
Density functional wavelet calculation of solid state systems
NASA Astrophysics Data System (ADS)
Daykov, I. P.; Engeness, T. D.; Arias, T. A.
2001-03-01
We present, to our knowledge, the first all-electron wavelet calculations of the electronic structure of solids within density functional theory. To make these calculations competitive with traditional approaches, we employ recent developments in algorithms for multiresolution analysis (MRA) which speed density functional calculations by three to four orders of magnitude[1,2]. MRA provides a fully systematic, integrated treatment of core and valence electrons and is ideal for exploring the limits of the accuracy of density functional theory in the calculation of EELS spectra, which involve matrix elements between the core and valence states. We shall present results for EELS spectra as well as the resolution of technical issues which arise in carrying out solid-state calculations within a wavelet-like basis. [1] ``Multiscale computation with interpolating wavelets,'' by Ross A. Lippert, T.A. Arias and Alan Edelman, Journal of Computational Physics, 140:2, 278--310 (1 March 1998). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805283 . [2] ``Multiresolution analysis of electronic structure: semicardinal and wavelet bases,'' T.A. Arias, Reviews of Modern Physics 71:1, 267--311 (January 1999). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805262 .
Chemical reactivity in the framework of pair density functional theories.
Otero, Nicolás; Mandado, Marcos
2012-05-15
Chemical reactivity descriptors are derived within the framework of the pair density functional theory. These indices provide valuable information about bonding rearrangements and activating mechanisms upon electrophilic or nucleophilic reactions. Indices derived and tested in this work represent nonlocal counterparts of the local reactivity indices derived in the context of conceptual density functional theory (CDFT) and frequently used in reactivity studies; the Fukui function, the local softness and the dual descriptor. In this work, we show how these nonlocal indices provide a quantum chemical basis to explain the success of qualitative resonance models in chemical reactivity predictions. Also, local information is implicitly contained as CDFT indices are obtained by simple integration. As illustrative examples, we have considered in this work the Markovnikov's rule, the reactivity of enolate anion, the nucleophilic conjugate addition to α,β-unsaturated compounds and the electrophilic aromatic substitution of benzene derivatives. The densities used in this work were obtained with Hartree-Fock, Kohn-Sham DFT, and singles and doubles configuration interaction (CISD) approaches.
Surface regulated arsenenes as Dirac materials: From density functional calculations
NASA Astrophysics Data System (ADS)
Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu
2017-02-01
Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Density-Functional Theory Studies of Correlation Energy Effects at Metallic Surfaces.
NASA Astrophysics Data System (ADS)
Mohammed, Abdel-Raouf Eid
In this thesis we study the effects of correlation in the inhomogeneous electron gas at metallic surfaces. These studies are performed within the context of density-functional theory (DFT). Using accurate representations of the electronic density profile, we have estimated variationally the surface correlation energy of jellium metal. The accuracy of these estimates is founded in the assumption that the exchange -correlation energy functional of the density is approximated accurately by the wave-vector analysis method, and by the fact that the non-local exchange energy contributions are treated exactly. In contrast to the previously accepted conclusion that for surfaces correlation effects are as significant as exchange, our results indicate the ratio of these energies to lie between 34% - 97% over the metallic density range, the smaller ratios corresponding to the higher density metals. In this work we have also examined the local density (LDA) and gradient expansion approximations (GEA) (to O((DEL)('2))) for the correlation energy. We have demonstrated for realistic metal surface densities the cancellation of the errors in the LDA for exchange and correlation, and shown that the density profiles at surfaces would have to be unphysically slowly varying for the correlation energy GEA to converge. We have also studied the effects of correlation at surfaces by screening the exchange, and observe that the surface exchange energy for screened-Coulomb interaction decreases as the screening length is reduced. Thus, the more short-ranged the interaction, the easier it is to split the crystal in two. In addition we have derived the DFT first gradient correction coefficient in the GEA for the screened-Coulomb exchange energy, and shown it to be the same as that obtained within Hartree -Fock theory (HFT) for finite screening. This coefficient reduces to the DFT bare-Coulomb interaction value in the limit of no screening in which limit the HFT coefficient is singular. The GEA
Mardirossian, Narbe; Head-Gordon, Martin
2015-02-21
A meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional is presented. The functional form is selected from more than 10{sup 10} choices carved out of a functional space of almost 10{sup 40} possibilities. Raw data come from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filtered based on a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.
Density functional theory and chromium: Insights from the dimers
Würdemann, Rolf; Kristoffersen, Henrik H.; Moseler, Michael; Walter, Michael
2015-03-28
The binding in small Cr clusters is re-investigated, where the correct description of the dimer in three charge states is used as criterion to assign the most suitable density functional theory approximation. The difficulty in chromium arises from the subtle interplay between energy gain from hybridization and energetic cost due to exchange between s and d based molecular orbitals. Variations in published bond lengths and binding energies are shown to arise from insufficient numerical representation of electron density and Kohn-Sham wave-functions. The best functional performance is found for gradient corrected (GGA) functionals and meta-GGAs, where we find severe differences between functionals from the same family due to the importance of exchange. Only the “best fit” from Bayesian error estimation is able to predict the correct energetics for all three charge states unambiguously. With this knowledge, we predict small bond-lengths to be exclusively present in Cr{sub 2} and Cr{sub 2}{sup −}. Already for the dimer cation, solely long bond-lengths appear, similar to what is found in the trimer and in chromium bulk.
Franco-Pérez, Marco; Ayers, Paul W; Gázquez, José L; Vela, Alberto
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Franco-Pérez, Marco E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Ayers, Paul W. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Gázquez, José L. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Vela, Alberto E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Current density partitioning in time-dependent current density functional theory
Mosquera, Martín A.; Wasserman, Adam
2014-05-14
We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.
Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration.
Soniat, Marielle; Rogers, David M; Rempe, Susan B
2015-07-14
A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.
Differentiable but exact formulation of density-functional theory
Kvaal, Simen Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M.
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.
Differentiable but exact formulation of density-functional theory
NASA Astrophysics Data System (ADS)
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M.; Helgaker, Trygve
2014-05-01
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ɛ > 0, pairs of conjugate functionals (ɛE, ɛF) that converge to (E, F) pointwise everywhere as ɛ → 0+, and such that ɛF is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy ɛE(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for (ɛE, ɛF). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of ɛF, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Generation of time histories with a specified auto spectral density and probability density function
Smallwood, D.O.
1996-08-01
It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.
NASA Astrophysics Data System (ADS)
Ghasemi, S. Alireza; Hofstetter, Albert; Saha, Santanu; Goedecker, Stefan
2015-07-01
Based on an analysis of the short-range chemical environment of each atom in a system, standard machine-learning-based approaches to the construction of interatomic potentials aim at determining directly the central quantity, which is the total energy. This prevents, for instance, an accurate description of the energetics of systems in which long-range charge transfer or ionization is important. We propose therefore not to target directly with machine-learning methods the total energy but an intermediate physical quantity, namely, the charge density, which then in turn allows us to determine the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chemical accuracy, i.e., errors of less than a millihartree per atom compared to the reference density functional results for a huge data set of configurations with large structural variety. The introduction of physically motivated quantities which are determined by the short-range atomic environment via a neural network also leads to an increased stability of the machine-learning process and transferability of the potential.
Density-functional theory of interacting electrons in inhomogeneous quantum wires
NASA Astrophysics Data System (ADS)
Abedinpour, Saeed H.; Polini, Marco; Xianlong, Gao; Tosi, Mario P.
2007-03-01
Motivated by the experimental evidence of electron localization in cleaved edge overgrowth quantum wires and by the recent interest in the development of density-functional schemes for inhomogeneous Luttinger and Luther-Emery liquids, we present a novel density-functional study of a few interacting electrons confined by power-law external potentials into a short portion of a thin quantum wire. The theory employs the quasi-one-dimensional (Q1D) homogeneous electron liquid as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous system through a suitable local-density approximation (LDA) to the exchange and correlation energy functional. The LDA describes accurately ``liquid-like'' phases at weak coupling but fails in describing the emergence of ``Wigner molecules'' at strong coupling. A local spin-density approximation allowing for the formation of antiferromagnetic quasi-order with increasing coupling strength is proposed as a first step to overcome this problem.
Downlink Probability Density Functions for EOS-McMurdo Sound
NASA Technical Reports Server (NTRS)
Christopher, P.; Jackson, A. H.
1996-01-01
The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Density-dependence of functional spiking networks in vitro
Ham, Michael I; Gintautuas, Vadas; Rodriguez, Marko A; Bettencourt, Luis M A; Bennett, Ryan; Santa Maria, Cara L
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Density functional calculation of transition metal adatom adsorption on graphene.
Mao, Yuliang; Yuan, Jianmei; Zhong, Jianxin
2008-03-19
The functionalization of graphene (a single graphite layer) by the addition of transition metal atoms of Mn, Fe and Co to its surface has been investigated computationally using density functional theory. In the calculation, the graphene surface supercell was constructed from a single layer of graphite (0001) surface separated by vertical vacuum layers 2 nm thick. We found that the center of the hexagonal ring formed by carbon from graphene is the most stable site for Mn, Fe, Co to stay after optimization. The calculated spin-polarized band structures of the graphene encapsulating the Mn adatom indicate that the conduction bands are modified and move down due to the coupling between the Mn atom and graphene. For Fe adsorbed on the graphene surface, it is semi-half-metallic, and the spin polarization P is found to be 100%. The system of Co adatom on graphene exhibits metallic electronic structure due to the density of states (DOS) peak at the band center with both majority and minority spins. Local density of states analyses indicate a larger promotion of 4s electrons into the 3d state in Fe and Co, resulting in lower local moments compared to an Mn adatom on the graphite surface.
Stochastic Time-Dependent Current-Density Functional Theory
NASA Astrophysics Data System (ADS)
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Time-dependent density-functional description of nuclear dynamics
NASA Astrophysics Data System (ADS)
Nakatsukasa, Takashi; Matsuyanagi, Kenichi; Matsuo, Masayuki; Yabana, Kazuhiro
2016-10-01
The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in the description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.
Massively parallel density functional calculations for thousands of atoms: KKRnano
NASA Astrophysics Data System (ADS)
Thiess, A.; Zeller, R.; Bolten, M.; Dederichs, P. H.; Blügel, S.
2012-06-01
Applications of existing precise electronic-structure methods based on density functional theory are typically limited to the treatment of about 1000 inequivalent atoms, which leaves unresolved many open questions in material science, e.g., on complex defects, interfaces, dislocations, and nanostructures. KKRnano is a new massively parallel linear scaling all-electron density functional algorithm in the framework of the Korringa-Kohn-Rostoker (KKR) Green's-function method. We conceptualized, developed, and optimized KKRnano for large-scale applications of many thousands of atoms without compromising on the precision of a full-potential all-electron method, i.e., it is a method without any shape approximation of the charge density or potential. A key element of the new method is the iterative solution of the sparse linear Dyson equation, which we parallelized atom by atom, across energy points in the complex plane and for each spin degree of freedom using the message passing interface standard, followed by a lower-level OpenMP parallelization. This hybrid four-level parallelization allows for an efficient use of up to 100000 processors on the latest generation of supercomputers. The iterative solution of the Dyson equation is significantly accelerated, employing preconditioning techniques making use of coarse-graining principles expressed in a block-circulant preconditioner. In this paper, we will describe the important elements of this new algorithm, focusing on the parallelization and preconditioning and showing scaling results for NiPd alloys up to 8192 atoms and 65536 processors. At the end, we present an order-N algorithm for large-scale simulations of metallic systems, making use of the nearsighted principle of the KKR Green's-function approach by introducing a truncation of the electron scattering to a local cluster of atoms, the size of which is determined by the requested accuracy. By exploiting this algorithm, we show linear scaling calculations of more
Empirical relaxation function and spectral density for underdamped vibrations at low temperatures
NASA Astrophysics Data System (ADS)
Toutounji, Mohamad
2009-03-01
A new relaxation function which accounts for electronic dephasing (electronic phase loss and excited state lifetime) is presented, whose applicability for underdamped motion at low temperatures is examined in detail. This new empirical relaxation function φ(t ) yields linear and nonlinear spectral/temporal profiles that render accurate dephasing time in the underdamped regime. The relaxation function φ(t ) is normally expressed in terms of the coupling functions Mj' and Mj″ on which the time evolution of the vibrational modes in question depends. The corresponding spectral density, which is a central quantity in probing dynamics, is derived and compared to that of the multimode Brownian oscillator model. Derivation and discussion of the new position and momentum autocorrelation functions in terms of our new spectral density are presented. While the position autocorrelation function plays a key role in representing solvation structure in polar or nonpolar medium, the momentum correlation function projects out the molecular vibrational motion. The Liouville space generating function (LGF) for harmonic and anharmonic systems is expressed in terms of our new empirical φ(t ) and spectral density, leading to more physical observation. Several statistical quantities are derived from the position and momentum correlation function, which in turn contribute to LGF. Model calculations reflecting the infinite population decay in the low temperature limit in linear and nonlinear spectroscopic signals are presented. The herein quantum dipole moment correlation function is compared to that derived in [M. Toutounji, J. Chem. Phys. 118, 5319 (2003)] using mixed quantum-classical dynamics framework, yielding reasonable results, in fact identical at higher temperatures. The results herein are found to be informative, useful, and consistent with experiments.
Nonlocal van der Waals density functional made simple and efficient
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Gorni, Tommaso; de Gironcoli, Stefano
2013-01-01
We present a simple revision of the VV10 nonlocal density functional by Vydrov and Van Voorhis [J. Chem. Phys.JCPSA60021-960610.1063/1.3521275 133, 244103 (2010)] for dispersion interactions. Unlike the original functional our modification allows nonlocal correlation energy and its derivatives to be efficiently evaluated in a plane wave framework along the lines pioneered by Román-Pérez and Soler [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.096102 103, 096102 (2009)]. Our revised functional maintains the outstanding precision of the original VV10 in noncovalently bound complexes and performs well in representative covalent, ionic, and metallic solids.
Applications of large-scale density functional theory in biology
NASA Astrophysics Data System (ADS)
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Self-consistent van der Waals density functional study of benzene adsorption on Si(100)
NASA Astrophysics Data System (ADS)
Hamamoto, Yuji; Hamada, Ikutaro; Inagaki, Kouji; Morikawa, Yoshitada
2016-06-01
The adsorption of benzene on the Si(100) surface is studied theoretically using the self-consistent van der Waals density functional (vdW-DF) method. The adsorption energies of two competing adsorption structures, butterfly (BF) and tight-bridge (TB) structures, are calculated with several vdW-DFs at saturation coverage. Our results show that recently proposed vdW-DFs with high accuracy all prefer TB to BF, in accord with more accurate calculations based on exact exchange and correlation within the random-phase approximation. Detailed analyses reveal the important roles played by the molecule-surface interaction and molecular deformation upon adsorption, and we suggest that their precise description is a prerequisite for accurate prediction of the most stable adsorption structure of organic molecules on semiconductor surfaces.
Structural evolution of amino acid crystals under stress from a non-empirical density functional
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Küçükbenli, Emine; Kolb, Brian; Thonhauser, T.; de Gironcoli, Stefano
2012-10-01
Use of the non-local correlation functional vdW-DF (from ‘van der Waals density functional’ Dion M et al 2004 Phys. Rev. Lett. 92 246401) has become a popular approach for including van der Waals interactions within density functional theory. In this work, we extend the vdW-DF theory and derive the corresponding stress tensor in a fashion similar to the LDA and GGA approach, which allows for a straightforward implementation in any electronic structure code. We then apply our methodology to investigate the structural evolution of amino acid crystals of glycine and l-alanine under pressure up to 10 GPa—with and without van der Waals interactions—and find that for an accurate description of intermolecular interactions and phase transitions in these systems, the inclusion of van der Waals interactions is crucial. For glycine, calculations including the vdW-DF (vdW-DF-c09x) functional are found to systematically overestimate (underestimate) the crystal lattice parameters, yet the stability ordering of the different polymorphs is determined accurately, at variance with the GGA case. In the case of l-alanine, our vdW-DF results agree with recent experiments that question the phase transition reported for this crystal at 2.3 GPa, as the a and c cell parameters happen to become equal but no phase transition is observed.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Nuclear chiral and magnetic rotation in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Zhao, Pengwei
2016-05-01
Excitations of chiral rotation observed in triaxial nuclei and magnetic and/or antimagnetic rotations (AMR) seen in near-spherical nuclei have attracted a lot of attention. Unlike conventional rotation in well-deformed or superdeformed nuclei, here the rotational axis is not necessary coinciding with any principal axis of the nuclear density distribution. Thus, tilted axis cranking (TAC) is mandatory to describe these excitations self-consistently in the framework of covariant density functional theory (CDFT). We will briefly introduce the formalism of TAC-CDFT and its application for magnetic and AMR phenomena. Configuration-fixed CDFT and its predictions for nuclear chiral configurations and for favorable triaxial deformation parameters are also presented, and the discoveries of the multiple chiral doublets in 133Ce and 103Rh are discussed.
De Laender, Frederik; Taub, Frieda B; Janssen, Colin R
2011-12-01
Understanding whether and to what extent ecosystem functions respond to chemicals is a major challenge in environmental toxicology. The available data gathered by ecosystem-level experiments (micro- and mesocosms) often describe the responses of taxa densities to stress. However, whether these responses are proportional to the responses of associated ecosystem functions to stress is unclear. By combining a carbon budget modeling technique with data from a standardized microcosm experiment with a known community composition, we quantified three ecosystem functions (net primary production [NPP], net mesozooplankton production [NZP], and net bacterial production [NBP]) at three Cu concentrations, with a control. Changes of these ecosystem functions with increasing chemical concentrations were not always proportional to the Cu effects on the densities of the contributing functional groups. For example, Cu treatments decreased mesozooplankton density by 100-fold and increased phytoplankton density 10- to 100-fold while increasing NZP and leaving NPP unaltered. However, in contrast, Cu affected microzooplankton and the associated function (NBP) in a comparable way. We illustrate that differences in the response of phytoplankton/mesozooplankton densities and the associated ecosystem functions to stress occur because functional rates (e.g., photosynthesis rates/ingestion rates) vary among Cu treatments and in time. These variations could be explained by food web ecology but not by direct Cu effects, indicating that ecology may be a useful basis for understanding environmental effects of stressors.
Characterizing the Spatial Density Functions of Neural Arbors
NASA Astrophysics Data System (ADS)
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
Joint density-functional theory and its application to systems in solution
NASA Astrophysics Data System (ADS)
Petrosyan, Sahak A.
The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of density functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint density functional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical density functional fail when applied directly to water. The thesis then presents a computationally efficient density-functional
Nonlocal density functionals and the linear response of the homogeneous electron gas
NASA Astrophysics Data System (ADS)
Mazin, I. I.; Singh, D. J.
1998-03-01
The known and usable truly nonlocal functionals for exchange-correlation energy of the inhomogeneous electron gas are the ADA (average density approximation) and the WDA (weighted density approximation). ADA, by design, yields the correct linear response function of the uniform electron gas. The WDA is constructed so that it is exact in the opposite limit of one-electron systems, and it was conjectured that the WDA is also accurate in the uniform gas limit. To test this conjecture, we derive an expression for the linear response of the uniform gas in the WDA, and calculate it for several flavors of the WDA. We then compare the results with the Monte Carlo data on the exchange-correlation local-field correction, and identify the weak points of conventional WDA in the homogeneous limit. We suggest how the WDA can be modified to improve the response function. The resulting approximation is a good one in both opposite limits. Future testing should show whether it will also be better than conventional WDA and ADA for practical nonlocal density-functional calculations.
Graphene oxide and adsorption of chloroform: A density functional study
NASA Astrophysics Data System (ADS)
Kuisma, Elena; Hansson, C. Fredrik; Lindberg, Th. Benjamin; Gillberg, Christoffer A.; Idh, Sebastian; Schröder, Elsebeth
2016-05-01
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, and are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances are important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory, and the recently developed consistent-exchange functional for the van der Waals density-functional method is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likely oxidize, and thus adsorption onto graphene oxide, rather than clean graphene, is a more relevant process to study.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Electron response in van der Waals density functionals
NASA Astrophysics Data System (ADS)
Hyldgaard, Per
2013-03-01
There is significant interest in density functional theory (DFT) of dispersive or van der Waals (vdW) interactions and in DFT studies of sparse systems where vdW forces contribute to the cohesion and behavior. The Rutgers-Chalmers van der Waals density functional (vdW-DF) method [PRL 92, 246401 (2004); PRB 76, 125112 (2007)] is a nonempirical approach to calculate vdW bonding and for DFT characterizations of sparse matter. The vdW-DF framework is defined by a single exchange-correlation density functional that rests on a plasmon-type description for both semilocal components and for a parameter-free evaluation of nonlocal correlation. My talk summarizes a set of vdW-DF studies that seeks to map and analyze details in the vdW-DF electron-response nature. The purpose is in part to extract consequences that can facilitate an experiment-theory comparison that goes beyond binding geometries and energies. The aim is also to seek implications that can help develop the vdW-DF framework. I present an analysis of the relative importance of morphology, screening (image-plane formation), and collective effects in the vdW-DF description of molecular systems. In addition, I compare vdW-DF results with Cu(111) experiments that tests the electron-response behavior in terms of adsorption-induced band shifts, the form of the overall light-molecule physisorption potential, and the corrugation in the kinetic-energy repulsion of molecules at surfaces. Overall, the vdW-DF studies suggest the importance of benchmarking vdW methods across different length scales and by exploring the variation that arise when related structures have a different balance between exchange repulsion and vdW attraction.
García de la Vega, J M; Omar, S; San Fabián, J
2017-04-01
Spin-spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob's ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict (1) J O H , (2) J H H and (2h) J O O couplings, while (1h) J O H is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for (1) J O H and (2) J H H have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods. Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.
Quantification of Uncertainties in Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
Schunck, N.; McDonnell, J. D.; Higdon, D.; Sarich, J.; Wild, S.
2015-01-01
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Density Functional Study of the structural properties in Tamoxifen
NASA Astrophysics Data System (ADS)
de Coss-Martinez, Romeo; Tapia, Jorge A.; Quijano-Quiñones, Ramiro F.; Canto, Gabriel I.
2013-03-01
Using the density functional theory, we have studied the structural properties of Tamoxifen. The calculations were performed with two methodological approaches, which were implemented in SIESTA and Spartan codes. For SIESTA, we considerate a linear combination of atomic orbitals method, using pseudopotentials and the van der Waals approximation for the exchange-correlation potential. Here we analyzed and compared the atomic structure between our results and other theoretical study. We found differences in the bond lengths between the results, that could be attributed to code approaches in each one. This work was supported under Grant FOMIX 2011-09 N: 170297 of Ph.D. A. Tapia.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-03-01
Sodium azide is intriguing because it could potentially be used as a precursor to a high-nitrogen energetic material. Furthermore, recent absorption and Raman spectroscopic results have shown that novel nitrogen structures may indeed be attainable from sodium azide. First-principles density functional theory calculations were performed to characterize possible novel crystalline structures of sodium azide including their atomic structure, vibrational properties, Raman spectra, and equation of state up to 90 GPa. Calculated Raman peaks and intensities show good agreement with experiment.
Classical density functional study of wetting transitions on nanopatterned surfaces
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Parry, A. O.; Rascón, C.; Kalliadasis, S.
2017-03-01
Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.
Relativistic Energy Density Functionals: Exotic modes of excitation
Vretenar, D.; Paar, N.; Marketin, T.
2008-11-11
The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of {beta}-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.
Determining Ionospheric Irregularity Spectral Density Function from Japan GEONET
NASA Astrophysics Data System (ADS)
Lay, E. H.; Light, M. E.; Parker, P. A.; Carrano, C. S.; Haaser, R. A.
2015-12-01
Japan's GEONET GPS network is the densest GPS monitoring network in the world, with 1200+ receivers over the area of Japan. Measuring and calibrating the integrated total electron content (TEC) from each station has been done in many cases to provide detailed maps of ionospheric disturbances over Japan. We use TEC measurements from Japan's GEONET array to determine an empirically derived description of the 2-dimensional scale sizes of spatial irregularities above Japan. The contributions from various scale sizes will be included in a statistical description for the irregularity spectral density (ISD) function. We will compare the statistics of the spatial irregularities between calm and moderately scintillated conditions.
Augmented Lagrangian method for constrained nuclear density functional theory
NASA Astrophysics Data System (ADS)
Staszczak, A.; Stoitsov, M.; Baran, A.; Nazarewicz, W.
2010-10-01
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multi-dimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves the accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.
Dynamical density functional theory with hydrodynamic interactions in confined geometries
NASA Astrophysics Data System (ADS)
Goddard, B. D.; Nold, A.; Kalliadasis, S.
2016-12-01
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Probability Density Function at the 3D Anderson Transition
NASA Astrophysics Data System (ADS)
Rodriguez, Alberto; Vasquez, Louella J.; Roemer, Rudolf
2009-03-01
The probability density function (PDF) for the wavefunction amplitudes is studied at the metal-insulator transition of the 3D Anderson model, for very large systems up to L^3=240^3. The implications of the multifractal nature of the state upon the PDF are presented in detail. A formal expression between the PDF and the singularity spectrum f(α) is given. The PDF can be easily used to carry out a numerical multifractal analysis and it appears as a valid alternative to the more usual approach based on the scaling law of the general inverse participation rations.
Atomic volumes and polarizabilities in density-functional theory.
Kannemann, Felix O; Becke, Axel D
2012-01-21
Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.
Nuclear clustering in the energy density functional approach
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Gillespie, Dirk; Khair, Aditya S; Bardhan, Jaydeep P; Pennathur, Sumita
2011-07-15
The electrokinetic behavior of nanofluidic devices is dominated by the electrical double layers at the device walls. Therefore, accurate, predictive models of double layers are essential for device design and optimization. In this paper, we demonstrate that density functional theory (DFT) of electrolytes is an accurate and computationally efficient method for computing finite ion size effects and the resulting ion-ion correlations that are neglected in classical double layer theories such as Poisson-Boltzmann. Because DFT is derived from liquid-theory thermodynamic principles, it is ideal for nanofluidic systems with small spatial dimensions, high surface charge densities, high ion concentrations, and/or large ions. Ion-ion correlations are expected to be important in these regimes, leading to nonlinear phenomena such as charge inversion, wherein more counterions adsorb at the wall than is necessary to neutralize its surface charge, leading to a second layer of co-ions. We show that DFT, unlike other theories that do not include ion-ion correlations, can predict charge inversion and other nonlinear phenomena that lead to qualitatively different current densities and ion velocities for both pressure-driven and electro-osmotic flows. We therefore propose that DFT can be a valuable modeling and design tool for nanofluidic devices as they become smaller and more highly charged.
Ramanan, Narayanan; Lee, Bongmook; Misra, Veena
2015-06-15
Many dielectrics have been proposed for the gate stack or passivation of AlGaN/GaN based metal oxide semiconductor heterojunction field effect transistors, to reduce gate leakage and current collapse, both for power and RF applications. Atomic Layer Deposition (ALD) is preferred for dielectric deposition as it provides uniform, conformal, and high quality films with precise monolayer control of film thickness. Identification of the optimum ALD dielectric for the gate stack or passivation requires a critical investigation of traps created at the dielectric/AlGaN interface. In this work, a pulsed-IV traps characterization method has been used for accurate characterization of interface traps with a variety of ALD dielectrics. High-k dielectrics (HfO{sub 2}, HfAlO, and Al{sub 2}O{sub 3}) are found to host a high density of interface traps with AlGaN. In contrast, ALD SiO{sub 2} shows the lowest interface trap density (<2 × 10{sup 12 }cm{sup −2}) after annealing above 600 °C in N{sub 2} for 60 s. The trend in observed trap densities is subsequently explained with bonding constraint theory, which predicts a high density of interface traps due to a higher coordination state and bond strain in high-k dielectrics.
Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities
Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz
2005-03-01
Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP.
NASA Astrophysics Data System (ADS)
Ullrich, C. A.; Vignale, G.
2002-05-01
Time-dependent density-functional theory (TDFT) provides a way of calculating, in principle exactly, the linear response of interacting many-electron systems, and thus allows one to obtain their excitation energies. For extended systems, there exist excitations of a collective nature, such as bulk and surface plasmons in metals or intersubband plasmons in doped semiconductor quantum wells. This paper develops a quantitatively accurate first-principles description for the frequency and the linewidth of such excitations in inhomogeneous weakly disordered systems. A finite linewidth in general has intrinsic and extrinsic sources. At low temperatures and outside the region where electron-phonon interaction occurs, the only intrinsic damping mechanism is provided by electron-electron interaction. This kind of intrinsic damping can be described within TDFT, but one needs to go beyond the adiabatic approximation and include retardation effects. It has been shown [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)] that a density-functional response theory that is local in space but nonlocal in time has to be constructed in terms of the currents, rather than the density. This theory will be reviewed in the first part of this paper. For quantitatively accurate linewidths, extrinsic dissipation mechanisms, such as impurities or disorder, have to be included in the response theory. In the second part of this paper, we discuss how extrinsic dissipation can be described within the so-called memory-function formalism. This formalism will first be introduced and reviewed for homogeneous systems. We will then present a synthesis of TDFT with the memory function formalism for inhomogeneous systems, which allows one to simultaneously account for intrinsic and extrinsic damping of collective excitations. As an example where both sources of dissipation are important and where high-quality experimental data are available for comparison, we discuss intersubband
NASA Astrophysics Data System (ADS)
Wu, Su-Yong; Long, Xing-Wu; Yang, Kai-Yong
2009-09-01
To improve the current status of home multilayer optical coating design with low speed and poor efficiency when a large layer number occurs, the accurate calculation and fast realization of merit function’s gradient and Hesse matrix is pointed out. Based on the matrix method to calculate the spectral properties of multilayer optical coating, an analytic model is established theoretically. And the corresponding accurate and fast computation is successfully achieved by programming with Matlab. Theoretical and simulated results indicate that this model is mathematically strict and accurate, and its maximal precision can reach floating-point operations in the computer, with short time and fast speed. Thus it is very suitable to improve the optimal search speed and efficiency of local optimization methods based on the derivatives of merit function. It has outstanding performance in multilayer optical coating design with a large layer number.
Lithium adsorption on graphite from density functional theory calculations.
Valencia, Felipe; Romero, Aldo H; Ancilotto, Francesco; Silvestrelli, Pier Luigi
2006-08-03
The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.
Adsorption of large hydrocarbons on coinage metals: a van der Waals density functional study.
Björk, Jonas; Stafström, Sven
2014-09-15
The adsorption of organic molecules onto the close-packed facets of coinage metals is studied, and how accurately adsorption heights can be described by using recent advances of the van der Waals density functional (vdWDF), with optPBE/vdWDF, optB86b/vdWDF, vdWDF2, and rev/vdWDF2 functionals is illustrated. The adsorption of two prototypical aromatic hydrocarbons is investigated, and the calculated adsorption heights are compared to experimental literature values from normal incident X-ray standing wave absorption and a state-of-the-art semi-empirical method. It is shown that both the optB86b/vdWDF and rev/vdWDF2 functionals describe adsorption heights with an accuracy of 0.1 Å, compared to experimental values, and are concluded as reliable methods of choice for related systems.
Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Pellegrini, Camilla; Flick, Johannes; Tokatly, Ilya V.; Appel, Heiko; Rubio, Angel
2015-08-01
We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications.
Linear-scaling density functional theory using the projector augmented wave method
NASA Astrophysics Data System (ADS)
Hine, Nicholas D. M.
2017-01-01
Quantum mechanical simulation of realistic models of nanostructured systems, such as nanocrystals and crystalline interfaces, demands computational methods combining high-accuracy with low-order scaling with system size. Blöchl’s projector augmented wave (PAW) approach enables all-electron (AE) calculations with the efficiency and systematic accuracy of plane-wave pseudopotential calculations. Meanwhile, linear-scaling (LS) approaches to density functional theory (DFT) allow for simulation of thousands of atoms in feasible computational effort. This article describes an adaptation of PAW for use in the LS-DFT framework provided by the ONETEP LS-DFT package. ONETEP uses optimisation of the density matrix through in situ-optimised local orbitals rather than the direct calculation of eigenstates as in traditional PAW approaches. The method is shown to be comparably accurate to both PAW and AE approaches and to exhibit improved convergence properties compared to norm-conserving pseudopotential methods.
NASA Astrophysics Data System (ADS)
Gao, Mingliang; Teng, Qizhi; He, Xiaohai; Zuo, Chen; Li, ZhengJi
2016-01-01
Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed
Gao, Mingliang; Teng, Qizhi; He, Xiaohai; Zuo, Chen; Li, ZhengJi
2016-01-01
Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed
On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies.
Jacquemin, Denis; Perpète, Eric A; Ciofini, Ilaria; Adamo, Carlo; Valero, Rosendo; Zhao, Yan; Truhlar, Donald G
2010-07-13
We assessed the accuracy of the four members of the M06 family of functionals (M06-L, M06, M06-2X, and M06-HF) for the prediction of electronic excitation energies of main-group compounds by time-dependent density functional theory. This is accomplished by comparing the predictions both to high-level theoretical benchmark calculations and some experimental data for gas-phase excitation energies of small molecules and to experimental data for midsize and large chromogens in liquid-phase solutions. The latter comparisons are carried out using implicit solvation models to include the electrostatic effects of solvation. We find that M06-L is one of the most accurate local functionals for evaluating electronic excitation energies, that M06-2X outperforms BHHLYP, and that M06-HF outperforms HF, although in each case, the compared functionals have the same or a similar amount of Hartree-Fock exchange. For the majority of investigated excited states, M06 emerges as the most accurate functional among the four tested, and it provides an accuracy similar to the best of the other global hybrids such as B3LYP, B98, and PBE0. For 190 valence excited states, 20 Rydberg states, and 16 charge transfer states, we try to provide an overall assessment by comparing the quality of the predictions to those of time-dependent Hartree-Fock theory and nine other density functionals. For the valence excited states, M06 yields a mean absolute deviation (MAD) of 0.23 eV, whereas B3LYP, B98, and PBE0 have MADs in the range 0.19-0.22 eV. Of the functionals tested, M05-2X, M06-2X, and BMK are found to perform best for Rydberg states, and M06-HF performs best for charge transfer states, but no single functional performs satisfactorily for all three kinds of excitation. The performance of functionals with no Hartree-Fock exchange is of great practical interest because of their high computational efficiency, and we find that M06-L predicts more accurate excitation energies than other such functionals.
Ab initio molecular dynamics using hybrid density functionals.
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; VandeVondele, Joost
2008-06-07
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.
Ab initio molecular dynamics using hybrid density functionals
NASA Astrophysics Data System (ADS)
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; Vandevondele, Joost
2008-06-01
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.
NASA Astrophysics Data System (ADS)
Jones, Jasmine; Zhang, Rui; Heins, David; Castle, Katherine
In postmastectomy radiotherapy, an increasing number of patients have tissue expanders inserted subpectorally when receiving immediate breast reconstruction. These tissue expanders are composed of silicone and are inflated with saline through an internal metallic port; this serves the purpose of stretching the muscle and skin tissue over time, in order to house a permanent implant. The issue with administering radiation therapy in the presence of a tissue expander is that the port's magnetic core can potentially perturb the dose delivered to the Planning Target Volume, causing significant artifacts in CT images. Several studies have explored this problem, and suggest that density corrections must be accounted for in treatment planning. However, very few studies accurately calibrated commercial TP systems for the high density material used in the port, and no studies employed fusion imaging to yield a more accurate contour of the port in treatment planning. We compared depth dose values in the water phantom between measurement and TPS calculations, and we were able to overcome some of the inhomogeneities presented by the image artifact by fusing the KVCT and MVCT images of the tissue expander together, resulting in a more precise comparison of dose calculations at discrete locations. We expect this method to be pivotal in the quantification of dose distribution in the PTV. Research funded by the LS-AMP Award.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Schunck, N; McDonnell, J D; Higdon, D; Sarich, J; Wild, S M
2015-03-17
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.
BUILDING A UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL (UNEDF)
Nazarewicz, Witold
2012-07-01
The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties. Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data. Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Nuclear charge radii: density functional theory meets Bayesian neural networks
NASA Astrophysics Data System (ADS)
Utama, R.; Chen, Wei-Chia; Piekarewicz, J.
2016-11-01
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.
Direct Neutron Capture Calculations with Covariant Density Functional Theory Inputs
NASA Astrophysics Data System (ADS)
Zhang, Shi-Sheng; Peng, Jin-Peng; Smith, Michael S.; Arbanas, Goran; Kozub, Ray L.
2014-09-01
Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Supported by the U.S. Dept. of Energy, Office of Nuclear Physics.
Fluids Density Functional Theory of Diblock Copolymers for Electrolyte Applications
NASA Astrophysics Data System (ADS)
Brown, Jonathan R.; Hall, Lisa M.
We use classical, fluids density functional theory (fDFT) to study microphase separation in block copolymer systems. We are motivated by systems used as battery electrolytes or in other transport applications, in which the two blocks of the system have different mechanical, dielectric, and transport properties that allow one phase to act as a charge/penetrant carrier and the other to make the film mechanically strong. We find density profiles of penetrants, showing to what degree they segregate into the A phase and their concentration near the interface, depending on the penetrant-A and penetrant-B interaction strengths as well as the A-B segregation strength. We also study the effect of tapering, or adding a gradient region (taper) between the pure A and B blocks of an AB diblock copolymer; the taper changes in composition along its length from pure A to pure B (or from B to A for an inverse taper). The effect of both penetrants and tapering on microphase domain spacing as a function of segregation strength will be discussed. Adjusting taper length allows one to tune the phase behavior of the system for easier processing or access to specific desired microphase structures. Based upon work supported by NSF Grant 1454343 and DOE Grant SC0014209.
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.
2007-06-01
Atomistic simulations employing Density Functional Theory (DFT) have recently emerged as a powerful way of increasing our understanding of materials and processes in high energy density physics. Knowledge of the properties of water (equation of state, electrical conductivity, diffusion, low-energy opacity) is essential for correctly describing the physics of giant planets as well as shock waves in water. Although a qualitative picture of water electrical conductivity has emerged, the necessary quantitative information is scarce over a wide range of temperature and density. Since experiments can only access certain areas of phase space, and often require modeling as a part of the analysis, Quantum Molecular Dynamics simulations play a vital role. Using finite-temperature density functional theory (FT-DFT), we have investigated the structure and electronic conductivity of water across three phase transitions (molecular liquid/ ionic liquid/ superionic/ electronic liquid). The ionic contribution to the conduction is calculated from proton diffusion and the electronic contribution is calculated using the Kubo-Greenwood formula. The calculations are performed with VASP, a plane-wave pseudo-potential code. There is a rapid transition to ionic conduction at 2000 K and 2 g/cm^3, whereas electronic conduction dominates at temperatures at and above 6000 K&[tilde;1]. Contrary to earlier results using the Car-Parrinello method&[tilde;2], we predict that the fluid bordering the superionic phase is conducting above 4000 K and 100 GPa. Our comprehensive use of FT-DFT explains the new findings. The calculated conductivity is compared to experimental data. I gratefully acknowledge Mike Desjarlais, my collaborator in this effort. The LDRD office at Sandia supported this work. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL
Phipps, M J S; Fox, T; Tautermann, C S; Skylaris, C-K
2017-03-08
First-principles quantum mechanical calculations with methods such as density functional theory (DFT) allow the accurate calculation of interaction energies between molecules. These interaction energies can be dissected into chemically relevant components such as electrostatics, polarization, and charge transfer using energy decomposition analysis (EDA) approaches. Typically EDA has been used to study interactions between small molecules; however, it has great potential to be applied to large biomolecular assemblies such as protein-protein and protein-ligand interactions. We present an application of EDA calculations to the study of ligands that bind to the thrombin protein, using the ONETEP program for linear-scaling DFT calculations. Our approach goes beyond simply providing the components of the interaction energy; we are also able to provide visual representations of the changes in density that happen as a result of polarization and charge transfer, thus pinpointing the functional groups between the ligand and protein that participate in each kind of interaction. We also demonstrate with this approach that we can focus on studying parts (fragments) of ligands. The method is relatively insensitive to the protocol that is used to prepare the structures, and the results obtained are therefore robust. This is an application to a real protein drug target of a whole new capability where accurate DFT calculations can produce both energetic and visual descriptors of interactions. These descriptors can be used to provide insights for tailoring interactions, as needed for example in drug design.
Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions
NASA Astrophysics Data System (ADS)
Cappellari, Michele
2017-04-01
I start by providing an updated summary of the penalized pixel-fitting (PPXF) method that is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematics when the velocity dispersion σ is smaller than the velocity sampling ΔV that is generally, by design, close to the instrumental dispersion σinst. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when σ ≲ ΔV/2, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the undersampled kernel and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available PPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of σ. This is important e.g. for spectroscopic surveys targeting galaxies with σ ≪ σinst, for galaxy redshift determinations or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.
Cuny, Jerome; Korchagina, Kseniia; Menakbi, Chemseddine; Mineva, Tzonka
2017-03-01
Application of ab initio molecular dynamics to study free energy surfaces (FES) is still not commonly performed because of the extensive sampling required. Indeed, it generally necessitates computationally costly simulations of more than several hundreds of picoseconds. To achieve such studies, efficient density functional theory (DFT) formalisms, based on various levels of approximate computational schemes, have been developed, and provide a good alternative to commonly used DFT implementations. We report benchmark results on the conformational change FES of alanine dipeptide obtained with auxiliary density functional theory (ADFT) and second- and third-order density functional tight-binding (DFTB) methods coupled to metadynamics simulations. The influence of an explicit water solvent is also studied with DFTB, which was made possible by its lower computational cost compared to ADFT. Simulations lengths of 2.1 and 15 ns were achieved with ADFT and DFTB, respectively, in a reasonably short computational time. ADFT leads to a free energy difference (ΔF eq-ax) of ∼ -3 kcal mol(-1) between the two low energy conformers, C7eq and C7ax, which is lower by only 1.5 kcal mol(-1) than the ΔF eq-ax computed with DFTB. The two minima in ADFT FES are separated by an energy barrier of 9 kcal mol(-1), which is higher than the DFTB barriers by 2-4 kcal mol(-1). Despite these small quantitative differences, the DFTB method reveals FES shapes, confor-mation geometries and energies of the stationary points in good agreement with these found with ADFT. This validates the promising applicability of DFTB to FES of reactions occurring in larger-size systems placed in complex environments.
NASA Astrophysics Data System (ADS)
Gong, Sai; Liu, Bang-Gui
2012-05-01
TiO2 has been recently used to realize high-temperature ferromagnetic semiconductors. In fact, it has been widely used for a long time as white pigment and sunscreen because of its whiteness, high refractive index, and excellent optical properties. However, its electronic structures and the related properties have not been satisfactorily understood. Here, we use Tran and Blaha's modified Becke-Johnson (TB-mBJ) exchange potential (plus a local density approximation correlation potential) within the density functional theory to investigate electronic structures and optical properties of rutile and anatase TiO2. Our comparative calculations show that the energy gaps obtained from mBJ method agree better with the experimental results than that obtained from local density approximation (LDA) and generalized gradient approximation (GGA), in contrast with substantially overestimated values from many-body perturbation (GW) calculations. As for optical dielectric functions (both real and imaginary parts), refractive index, and extinction coefficients as functions of photon energy, our mBJ calculated results are in excellent agreement with the experimental curves. Our further analysis reveals that these excellent improvements are achieved because mBJ potential describes accurately the energy levels of Ti 3d states. These results should be helpful to understand the high temperature ferromagnetism in doped TiO2. This approach can be used as a standard to understand electronic structures and the related properties of such materials as TiO2.
Hakey, Patrick M; Allis, Damian G; Ouellette, Wayne; Korter, Timothy M
2009-04-30
The cryogenic terahertz spectrum of (+)-methamphetamine hydrochloride from 10.0 to 100.0 cm(-1) is presented, as is the complete structural analysis and vibrational assignment of the compound using solid-state density functional theory. This cryogenic investigation reveals multiple spectral features that were not previously reported in room-temperature terahertz studies of the title compound. Modeling of the compound employed eight density functionals utilizing both solid-state and isolated-molecule methods. The results clearly indicate the necessity of solid-state simulations for the accurate assignment of solid-state THz spectra. Assignment of the observed spectral features to specific atomic motions is based on the BP density functional, which provided the best-fit solid-state simulation of the experimental spectrum. The seven experimental spectral features are the result of thirteen infrared-active vibrational modes predicted at a BP/DNP level of theory with more than 90% of the total spectral intensity associated with external crystal vibrations.
Martínez-Araya, Jorge I
2016-09-30
By means of the conceptual density functional theory, the so-called dual descriptor (DD) has been adapted to be used in any closed-shell molecule that presents degeneracy in its frontier molecular orbitals. The latter is of paramount importance because a correct description of local reactivity will allow to predict the most favorable sites on a molecule to undergo nucleophilic or electrophilic attacks; on the contrary, an incomplete description of local reactivity might have serio us consequences, particularly for those experimental chemists that have the need of getting an insight about reactivity of chemical reagents before using them in synthesis to obtain a new compound. In the present work, the old approach based only on electronic densities of frontier molecular orbitals is replaced by the most accurate procedure that implies the use of total electronic densities thus keeping consistency with the essential principle of the DFT in which the electronic density is the fundamental variable and not the molecular orbitals. As a result of the present work, the DD will be able to properly describe local reactivities only in terms of total electronic densities. To test the proposed operational formula, 12 very common molecules were selected as the original definition of the DD was not able to describe their local reactivities properly. The ethylene molecule was additionally used to test the capability of the proposed operational formula to reveal a correct local reactivity even in absence of degeneracy in frontier molecular orbitals. © 2016 Wiley Periodicals, Inc.
Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2010-05-01
A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.
2011-04-07
absolute and relative errors to approximate the derivatives of functions f : [−1, 1] → R with bandlimit roughly c with differentiation matrices constructed...of dimension N − 2 Ec = relative l2 error when D or DC is used to approximate the second derivatives of the functions sin(cx)− x sin(c) and cos(cx...dates back to the first half of the nineteenth century, is the finite difference method. It approximates the derivative of a function f : R → R at a
Dynamic kinetic energy potential for orbital-free density functional theory.
Neuhauser, Daniel; Pistinner, Shlomo; Coomar, Arunima; Zhang, Xu; Lu, Gang
2011-04-14
A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) density function theory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free density functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.
NASA Astrophysics Data System (ADS)
Huang, Chen; Muñoz-García, Ana Belén; Pavone, Michele
2016-12-01
Density-functional embedding theory provides a general way to perform multi-physics quantum mechanics simulations of large-scale materials by dividing the total system's electron density into a cluster's density and its environment's density. It is then possible to compute the accurate local electronic structures and energetics of the embedded cluster with high-level methods, meanwhile retaining a low-level description of the environment. The prerequisite step in the density-functional embedding theory is the cluster definition. In covalent systems, cutting across the covalent bonds that connect the cluster and its environment leads to dangling bonds (unpaired electrons). These represent a major obstacle for the application of density-functional embedding theory to study extended covalent systems. In this work, we developed a simple scheme to define the cluster in covalent systems. Instead of cutting covalent bonds, we directly split the boundary atoms for maintaining the valency of the cluster. With this new covalent embedding scheme, we compute the dehydrogenation energies of several different molecules, as well as the binding energy of a cobalt atom on graphene. Well localized cluster densities are observed, which can facilitate the use of localized basis sets in high-level calculations. The results are found to converge faster with the embedding method than the other multi-physics approach ONIOM. This work paves the way to perform the density-functional embedding simulations of heterogeneous systems in which different types of chemical bonds are present.
Huang, Chen; Muñoz-García, Ana Belén; Pavone, Michele
2016-12-28
Density-functional embedding theory provides a general way to perform multi-physics quantum mechanics simulations of large-scale materials by dividing the total system's electron density into a cluster's density and its environment's density. It is then possible to compute the accurate local electronic structures and energetics of the embedded cluster with high-level methods, meanwhile retaining a low-level description of the environment. The prerequisite step in the density-functional embedding theory is the cluster definition. In covalent systems, cutting across the covalent bonds that connect the cluster and its environment leads to dangling bonds (unpaired electrons). These represent a major obstacle for the application of density-functional embedding theory to study extended covalent systems. In this work, we developed a simple scheme to define the cluster in covalent systems. Instead of cutting covalent bonds, we directly split the boundary atoms for maintaining the valency of the cluster. With this new covalent embedding scheme, we compute the dehydrogenation energies of several different molecules, as well as the binding energy of a cobalt atom on graphene. Well localized cluster densities are observed, which can facilitate the use of localized basis sets in high-level calculations. The results are found to converge faster with the embedding method than the other multi-physics approach ONIOM. This work paves the way to perform the density-functional embedding simulations of heterogeneous systems in which different types of chemical bonds are present.
Structural Stability and Functional Remodeling of High-Density Lipoproteins
Gursky, Olga
2015-01-01
Lipoproteins are protein-lipid nanoparticles that transport lipids in circulation and are central in atherosclerosis and other disorders of lipid metabolism. Apolipoproteins form flexible structural scaffolds and important functional ligands on the particle surface and direct lipoprotein metabolism. Lipoproteins undergo multiple rounds of metabolic remodeling that is crucial to lipid transport. Important aspects of this remodeling, including apolipoprotein dissociation and particle fusion, are mimicked in thermal or chemical denaturation and are modulated by free energy barriers. Here we review our biophysical studies that revealed kinetic mechanism of lipoprotein stabilization and unraveled its structural basis. The main focus is on high-density lipoprotein (HDL). An inverse correlation between stability and functions of various HDLs in cholesterol transport suggests functional role of structural disorder. A mechanism for conformational adaptation of the major HDL proteins, apoA-I and apoA-II, to the increasing lipid load is proposed. Together, these studies help understand why HDL form discrete subclasses separated by kinetic barriers, which have distinct composition, conformation and functional properties. Understanding these properties may help improve HDL quality and develop novel therapies for cardiovascular disease. PMID:25749369
Abnormal Functional Connectivity Density in Post-traumatic Stress Disorder.
Zhang, Youxue; Xie, Bing; Chen, Heng; Li, Meiling; Liu, Feng; Chen, Huafu
2016-05-01
Post-traumatic stress disorder (PTSD) is a psychiatric disorder that occurs in individuals who have experienced life-threatening mental traumas. Previous neuroimaging studies have indicated that the pathology of PTSD may be associated with the abnormal functional integration among brain regions. In the current study, we used functional connectivity density (FCD) mapping, a novel voxel-wise data-driven approach based on graph theory, to explore aberrant FC through the resting-state functional magnetic resonance imaging of the PTSD. We calculated both short- and long-range FCD in PTSD patients and healthy controls (HCs). Compared with HCs, PTSD patients showed significantly increased long-range FCD in the left dorsolateral prefrontal cortex (DLPFC), but no abnormal short-range FCD was found in PTSD. Furthermore, seed-based FC analysis of the left DLPFC showed increased connectivity in the left superior parietal lobe and visual cortex of PTSD patients. The results suggested that PTSD patients experienced a disruption of intrinsic long-range functional connections in the fronto-parietal network and visual cortex, which are associated with attention control and visual information processing.
Daubechies wavelets for linear scaling density functional theory.
Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Towards simple orbital-dependent density functionals for molecular dissociation
NASA Astrophysics Data System (ADS)
Zhang, Igor Ying; Richter, Patrick; Scheffler, Matthias
2015-03-01
Density functional theory (DFT) is one of the leading first-principles electronic-structure theories. However, molecular dissociation remains a challenge, because it requires a well-balanced description of the drastically different electronic structure at different bond lengths. One typical and well-documented case is the dissociation of both H2+ and H2, for which all popular DFT functionals fail. We start from the Bethe-Goldstone equation to propose a simple orbital-dependent correlation functional which generalizes the linear adiabatic connection approach. The resulting scheme is based on second-order perturbation theory (PT2), but includes the self-consistent coupling of electron-hole pairs, which ensures the correct H2 dissociation limit and gives a finite correlation energy for systems with a (near)-degenerate energy gap. This coupling PT2-like (CPT2) approximation delivers a significant improvement over all existing functionals for both H2 and H2+ dissociation. We will demonstrate the reason for this improvement analytically for H2 in a minimal basis.
NASA Astrophysics Data System (ADS)
García-Aldea, David; Alvarellos, J. E.
2009-03-01
We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac'on-Alvarellos-Tarazona, Garc'ia-Gonz'alez et al., Wang-Govind-Carter and Garc'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same ansatz can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined).
Benchmarking Density Functionals for Chemical Bonds of Gold.
Kepp, Kasper P
2017-03-09
Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark data set probes all types of bonding to gold from very electronegative halides that force Au(+) electronic structure, via covalently bonded systems, hard and soft Lewis acids and bases that either work against or complement the softness of gold, the Au2 molecule probing gold's bond with itself, and weak bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au-X bonds, ∼ 11-12 kJ/mol except for Au-H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP correlation produce weaker bonds to gold. Most functionals provide similar trend accuracy, though somewhat lower for M06 and M06L, but very different numerical accuracy. Notably, PBE and TPSS functionals with dispersion display the smallest numerical errors and very small mean signed errors (0-6 kJ/mol), i.e. no bias toward over- or under-binding. Errors are evenly distributed versus atomic number, suggesting that relativistic effects are treated fairly; the mean absolute error is almost halved from B3LYP (45 kJ/mol) to TPSS and PBE (23 kJ/mol, including difficult cases); 23 kJ/mol is quite respectable considering the diverse bonds to gold and the complication of relativistic effects. Thus, studies that use DFT with effective core potentials for gold chemistry, with no alternative due
Cluster density functional theory for lattice models based on the theory of Möbius functions
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2005-08-01
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Interaction of boron with graphite: A van der Waals density functional study
NASA Astrophysics Data System (ADS)
Liu, Juan; Wang, Chen; Liang, Tongxiang; Lai, Wensheng
2016-08-01
Boron doping has been widely investigated to improve oxidation resistance of graphite. In this work the interaction of boron with graphite is investigated by a van der Waals density-functional approach (vdW-DF). The traditional density-functional theory (DFT) is well accounted for the binding in boron-substituted graphite. However, to investigate the boron atom on graphite surface and the interstitial impurities require use of a description of graphite interlayer binding. Traditional DFT cannot describe the vdW physics, for instance, GGA calculations show no relevant binding between graphite sheets. LDA shows some binding, but they fail to provide an accurate account of vdW forces. In this paper, we compare the calculation results of graphite lattice constant and cohesive energy by several functionals, it shows that vdW-DF such as two optimized functionals optB88-vdW and optB86b-vdW give much improved results than traditional DFT. The vdW-DF approach is then applied to study the interaction of boron with graphite. Boron adsorption, substitution, and intercalation are discussed in terms of structural parameters and electronic structures. When adsorbing on graphite surface, boron behaves as π electron acceptor. The π electron approaches boron atom because of more electropositive of boron than carbon. For substitution situation, the hole introduced by boron mainly concentrates on boron and the nearest three carbon atoms. The B-doped graphite system with the hole has less ability to offer electrons to oxygen, ultimately resulted in the inhibition of carbon oxidation. For interstitial doping, vdW-DFs show more accurate formation energy than LDA. PBE functional cannot describe the interstitial boron in graphite reasonably because of the ignoring binding of graphite sheets. The investigation of electron structures of boron doped graphite will play an important role in understanding the oxidation mechanism in further study.
Accurate and efficient calculation of discrete correlation functions and power spectra
NASA Astrophysics Data System (ADS)
Xu, Y. F.; Liu, J. M.; Zhu, W. D.
2015-07-01
Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass-spring-damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate
An extended set of yeast-based functional assays accurately identifies human disease mutations
Sun, Song; Yang, Fan; Tan, Guihong; Costanzo, Michael; Oughtred, Rose; Hirschman, Jodi; Theesfeld, Chandra L.; Bansal, Pritpal; Sahni, Nidhi; Yi, Song; Yu, Analyn; Tyagi, Tanya; Tie, Cathy; Hill, David E.; Vidal, Marc; Andrews, Brenda J.; Boone, Charles; Dolinski, Kara; Roth, Frederick P.
2016-01-01
We can now routinely identify coding variants within individual human genomes. A pressing challenge is to determine which variants disrupt the function of disease-associated genes. Both experimental and computational methods exist to predict pathogenicity of human genetic variation. However, a systematic performance comparison between them has been lacking. Therefore, we developed and exploited a panel of 26 yeast-based functional complementation assays to measure the impact of 179 variants (101 disease- and 78 non-disease-associated variants) from 22 human disease genes. Using the resulting reference standard, we show that experimental functional assays in a 1-billion-year diverged model organism can identify pathogenic alleles with significantly higher precision and specificity than current computational methods. PMID:26975778
Holland, Jason P; Green, Jennifer C
2010-04-15
The electronic absorption spectra of a range of copper and zinc complexes have been simulated by using time-dependent density functional theory (TD-DFT) calculations implemented in Gaussian03. In total, 41 exchange-correlation (XC) functionals including first-, second-, and third-generation (meta-generalized gradient approximation) DFT methods were compared in their ability to predict the experimental electronic absorption spectra. Both pure and hybrid DFT methods were tested and differences between restricted and unrestricted calculations were also investigated by comparison of analogous neutral zinc(II) and copper(II) complexes. TD-DFT calculated spectra were optimized with respect to the experimental electronic absorption spectra by use of a Matlab script. Direct comparison of the performance of each XC functional was achieved both qualitatively and quantitatively by comparison of optimized half-band widths, root-mean-squared errors (RMSE), energy scaling factors (epsilon(SF)), and overall quality-of-fit (Q(F)) parameters. Hybrid DFT methods were found to outperform all pure DFT functionals with B1LYP, B97-2, B97-1, X3LYP, and B98 functionals providing the highest quantitative and qualitative accuracy in both restricted and unrestricted systems. Of the functionals tested, B1LYP gave the most accurate results with both average RMSE and overall Q(F) < 3.5% and epsilon(SF) values close to unity (>0.990) for the copper complexes. The XC functional performance in spin-restricted TD-DFT calculations on the zinc complexes was found to be slightly worse. PBE1PBE, mPW1PW91 and B1LYP gave the most accurate results with typical RMSE and Q(F) values between 5.3 and 7.3%, and epsilon(SF) around 0.930. These studies illustrate the power of modern TD-DFT calculations for exploring excited state transitions of metal complexes.
Density functional theory based generalized effective fragment potential method
Nguyen, Kiet A. E-mail: ruth.pachter@wpafb.af.mil; Pachter, Ruth E-mail: ruth.pachter@wpafb.af.mil; Day, Paul N.
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.
Specification of optical components using the power spectral density function
Lawson, J.K.; Wolfe, C.R.; Manes, K.R.; Trenholme, J.B.; Aikens, D.M.; English, R.E. Jr.
1995-06-20
This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as ``residuals.`` A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.
Density Functional Theory Study on Interaction between Catechin and Thymine
NASA Astrophysics Data System (ADS)
Cai, Wan-fei; Zheng, Yan; Li, Lai-cai; Tian, An-min
2012-12-01
The interacting patterns and mechanism of the catechin and thymine have been investigated with the density functional theory Becke's three-parameter nonlocal exchange functional and the Lee, Yang, and Parr nonlocal correlation functional (B3LYP) method by 6-31+G* basis set. Thirteen stable structures for the catechin-thymine complexes have been found which form two hydrogen bonds at least. The vibrational frequencies are also studied at the same level to analyze these complexes. The results indicated that catechin interacted with thymine by three different hydrogen bonds as N—H···O, C—H···O, O—H···O and the complexes are mainly stabilized by the hydrogen bonding interactions. Theories of atoms in molecules and natural bond orbital have been adopted to investigate the hydrogen bonds involved in all systems. The interaction energies of all complexes have been corrected for basis set superposition error, which are from -18.15 kJ/mol to -32.99 kJ/mol. The results showed that the hydrogen bonding contribute to the interaction energies dominantly. The corresponding bonds stretching motions in all complexes are red-shifted relative to that of the monomer, which is in agreement with experimental results.
Insights into phase transitions and entanglement from density functional theory
NASA Astrophysics Data System (ADS)
Wei, Bo-Bo
2016-11-01
Density functional theory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.
Particle-vibration coupling within covariant density functional theory
Litvinova, E.; Ring, P.; Tselyaev, V.
2007-06-15
Covariant density functional theory, which has so far been applied only within the framework of static and time-dependent mean-field theory, is extended to include particle-vibration coupling (PVC) in a consistent way. Starting from a conventional energy functional, we calculate the low-lying collective vibrations in the relativistic random phase approximation (RRPA) and construct an energy-dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole (p-h) channel is solved in the time blocking approximation (TBA). No additional parameters are used, and double counting is avoided by a proper subtraction method. The same energy functional, i.e., the same set of coupling constants, generates the Dirac-Hartree single-particle spectrum, the static part of the residual p-h interaction, and the particle-phonon coupling vertices. Therefore, a fully consistent description of nuclear excited states is developed. This method is applied for an investigation of damping phenomena in the spherical nuclei with closed shells {sup 208}Pb and {sup 132}Sn. Since the phonon coupling terms enrich the RRPA spectrum with a multitude of p-hxphonon components, a noticeable fragmentation of the giant resonances is found, which is in full agreement with experimental data and with results of the semiphenomenological nonrelativistic approach.
Density functional theory and phytochemical study of 8-hydroxyisodiospyrin
NASA Astrophysics Data System (ADS)
Ullah, Zakir; Ata-ur-Rahman; Fazl-i-Sattar; Rauf, Abdur; Yaseen, Muhammad; Hassan, Waseem; Tariq, Muhammad; Ayub, Khurshid; Tahir, Asif Ali; Ullah, Habib
2015-09-01
Comprehensive theoretical and experimental studies of a natural product, 8-hydroxyisodiospyrin (HDO) have been carried out. Based on the correlation of experimental and theoretical data, an appropriate computational model was developed for obtaining the electronic, spectroscopic, and thermodynamic parameters of HDO. First of all, the exact structure of HDO is confirmed from the nice correlation of theory and experiment, prior to determination of its electroactive nature. Hybrid density functional theory (DFT) is employed for all theoretical simulations. The experimental and predicted IR and UV-vis spectra [B3LYP/6-31+G(d,p) level of theory] have excellent correlation. Inter-molecular non-covalent interaction of HDO with different gases such as NH3, CO2, CO, H2O is investigated through geometrical counterpoise (gCP) i.e., B3LYP-gCP-D3/6-31G∗ method. Furthermore, the inter-molecular interaction is also supported by geometrical parameters, electronic properties, thermodynamic parameters and charge analysis. All these characterizations have corroborated each other and confirmed the electroactive nature (non-covalent interaction ability) of HDO for the studied gases. Electronic properties such as Ionization Potential (IP), Electron Affinities (EA), electrostatic potential (ESP), density of states (DOS), HOMO, LUMO, and band gap of HDO have been estimated for the first time theoretically.
Nuclear structure and dynamics with density functional theory
NASA Astrophysics Data System (ADS)
Stetcu, Ionel
2015-10-01
Even in the absence of ab initio methods capable of tackling heavy nuclei without restrictions, one can obtain an ab initio description of ground-state properties by means of the density functional theory (DFT), and its extension to superfluid systems in its local variant, the superfluid local density approximation (SLDA). Information about the properties of excited states can be obtained in the same framework by using an extension to the time-dependent (TD) phenomena. Unlike other approaches in which the nuclear structure information is used as a separate input into reaction models, the TD approach treats on the same footing the nuclear structure and dynamics, and is well suited to provide more reliable description for a large number of processes involving heavy nuclei, from the nuclear response to electroweak probes, to nuclear reactions, such as neutron-induced reactions, or nuclear fusion and fission. Such processes, sometimes part of integrated nuclear systems, have important applications in astrophysics, energy production, global security, etc. In this talk, I will present the simulation of a simple reaction, that is the Coulomb excitation of a 238U nucleus, and discuss the application of the TD-DFT formalism to the description of induced fission. I gratefully acknowledge partial support of the U.S. Department of Energy through an Early Career Award of the LANL/LDRD Program.
Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides
NASA Astrophysics Data System (ADS)
Millis, Andrew
2015-03-01
The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Vibrational spectroscopy and density functional theory study of 4-mercaptophenol
NASA Astrophysics Data System (ADS)
Li, Ran; Ji, Wei; Chen, Lei; Lv, Haiming; Cheng, Jianbo; Zhao, Bing
2014-03-01
In this paper, 4-mercaptophenol (4-MPH) was designed as a model molecule for theoretical and experimental studies of the molecule structure. Density functional theory (DFT) calculations have been performed to predict the IR and Raman spectra for the molecule. In addition, Fourier transform infrared (FTIR) and Raman spectra of the compound have been obtained experimentally. All FTIR and Raman bands of the compound obtained experimentally were assigned based on the modeling results obtained at the B3LYP/6-311 + G** level. Our calculated vibrational frequencies are in good agreement with the experimental vales. The molecular electrostatic potential surface calculation was performed and the result suggested that the 4-MPH has two hydrogen bond donors and three hydrogen bond acceptors. HOMO-LUMO gap was also obtained theoretically at B3LYP/6-311 + G** level.
Density functional theory and simulations of colloidal triangular prisms.
Marechal, Matthieu; Dussi, Simone; Dijkstra, Marjolein
2017-03-28
Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlocomputer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld's version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms.
Native defects in Tl6SI4: Density functional calculations
NASA Astrophysics Data System (ADS)
Shi, Hongliang; Du, Mao-Hua
2015-05-01
Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges and large static dielectric constant, which provides effective screening of charged defects and impurities.
Direct recursive identification of the Preisach hysteresis density function
NASA Astrophysics Data System (ADS)
Ruderman, Michael
2013-12-01
In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.
The photochemistry of transition metal complexes using density functional theory.
Garino, Claudio; Salassa, Luca
2013-07-28
The use of density functional theory (DFT) and time-dependent DFT (TD-DFT) to study the photochemistry of metal complexes is becoming increasingly important among chemists. Computational methods provide unique information on the electronic nature of excited states and their atomic structure, integrating spectroscopy observations on transient species and excited-state dynamics. In this contribution, we present an overview on photochemically active transition metal complexes investigated by DFT. In particular, we discuss a representative range of systems studied up to now, which include CO- and NO-releasing inorganic and organometallic complexes, haem and haem-like complexes dissociating small diatomic molecules, photoactive anti-cancer Pt and Ru complexes, Ru polypyridyls and diphosphino Pt derivatives.
Nitrotyrosine adsorption on defective graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Majidi, R.; Karami, A. R.
2015-06-01
We have applied density functional theory to study adsorption of nitrotyrosine on perfect and defective graphene sheets. The graphene sheets with Stone-Wales (SW) defect, pentagon-nonagon (5-9) single vacancy, and pentagon-octagon-pentagon (5-8-5) double vacancy were considered. The calculations of adsorption energy showed that nitrotyrosine presents a more strong interaction with defective graphene rather than with perfect graphene sheet. The order of interaction strength is: SW>5-9>5-8-5>perfect graphene. It is found that the electronic properties of perfect and defective graphene are sensitive to the presence of nitrotyrosine. Hence, graphene sheets can be considered as a good sensor for detection of nitrotyrosine molecule which is observed in connection with several human disorders, such as Parkinson's and Alzheimer's disease.
Density Functional Approach and Random Matrix Theory in Proteogenesis
NASA Astrophysics Data System (ADS)
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Native defects in Tl6SI4: Density functional calculations
Shi, Hongliang; Du, Mao -Hua
2015-05-05
In this study, Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges andmore » large static dielectric constant, which provides effective screening of charged defects and impurities.« less
Descriptions of carbon isotopes within the energy density functional theory
Ismail, Atef; Cheong, Lee Yen; Yahya, Noorhana; Tammam, M.
2014-10-24
Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.
Density functional theory studies of HCOOH decomposition on Pd(111)
NASA Astrophysics Data System (ADS)
Scaranto, Jessica; Mavrikakis, Manos
2016-08-01
The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, density functional theory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.
Density functional theory study of hexagonal carbon phases.
Wang, Zhibin; Gao, Faming; Li, Na; Qu, Nianrui; Gou, Huiyang; Hao, Xianfeng
2009-06-10
It is reported frequently that the new carbon phases may be harder than diamond (Wang et al 2004 Proc. Natl Acad. Sci. 101 13699 and Mao et al 2003 Science 302 425). However, the mechanism is still unclear. In this paper we systematically investigate the structural, electronic, and mechanical properties of the diamond polytypes using first-principles density functional calculations. The results show that the bulk modulus and shear modulus for the hexagonal form of diamond approach those of diamond, suggesting they might be hard and low compressibility materials. According to the semiempirical method for hardness based on the Mulliken overlap population, the hardnesses for hexagonal forms have been evaluated and compared to diamond. The results indicate that these phases are superhard. More importantly, the bonds in some specific directions of the hexagonal phases are harder than those in diamond, which may lead to the noticeable indentation marks on the diamond anvils observed in experiments.
Reproducibility in density functional theory calculations of solids.
Lejaeghere, Kurt; Bihlmayer, Gustav; Björkman, Torbjörn; Blaha, Peter; Blügel, Stefan; Blum, Volker; Caliste, Damien; Castelli, Ivano E; Clark, Stewart J; Dal Corso, Andrea; de Gironcoli, Stefano; Deutsch, Thierry; Dewhurst, John Kay; Di Marco, Igor; Draxl, Claudia; Dułak, Marcin; Eriksson, Olle; Flores-Livas, José A; Garrity, Kevin F; Genovese, Luigi; Giannozzi, Paolo; Giantomassi, Matteo; Goedecker, Stefan; Gonze, Xavier; Grånäs, Oscar; Gross, E K U; Gulans, Andris; Gygi, François; Hamann, D R; Hasnip, Phil J; Holzwarth, N A W; Iuşan, Diana; Jochym, Dominik B; Jollet, François; Jones, Daniel; Kresse, Georg; Koepernik, Klaus; Küçükbenli, Emine; Kvashnin, Yaroslav O; Locht, Inka L M; Lubeck, Sven; Marsman, Martijn; Marzari, Nicola; Nitzsche, Ulrike; Nordström, Lars; Ozaki, Taisuke; Paulatto, Lorenzo; Pickard, Chris J; Poelmans, Ward; Probert, Matt I J; Refson, Keith; Richter, Manuel; Rignanese, Gian-Marco; Saha, Santanu; Scheffler, Matthias; Schlipf, Martin; Schwarz, Karlheinz; Sharma, Sangeeta; Tavazza, Francesca; Thunström, Patrik; Tkatchenko, Alexandre; Torrent, Marc; Vanderbilt, David; van Setten, Michiel J; Van Speybroeck, Veronique; Wills, John M; Yates, Jonathan R; Zhang, Guo-Xu; Cottenier, Stefaan
2016-03-25
The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.
NASA Astrophysics Data System (ADS)
Riquelme-Galván, Mauricio; Robledo, Alberto
2017-02-01
We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of inhomogeneous systems and of the renormalization group (RG) method in nonlinear dynamics to provide a more accurate, formal, approach to the subject. The description of this remarkable correspondence encompasses, on the one hand, the density functional formalism, where classical and quantum mechanical analogues match the procedure for one-dimensional clusters, and, on the other, the RG fixed-point map of functional compositions that captures the essential dynamical behavior. We provide details of how the above-referred theoretical approaches interrelate and discuss the implications of the correspondence between the high-dimensional (degrees of freedom) phenomenon and low-dimensional dynamics.
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
Origin of anomeric effect: A density functional steric analysis
Huang, Ying; Zhong, Ai-Guo; Yang, Qinsong; Liu, Shubin
2011-01-01
The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial–equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange–correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial–equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostaticinteractions, synchronously working together. Another explanation in terms of exchange–correlation and electrostaticinteractions has also been obtained in this work.
Jordan, Daniel K; Mazziotti, David A
2005-02-22
Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.
The Luminosity Function and Mean Galaxy Density from the ESP Galaxy Redshift Survey
NASA Astrophysics Data System (ADS)
Zucca, Elena; Zamorani, G.; Vettolani, G.; Cappi, A.; Merighi, R.; Mignoli, M.; Stirpe, G. M.; MacGillivray, H.; Collins, C.; Balkowski, C.; Cayatte, V.; Maurogordato, S.; Proust, D.; Chincarini, G.; Guzzo, L.; Maccagni, D.; Scaramella, R.; Blanchard, A.; Ramella, M.
We summarise the main results obtained over the last two years by the ESO Slice Project (ESP) redshift survey, concerning the luminosity function and mean density of galaxies, and their implications for the galaxy number counts at bright magnitudes. The bj-band luminosity function is characterised by a steep faint-end, which raises above a "global" Schechter fit for M_bj > -17 + 5log(h) and is well described by a power-law with slope ~ -1.6. This steepening is mostly produced by galaxies with emission lines, with a clear trend for galaxies with larger [OII] equivalent widths to show a steeper faint end (and a fainter M*). The normalization of the luminosity function is about a factor of 1.6 higher that that from the Stromlo-APM survey. We find that, in fact, the mean density can be seen to increase out to ~140/h Mpc. If we take this into account when computing the expected cumulative number counts from the observed luminosity function, we are able to reproduce the observed steep counts at bright (bj<17) magnitudes very accurately.
Wang, Ke; Yu, Yang-Xin; Gao, Guang-Hua
2004-07-01
A density functional theory (DFT) is presented for describing the distributions of small ions around an isolated infinitely long polyanionic DNA molecule in the framework of the restricted primitive model. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion. The predictions from the DFT are compared with integral equation theory (IET), the nonlinear Poisson-Boltzmann (PB) equation, and computer simulation data for the ionic density profiles, electrostatic potentials, and charge compensation functions at varieties of solution conditions. Good agreement between the DFT and computer simulations is achieved. The charge inversion phenomena of DNA are observed in a moderately concentrated solution of 2:1 and 2:2 electrolytes using the DFT, IET, and computer simulation, but can never be predicted from the PB equation. The predictions of charge inversion from the DFT prove to be more accurate than those from the IET when compared with computer simulation data. The preferential interaction coefficients from the DFT are also compared with those from the PB equation and Monte Carlo simulation, and it is shown that the DFT is superior to the PB equation.
Assessment of the accuracy of density functional theory for first principles simulations of water
NASA Astrophysics Data System (ADS)
Grossman, J. C.; Schwegler, E.; Draeger, E.; Gygi, F.; Galli, G.
2004-03-01
We present a series of Car-Parrinello (CP) molecular dynamics simulation in order to better understand the accuracy of density functional theory for the calculation of the properties of water [1]. Through 10 separate ab initio simulations, each for 20 ps of ``production'' time, a number of approximations are tested by varying the density functional employed, the fictitious electron mass, μ, in the CP Langrangian, the system size, and the ionic mass, M (we considered both H_2O and D_2O). We present the impact of these approximations on properties such as the radial distribution function [g(r)], structure factor [S(k)], diffusion coefficient and dipole moment. Our results show that structural properties may artificially depend on μ, and that in the case of an accurate description of the electronic ground state, and in the absence of proton quantum effects, we obtained an oxygen-oxygen correlation function that is over-structured compared to experiment, and a diffusion coefficient which is approximately 10 times smaller. ^1 J.C. Grossman et. al., J. Chem. Phys. (in press, 2004).
A method for the accurate and smooth approximation of standard thermodynamic functions
NASA Astrophysics Data System (ADS)
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
NASA Astrophysics Data System (ADS)
Krieger, J. B.; Chen, Jiqiang; Iafrate, G. J.; Savin, A.
1998-03-01
We have obtained an analytic approximation to E_c(r_g, ζ,G) where G is an energy gap separating the occupied and unoccupied states of a homogeneous electron gas for ζ=3D0 and ξ=3D1. When G=3D0, E_c(r_g, ζ) reduces to the usual LSD result. This functional is employed in calculating correlation energies for unpolarized atoms and ions for Z <= 18 by taking G[n]=3D1/8|nabla ln n|^2, which reduces to the ionization energy in the large r limit in an exact Kohn-Sham (KS) theory. The resulting functional is self-interaction-corrected employing a method which is invariant under a unitary transformation. We find that the application of this approach to the calculation of the Ec functional reduces the error in the LSD result by more than 95%. When the value of G is approximately corrected to include the effect of higher lying unoccupied localized states, the resulting values of Ec are within a few percent of the exact results.
NASA Astrophysics Data System (ADS)
Xu, Xin; Zhang, Qingsong; Muller, Richard P.; Goddard, William A.
2005-01-01
We derive here the form for the exact exchange energy density for a density that decays with Gaussian-type behavior at long range. This functional is intermediate between the B88 and the PW91 exchange functionals. Using this modified functional to match the form expected for Gaussian densities, we propose the X3LYP extended functional. We find that X3LYP significantly outperforms Becke three parameter Lee-Yang-Parr (B3LYP) for describing van der Waals and hydrogen bond interactions, while performing slightly better than B3LYP for predicting heats of formation, ionization potentials, electron affinities, proton affinities, and total atomic energies as validated with the extended G2 set of atoms and molecules. Thus X3LYP greatly enlarges the field of applications for density functional theory. In particular the success of X3LYP in describing the water dimer (with Re and De within the error bars of the most accurate determinations) makes it an excellent candidate for predicting accurate ligand-protein and ligand-DNA interactions.
Adidharma, Hertanto; Tan, Sugata P
2016-07-07
Canonical Monte Carlo simulations on face-centered cubic (FCC) and hexagonal closed packed (HCP) Lennard-Jones (LJ) solids are conducted at very low temperatures (0.10 ≤ T(∗) ≤ 1.20) and high densities (0.96 ≤ ρ(∗) ≤ 1.30). A simple and robust method is introduced to determine whether or not the cutoff distance used in the simulation is large enough to provide accurate thermodynamic properties, which enables us to distinguish the properties of FCC from that of HCP LJ solids with confidence, despite their close similarities. Free-energy expressions derived from the simulation results are also proposed, not only to describe the properties of those individual structures but also the FCC-liquid, FCC-vapor, and FCC-HCP solid phase equilibria.
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Martin, Jan M. L.; Kwak, Dochan (Technical Monitor)
2002-01-01
The CCSD(T) method has been used to compute a highly accurate quartic force field and fundamental frequencies for all N-14 and N-15 isotopomers of the high energy density material T(sub d)N(sub 4). The computed fundamental frequencies show beyond doubt that the bands observed in a matrix isolation experiment by Radziszewski and coworkers are not due to different isotopomers of T(sub d)N(sub 4). The most sophisticated thermochemical calculations to date yield a N(sub 4) -> 2N(sub 2) heat of reaction of 182.22 +/- 0.5 kcal/mol at 0 K (180.64 +/- 0.5 at 298 K). It is hoped that the data reported herein will aid in the ultimate detection of T(sub d)N(sub 4).
NASA Astrophysics Data System (ADS)
Adidharma, Hertanto; Tan, Sugata P.
2016-07-01
Canonical Monte Carlo simulations on face-centered cubic (FCC) and hexagonal closed packed (HCP) Lennard-Jones (LJ) solids are conducted at very low temperatures (0.10 ≤ T∗ ≤ 1.20) and high densities (0.96 ≤ ρ∗ ≤ 1.30). A simple and robust method is introduced to determine whether or not the cutoff distance used in the simulation is large enough to provide accurate thermodynamic properties, which enables us to distinguish the properties of FCC from that of HCP LJ solids with confidence, despite their close similarities. Free-energy expressions derived from the simulation results are also proposed, not only to describe the properties of those individual structures but also the FCC-liquid, FCC-vapor, and FCC-HCP solid phase equilibria.
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
A density functional for core-valence correlation energy
NASA Astrophysics Data System (ADS)
Ranasinghe, Duminda S.; Frisch, Michael J.; Petersson, George A.
2015-12-01
A density functional, ɛCV-DFT(ρc, ρv), describing the core-valence correlation energy has been constructed as a linear combination of ɛLY Pcorr(ρc), ɛV WN5corr(ρc, ρv), ɛPBEcorr(ρc, ρv), ɛSlaterex(ρc, ρv), ɛHCTHex(ρc, ρv), ɛHFex(ρc, ρv), and F CV -DFT (" separators=" N i , Z i ) , a function of the nuclear charges. This functional, with 6 adjustable parameters, reproduces (±0.27 kcal/mol rms error) a benchmark set of 194 chemical energy changes including 9 electron affinities, 18 ionization potentials, and 167 total atomization energies covering the first- and second-rows of the periodic table. This is almost twice the rms error (±0.16 kcal/mol) obtained with CCSD(T)/MTsmall calculations, but less than half the rms error (±0.65 kcal/mol) obtained with MP2/GTlargeXP calculations, and somewhat smaller than the rms error (±0.39 kcal/mol) obtained with CCSD/MTsmall calculations. The largest positive and negative errors from ɛCV-DFT(ρc, ρv) were 0.88 and -0.75 kcal/mol with the set of 194 core-valence energy changes ranging from +3.76 kcal/mol for the total atomization energy of propyne to -9.05 kcal/mol for the double ionization of Mg. Evaluation of the ɛCV-DFT(ρc, ρv) functional requires less time than a single SCF iteration, and the accuracy is adequate for any model chemistry based on the CCSD(T) level of theory.
NASA Astrophysics Data System (ADS)
Gao Xianlong; Asgari, Reza
2008-03-01
We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with a Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikov-type phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew J.; Marianetti, Chris A.
2015-07-01
Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the "plus U" extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare-earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.
Nucleobase-functionalized graphene nanoribbons for accurate high-speed DNA sequencing
NASA Astrophysics Data System (ADS)
Paulechka, Eugene; Wassenaar, Tsjerk A.; Kroenlein, Kenneth; Kazakov, Andrei; Smolyanitsky, Alex
2016-01-01
We propose a water-immersed nucleobase-functionalized suspended graphene nanoribbon as an intrinsically selective device for nucleotide detection. The proposed sensing method combines Watson-Crick selective base pairing with graphene's capacity for converting anisotropic lattice strain to changes in an electrical current at the nanoscale. Using detailed atomistic molecular dynamics (MD) simulations, we study sensor operation at ambient conditions. We combine simulated data with theoretical arguments to estimate the levels of measurable electrical signal variation in response to strains and determine that the proposed sensing mechanism shows significant promise for realistic DNA sensing devices without the need for advanced data processing, or highly restrictive operational conditions.We propose a water-immersed nucleobase-functionalized suspended graphene nanoribbon as an intrinsically selective device for nucleotide detection. The proposed sensing method combines Watson-Crick selective base pairing with graphene's capacity for converting anisotropic lattice strain to changes in an electrical current at the nanoscale. Using detailed atomistic molecular dynamics (MD) simulations, we study sensor operation at ambient conditions. We combine simulated data with theoretical arguments to estimate the levels of measurable electrical signal variation in response to strains and determine that the proposed sensing mechanism shows significant promise for realistic DNA sensing devices without the need for advanced data processing, or highly restrictive operational conditions. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr07061a
Two functionally distinct kinetochore pools of BubR1 ensure accurate chromosome segregation
Zhang, Gang; Mendez, Blanca Lopez; Sedgwick, Garry G.; Nilsson, Jakob
2016-01-01
The BubR1/Bub3 complex is an important regulator of chromosome segregation as it facilitates proper kinetochore–microtubule interactions and is also an essential component of the spindle assembly checkpoint (SAC). Whether BubR1/Bub3 localization to kinetochores in human cells stimulates SAC signalling or only contributes to kinetochore–microtubule interactions is debated. Here we show that two distinct pools of BubR1/Bub3 exist at kinetochores and we uncouple these with defined BubR1/Bub3 mutants to address their function. The major kinetochore pool of BubR1/Bub3 is dependent on direct Bub1/Bub3 binding and is required for chromosome alignment but not for the SAC. A distinct pool of BubR1/Bub3 localizes by directly binding to phosphorylated MELT repeats on the outer kinetochore protein KNL1. When we prevent the direct binding of BubR1/Bub3 to KNL1 the checkpoint is weakened because BubR1/Bub3 is not incorporated into checkpoint complexes efficiently. In conclusion, kinetochore localization supports both known functions of BubR1/Bub3. PMID:27457023
Augmented Lagrangian formulation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Suryanarayana, Phanish; Phanish, Deepa
2014-10-01
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas-Fermi-von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Self-interaction corrections in density functional theory
Tsuneda, Takao; Hirao, Kimihiko
2014-05-14
Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications. The self-interaction corrections get rid of the self-interaction error, which is the sum of the Coulomb and exchange self-interactions that remains because of the use of an approximate exchange functional. The most frequently used self-interaction correction is the Perdew-Zunger correction. However, this correction leads to instabilities in the electronic state calculations of molecules. To avoid these instabilities, several self-interaction corrections have been developed on the basis of the characteristic behaviors of self-interacting electrons, which have no two-electron interactions. These include the von Weizsäcker kinetic energy and long-range (far-from-nucleus) asymptotic correction. Applications of self-interaction corrections have shown that the self-interaction error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons. This finding is supported by the fact that the distribution of self-interacting electrons indicates that they are near atomic nuclei rather than in chemical bonds.
Density functional computations for inner-shell excitation spectroscopy
NASA Astrophysics Data System (ADS)
Hu, Ching-Han; Chong, Delano P.
1996-11-01
The 1 s → π ∗ inner-shell excitation spectra of seven molecules have been studied using density functional theory along with the unrestricted generalized transition state (uGTS) approach. The exchange-correlation potential is based on a combined functional of Becke's exchange (B88) and Perdew's correlation (P86). A scaling procedure based on Clementi and Raimondi's rules for atomic screening is applied to the cc-pVTZ basis set of atoms where a partial core-hole is created in the uGTS calculations. The average absolute deviation between our predicted 1 s → π ∗ excitations eneergies and experimental values is only 0.16 eV. Singlet-triplet splittings of C 1 s → π ∗ transitions of CO, C 2H 2, C 2H 4, and C 6H 6 also agree with experimental observations. The average absolute deviation of our predicted core-electron binding energies and term values is 0.23 and 0.29 eV, respectively.
Density functional steric analysis of linear and branched alkanes.
Ess, Daniel H; Liu, Shubin; De Proft, Frank
2010-12-16
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E(s)[ρ]), an electrostatic energy term (E(e)[ρ]), and a fermionic quantum energy term (E(q)[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.
Density Functional Steric Analysis of Linear and Branched Alkanes
Ess, Daniel H.; Liu, Shubin; De Proft, Frank
2010-11-18
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E_{e}[[ρ]), an electrostatic energy term (E_{e}[ρ]), and a fermionic quantum energy term (E_{q}[[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.
Hardness of FeB4: density functional theory investigation.
Zhang, Miao; Lu, Mingchun; Du, Yonghui; Gao, Lili; Lu, Cheng; Liu, Hanyu
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).
Metallophilic interactions from dispersion-corrected density-functional theory
Otero-de-la-Roza, Alberto Mallory, Joel D.; Johnson, Erin R.
2014-05-14
In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH{sub 3}){sub 4}]{sup +} cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal.
Extracting electron transfer coupling elements from constrained density functional theory
NASA Astrophysics Data System (ADS)
Wu, Qin; Van Voorhis, Troy
2006-10-01
Constrained density functional theory (DFT) is a useful tool for studying electron transfer (ET) reactions. It can straightforwardly construct the charge-localized diabatic states and give a direct measure of the inner-sphere reorganization energy. In this work, a method is presented for calculating the electronic coupling matrix element (Hab) based on constrained DFT. This method completely avoids the use of ground-state DFT energies because they are known to irrationally predict fractional electron transfer in many cases. Instead it makes use of the constrained DFT energies and the Kohn-Sham wave functions for the diabatic states in a careful way. Test calculations on the Zn2+ and the benzene-Cl atom systems show that the new prescription yields reasonable agreement with the standard generalized Mulliken-Hush method. We then proceed to produce the diabatic and adiabatic potential energy curves along the reaction pathway for intervalence ET in the tetrathiafulvalene-diquinone (Q-TTF-Q) anion. While the unconstrained DFT curve has no reaction barrier and gives Hab≈17kcal /mol, which qualitatively disagrees with experimental results, the Hab calculated from constrained DFT is about 3kcal /mol and the generated ground state has a barrier height of 1.70kcal/mol, successfully predicting (Q-TTF-Q)- to be a class II mixed-valence compound.
Acrolein impairs the cholesterol transport functions of high density lipoproteins.
Chadwick, Alexandra C; Holme, Rebecca L; Chen, Yiliang; Thomas, Michael J; Sorci-Thomas, Mary G; Silverstein, Roy L; Pritchard, Kirkwood A; Sahoo, Daisy
2015-01-01
High density lipoproteins (HDL) are considered athero-protective, primarily due to their role in reverse cholesterol transport, where they transport cholesterol from peripheral tissues to the liver for excretion. The current study was designed to determine the impact of HDL modification by acrolein, a highly reactive aldehyde found in high abundance in cigarette smoke, on the cholesterol transport functions of HDL. HDL was chemically-modified with acrolein and immunoblot and mass spectrometry analyses confirmed apolipoprotein crosslinking, as well as acrolein adducts on apolipoproteins A-I and A-II. The ability of acrolein-modified HDL (acro-HDL) to serve as an acceptor of free cholesterol (FC) from COS-7 cells transiently expressing SR-BI was significantly decreased. Further, in contrast to native HDL, acro-HDL promotes higher neutral lipid accumulation in murine macrophages as judged by Oil Red O staining. The ability of acro-HDL to mediate efficient selective uptake of HDL-cholesteryl esters (CE) into SR-BI-expressing cells was reduced compared to native HDL. Together, the findings from our studies suggest that acrolein modification of HDL produces a dysfunctional particle that may ultimately promote atherogenesis by impairing functions that are critical in the reverse cholesterol transport pathway.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Computational characterization of sodium selenite using density functional theory.
Barraza-Jiménez, Diana; Flores-Hidalgo, Manuel Alberto; Galvan, Donald H; Sánchez, Esteban; Glossman-Mitnik, Daniel
2011-04-01
In this theoretical study we used density functional theory to calculate the molecular and crystalline structures of sodium selenite. Our structural results were compared with experimental data. From the molecular structure we determined the ionization potential, electronic affinity, and global reactivity parameters like electronegativity, hardness, softness and global electrophilic index. A significant difference in the IP and EA values was observed, and this difference was dependent on the calculation method used (employing either vertical or adiabatic energies). Thus, values obtained for the electrophilic index (2.186 eV from vertical energies and 2.188 eV from adiabatic energies) were not significantly different. Selectivity was calculated using the Fukui functions. Since the Mulliken charge study predicted a negative value, it is recommended that AIM should be used in selectivity characterization. It was evident from the selectivity index that sodium atoms are the most sensitive sites to nucleophilic attack. The results obtained in this work provide data that will aid the characterization of compounds used in crop biofortification.
Antisites in III-V semiconductors: Density functional theory calculations
Chroneos, A.; Tahini, H. A.; Schwingenschlögl, U.; Grimes, R. W.
2014-07-14
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
Ganesh, P; Kim, Jeongnim; Park, Changwon; Yoon, Mina; Reboredo, Fernando A; Kent, Paul R C
2014-12-09
Highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based on point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. The results demonstrate that the lithium-carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches.
Ganesh, P.; Kim, Jeongnim; Park, Changwon; Yoon, Mina; Reboredo, Fernando A.; Kent, Paul R. C.
2014-11-03
In highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Moreover, the highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based on point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. Our results demonstrate that the lithium carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches.
Zhang, Changzhe; Bu, Yuxiang
2017-01-25
In this work, the effect of diffuse function types (atom-centered diffuse functions versus floating functions and s-type versus p-type diffuse functions) on the structures and properties of three representative water cluster anions featuring a surface-bound excess electron is studied and we find that an effective combination of such two kinds of diffuse functions can not only reduce the computational cost but also, most importantly, considerably improve the accuracy of results and even avoid incorrect predictions of spectra and the EE shape. Our results indicate that (a) simple augmentation of atom-centered diffuse functions is beneficial for the vertical detachment energy convergence, but it leads to very poor descriptions for the singly occupied molecular orbital (SOMO) and lowest unoccupied molecular orbital (LUMO) distributions of the water cluster anions featuring a surface-bound excess electron and thus a significant ultraviolet spectrum redshift; (b) the ghost-atom-based floating diffuse functions can not only contribute to accurate electronic calculations of the ground state but also avoid poor and even incorrect descriptions of the SOMO and the LUMO induced by excessive augmentation of atom-centered diffuse functions; (c) the floating functions can be realized by ghost atoms and their positions could be determined through an optimization routine along the dipole moment vector direction. In addition, both the s- and p-type floating functions are necessary to supplement in the basis set which are responsible for the ground (s-type character) and excited (p-type character) states of the surface-bound excess electron, respectively. The exponents of the diffuse functions should also be determined to make the diffuse functions cover the main region of the excess electron distribution. Note that excessive augmentation of such diffuse functions is redundant and even can lead to unreasonable LUMO characteristics.
NASA Astrophysics Data System (ADS)
Sundararaman, Ravishankar; Weaver, Kendra; Arias, Tomas
2012-02-01
The study of electrochemical systems within electronic density functional theory requires the handling of non-neutral electronic systems in the plane-wave basis in order to accurately describe charged metallic surfaces; this can be accomplished in joint density functional theory by adding an electrolyte with Debye screening ootnotetextK. L. Weaver and T. A. Arias (under preparation). This capability opens up the opportunity to work in the grand canonical ensemble at fixed chemical potential μ for the electrons, which corresponds directly to the experimental setting in electrochemistry. We present efficient techniques for electronic density functional calculations at fixed μ, and demonstrate the improvement in predictive power over conventional neutral calculations using the underpotential deposition of Cu/Pt(111) as an example: for the first time, we calculate absolute voltages for electrochemical processes in excellent agreement with experiment, instead of voltage shifts alone.
Minimizing density functional failures for non-covalent interactions beyond van der Waals complexes.
Corminboeuf, Clemence
2014-11-18
CONSPECTUS: Kohn-Sham density functional theory offers a powerful and robust formalism for investigating the electronic structure of many-body systems while providing a practical balance of accuracy and computational cost unmatched by other methods. Despite this success, the commonly used semilocal approximations have difficulties in properly describing attractive dispersion interactions that decay with R(-6) at large intermolecular distances. Even in the short to medium range, most semilocal density functionals fail to give an accurate description of weak interactions. The omnipresence of dispersion interactions, which are neglected in the most popular electronic structure framework, has stimulated intense developments during the past decade. In this Account, we summarize our effort to develop and implement dispersion corrections that dramatically reduce the failures of both inter- and intramolecular interaction energies. The proposed schemes range from improved variants of empirical atom pairwise dispersion correction (e.g., dD10) to robust formulations dependent upon the electron density. Emphasis has been placed on introducing more physics into a modified Tang and Toennies damping function and deriving accurate dispersion coefficients. Our most sophisticated and established density-dependent correction, dDsC, is based on a simple generalized gradient approximation (GGA)-like reformulation of the exchange hole dipole moment introduced by Becke and Johnson. Akin to its empirical precursor, dDsC dramatically improves the interaction energy of a variety of standard density functionals simultaneously for typical intermolecular complexes and shorter-range interactions occurring within molecules. The broad applicability and robustness of the dDsC scheme is demonstrated on various representative reaction energies, geometries, and molecular dynamic simulations. The suitability of the a posteriori correction is also established through comparisons with the more
Swanson, Jon; Audie, Joseph
2017-01-16
A fundamental and unsolved problem in biophysical chemistry is the development of a computationally simple, physically intuitive, and generally applicable method for accurately predicting and physically explaining protein-protein binding affinities from protein-protein interaction (PPI) complex coordinates. Here, we propose that the simplification of a previously described six-term PPI scoring function to a four term function results in a simple expression of all physically and statistically meaningful terms that can be used to accurately predict and explain binding affinities for a well-defined subset of PPIs that are characterized by (1) crystallographic coordinates, (2) rigid-body association, (3) normal interface size, and hydrophobicity and hydrophilicity, and (4) high quality experimental binding affinity measurements. We further propose that the four-term scoring function could be regarded as a core expression for future development into a more general PPI scoring function. Our work has clear implications for PPI modeling and structure-based drug design.
NASA Astrophysics Data System (ADS)
Lovett, Ronald
1988-06-01
All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the density functional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these equations which are satisified by the correct kernels, which guarantee a unique solution to the integral equations, and which provide a natural constraint on approximations which can be used in density functional theory. It is also shown that this sensitive behavior is a general property of density functional problems and that the methodology for constructing the constraints is equally general. A variety of applications of density functional theory are reviewed to illustrate practical consequences of this sensitivity.
Velocity analysis with local event slopes related probability density function
NASA Astrophysics Data System (ADS)
Zhang, Peng; Lu, Wenkai; Zhang, Yingqiang
2015-12-01
Macro velocity model plays a key role in seismic imaging and inversion. The performance of traditional velocity analysis methods is degraded by multiples and amplitude-versus-offset (AVO) anomalies. Local event slopes, containing the subsurface velocity information, have been widely used to accomplish common time-domain seismic processing, imaging and velocity estimation. In this paper, we propose a method for velocity analysis with probability density function (PDF) related to local event slopes. We first estimate local event slopes with phase information in the Fourier domain. An adaptive filter is applied to improve the performance of slopes estimator in the low signal-to-noise ratio (SNR) situation. Second, the PDF is approximated with the histogram function, which is related to attributes derived from local event slopes. As a graphical representation of the data distribution, the histogram function can be computed efficiently. By locating the ray path of the first arrival on the semblance image with straight-ray segments assumption, automatic velocity picking is carried out to establish velocity model. Unlike local event slopes based velocity estimation strategies such as averaging filters and image warping, the proposed method does not make the assumption that the errors of mapped velocity values are symmetrically distributed or that the variation of amplitude along the offset is slight. Extension of the method to prestack time-domain migration velocity estimation is also given. With synthetic and field examples, we demonstrate that our method can achieve high resolution, even in the presence of multiples, strong amplitude variations and polarity reversals.
Understanding density functional theory (DFT) and completing it in practice
Bagayoko, Diola
2014-12-15
We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice.
Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model.
Studholme, C; Constable, R T; Duncan, J S
2000-11-01
Mapping of functional magnetic resonance imaging (fMRI) to conventional anatomical MRI is a valuable step in the interpretation of fMRI activations. One of the main limits on the accuracy of this alignment arises from differences in the geometric distortion induced by magnetic field inhomogeneity. This paper describes an approach to the registration of echo planar image (EPI) data to conventional anatomical images which takes into account this difference in geometric distortion. We make use of an additional spin echo EPI image and use the known signal conservation in spin echo distortion to derive a specialized multimodality nonrigid registration algorithm. We also examine a plausible modification using log-intensity evaluation of the criterion to provide increased sensitivity in areas of low EPI signal. A phantom-based imaging experiment is used to evaluate the behavior of the different criteria, comparing nonrigid displacement estimates to those provided by a imagnetic field mapping acquisition. The algorithm is then applied to a range of nine brain imaging studies illustrating global and local improvement in the anatomical alignment and localization of fMRI activations.
Marelli, Damián; Baumgartner, Robert; Majdak, Piotr
2015-01-01
Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology and are essential for listeners to localize sound sources in virtual auditory displays. Since rendering complex virtual scenes is computationally demanding, we propose four algorithms for efficiently representing HRTFs in subbands, i.e., as an analysis filterbank (FB) followed by a transfer matrix and a synthesis FB. All four algorithms use sparse approximation procedures to minimize the computational complexity while maintaining perceptually relevant HRTF properties. The first two algorithms separately optimize the complexity of the transfer matrix associated to each HRTF for fixed FBs. The other two algorithms jointly optimize the FBs and transfer matrices for complete HRTF sets by two variants. The first variant aims at minimizing the complexity of the transfer matrices, while the second one does it for the FBs. Numerical experiments investigate the latency-complexity trade-off and show that the proposed methods offer significant computational savings when compared with other available approaches. Psychoacoustic localization experiments were modeled and conducted to find a reasonable approximation tolerance so that no significant localization performance degradation was introduced by the subband representation. PMID:26681930
Fromager, Emmanuel; Toulouse, Julien; Jensen, Hans Jorgen Aa
2007-02-21
In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy) adequately which, on the other hand, can be described in wave-function theory (WFT), for example, with a multiconfigurational self-consistent field (MCSCF) model. It is therefore of high interest to develop a hybrid model which combines the best of both WFT and DFT approaches. The merge of WFT and DFT can be achieved by splitting the two-electron interaction into long-range and short-range parts. The long-range part is then treated by WFT and the short-range part by DFT. In this work the authors consider the so-called "erf" long-range interaction erf(micror12)/r12, which is based on the standard error function, and where mu is a free parameter which controls the range of the long-/short-range decomposition. In order to formulate a general method, they propose a recipe for the definition of an optimal microopt parameter, which is independent of the approximate short-range functional and the approximate wave function, and they discuss its universality. Calculations on a test set consisting of He, Be, Ne, Mg, H2, N2, and H2O yield microopt approximately 0.4 a.u.. A similar analysis on other types of test systems such as actinide compounds is currently in progress. Using the value of 0.4 a.u. for micro, encouraging results are obtained with the hybrid MCSCF-DFT method for the dissociation energies of H2, N2, and H2O, with both short-range local-density approximation and PBE-type functionals.
Efficient basis sets for non-covalent interactions in XDM-corrected density-functional theory.
Johnson, Erin R; Otero-de-la-Roza, Alberto; Dale, Stephen G; DiLabio, Gino A
2013-12-07
In the development and application of dispersion-corrected density-functional theory, the effects of basis set incompleteness have been largely mitigated through the use of very large, nearly-complete basis sets. However, the use of such large basis sets makes application of these methods inefficient for large systems. In this work, we examine a series of basis sets, including Pople-style, correlation-consistent, and polarization-consistent bases, for their ability to efficiently and accurately predict non-covalent interactions when used in conjunction with the exchange-hole dipole moment (XDM) dispersion model. We find that the polarization-consistent 2 (pc-2) basis sets, and two modifications thereof with some diffuse functions removed, give performance of comparable quality to that obtained with aug-cc-pVTZ basis sets, while being roughly 12 to 23 times faster computationally. The behavior is explained, in part, by the role of diffuse functions in recovering small density changes in the intermolecular region. The general performance of the modified basis sets is tested by application of XDM to standard intermolecular benchmark sets at, and away from, equilibrium.
Electronic structure modeling of InAs/GaSb superlattices with hybrid density functional theory
NASA Astrophysics Data System (ADS)
Garwood, T.; Modine, N. A.; Krishna, S.
2017-03-01
The application of first-principles calculations holds promise for greatly improving our understanding of semiconductor superlattices. Developing a procedure to accurately predict band gaps using hybrid density functional theory lays the groundwork for future studies investigating more nuanced properties of these structures. Our approach allows a priori prediction of the properties of SLS structures using only the band gaps of the constituent materials. Furthermore, it should enable direct investigation of the effects of interface structure, e.g., intermixing or ordering at the interface, on SLS properties. In this paper, we present band gap data for various InAs/GaSb type-II superlattice structures calculated using the generalized Kohn-Sham formulation of density functional theory. A PBE0-type hybrid functional was used, and the portion of the exact exchange was tuned to fit the band gaps of the binary compounds InAs and GaSb with the best agreement to bulk experimental values obtained with 18% of the exact exchange. The heterostructures considered in this study are 6 monolayer (ML) InAs/6 ML GaSb, 8 ML InAs/8 ML GaSb and 10 ML InAs/10 ML GaSb with deviations from the experimental band gaps ranging from 3% to 11%.
Wang, RuLin; Zheng, Xiao; Kwok, YanHo; Xie, Hang; Chen, GuanHua; Yam, ChiYung
2015-04-14
Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.
Spin propensities of octahedral complexes from density functional theory.
Mortensen, Sara R; Kepp, Kasper P
2015-04-30
The fundamental balance between high- and low-spin states of transition metal systems depends on both the metal ion and the ligands surrounding it, as often visualized by the spectrochemical series. Most density functionals do not reproduce this balance, and real spin state propensities depend on orbital pairing and vibrational entropies absent in the spectrochemical series. Thus, we systematically computed the tendency toward high or low spin of "text-book" octahedral metal complexes versus ligand and metal type, using eight density functionals. Dispersion effects were generally <5 kJ/mol, favoring low-spin states. Zero-point energies favored high-spin states up to 33 kJ/mol for strong ligands, but down to a few kilojoules per mole for weak ligands. Vibrational entropy also favored high-spin states up to 40 kJ/mol, most for strong ligands. Jahn-Teller distortion in Co(II) low-spin states, particularly stable d(6) low-spin states, and entropy corrections were consistent with experiment. Entropy and zero-point energy corrections were markedly lower for Co(II) and Mn(III), viz., the differential ligand field stabilization energy, and can only be ignored for weak ligands. The data enable simple assessment of spin state propensities versus ligand and metal type and reveal, e.g., that CN(-) is consistently weaker than CO for M(II) but stronger than CO for M(III) and SCN(-) and NCS(-) change order in M(II) versus M(III) complexes. Contrary to expectation based on the spectrochemical series, Cl(-) and Br(-) are very close in spin state propensity because the pairing penalty for low spin is smaller in Br(-). Thus, for the M(II) complexes, we find a consensus order of Br(-) ∼ Cl(-) < H2O < SCN(-) < NCS(-) ∼ NH3 < CN(-) < CO, whereas for the M(III) complexes, an approximate order is Br(-) ∼ Cl(-) < H2O ∼ NCS(-) ∼ SCN(-)< NH3 < CO < CN(-).
Subsystem functional and the missing ingredient of confinement physics in density functionals.
Armiento, Rickard Roberto; Mattsson, Ann Elisabet; Hao, Feng
2010-08-01
The subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The 'confinement physics,' an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential {yields} density and the density {yields} exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed.
Dai, Yafei; Li, Zhenyu; Yang, Jinlong
2015-08-06
The atomically precise edge chlorination of nanographenes has recently been reported as a crucial technology of functionalization through which the planar structure and optical properties of nanographenes can be significantly changed. To check the effects of molecular size, geometrical symmetry and edge functionalization of nanographenes on their optical properties, a series of nanographenes is studied in the framework of density functional theory with the B3LYP functional. Our results indicate that edge functionalization remarkably changes the nonlinear optical properties and increases the anisotropy of nanographenes compared to the effects of the molecular size and system geometric symmetry. Furthermore, the nonlinear optical properties of nanographenes can be tuned by precise edge functionalization, which opens a new avenue for using nanographenes as nonlinear optical materials.
Density-functional theory study of gramicidin A ion channel geometry and electronic properties.
Todorović, Milica; Bowler, David R; Gillan, Michael J; Miyazaki, Tsuyoshi
2013-12-06
Understanding the mechanisms underlying ion channel function from the atomic-scale requires accurate ab initio modelling as well as careful experiments. Here, we present a density functional theory (DFT) study of the ion channel gramicidin A (gA), whose inner pore conducts only monovalent cations and whose conductance has been shown to depend on the side chains of the amino acids in the channel. We investigate the ground state geometry and electronic properties of the channel in vacuum, focusing on their dependence on the side chains of the amino acids. We find that the side chains affect the ground state geometry, while the electrostatic potential of the pore is independent of the side chains. This study is also in preparation for a full, linear scaling DFT study of gA in a lipid bilayer with surrounding water. We demonstrate that linear scaling DFT methods can accurately model the system with reasonable computational cost. Linear scaling DFT allows ab initio calculations with 10,000-100,000 atoms and beyond, and will be an important new tool for biomolecular simulations.
Global and local curvature in density functional theory
NASA Astrophysics Data System (ADS)
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Calaminici, Patrizia; Janetzko, Florian; Köster, Andreas M; Mejia-Olvera, Roberto; Zuniga-Gutierrez, Bernardo
2007-01-28
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
Density-functional study of plutonium monoxide monohydride
NASA Astrophysics Data System (ADS)
Qiu, Ruizhi; Lu, Haiyan; Ao, Bingyun; Tang, Tao; Chen, Piheng
2017-03-01
The structural, electronic, mechanical, optical, thermodynamic properties of plutonium monoxide monohydride (PuOH) are studied by density-functional calculations within the framework of LDA/GGA and LDA/GGA+U. From the total energy calculation, the lowest-energy crystal structure of PuOH is predicted to have space group F 4 bar 3 m (No. 216). Within the LDA+U framework, the calculated lattice parameter of F 4 bar 3 m -PuOH is in good agreement with the experimental value and the corresponding ground state is predicted to be an antiferromagnetic charge-transfer insulator. Furthermore, we investigate the bonding character of PuOH by analyzing the electron structure and find that there are a stronger Pu-O bond and a weaker Pu-H bond. The mechanical properties including the elastic constants, elastic moduli and Debye's temperature, and the optical properties including the reflectivity and absorption coefficient are also calculated. We then compute the phonon spectrum which verified the dynamical stability of F 4 bar 3 m -PuOH. Some thermodynamic quantities such as the specific heat are evaluated. Finally we calculate the formation energy of PuOH, and the reaction energies for the oxidation of PuOH and PuOH-coated Pu, which are in reasonable agreement with the experimental values.
Dynamical Density Functional Theory and Hydrodynamic Interactions in Confined Systems
NASA Astrophysics Data System (ADS)
Goddard, Benjamin; Nold, Andreas; Kalliadasis, Serafim
2016-11-01
Colloidal systems consist of nano- to micrometer-sized particles suspended in a bath of many more, much smaller and much lighter particles. Motion of the colloidal particles through the bath, e.g. when driven by external forces such as gravity, induces flows in the bath. These flows in turn impart forces on the colloid particles. These bath-mediated forces, known as Hydrodynamic Interactions (HIs) strongly influence the dynamics of the colloid particles. This is particularly true in confined systems, in which the presence of walls substantially modifies the HIs compared to unbounded geometries. For many-particle systems, the many of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. We employ elements from the statistical mechanics of classical fluids, namely Dynamical Density Functional Theory (DDFT), the computational complexity of which is independent of the number of particles to include both inter-particle and particle-wall HI and demonstrate the physical importance of using the correct description of HIs in confined systems. In addition, DDFT allows us to isolate and investigate different components of HIs. Supported by EPSRC Grant EP/L025159.
Van der Waals interactions in density functional theory
NASA Astrophysics Data System (ADS)
Langreth, David C.
2009-03-01
The van der Waals density functional which we introduced half a decade agoootnotetextM. Dion et al. Phys. Rev. Lett. 92, 246401 (2004). and its self-consistent generalizationootnotetextT. Thonhauser et al., Phys. Rev. B 76, 125112 (2007). will be briefly reviewed. There are many collaborators in the application review that will follow, not only those who worked in the physics department at Rutgers% ootnotetextMaxime Dion, Aaron Puzder, T. Thonhauser, Valentino R. Cooper, Shen Li, Eamonn Murray, Lingzhu Kong, and Kyuho Lee. and at Chalmers,% ootnotetextHenrik Rydberg, Svetla Chakarova-K"ack, Jesper Kleis, Elsebeth Schr"oder, Per Hyldgaard, and Bengt I. Lundqvist. but also at Denmarks Technical University,% ootnotetextAndrei Kelkkanen, Poul G. Moses, Jesper Kleis, and Bengt I. Lundqvist. the chemistry department at Rutgers,% ootnotetextKonhoa Li, Jing Li, Yves Chabal, and Wilma K. Olson. and most recently at the University of Texas at Dallas.% ootnotetextNour Nijem and Yves Chabal. I will expand on our recent review article,ootnotetextD. C. Langreth et al., J. Phys. Cond. Mat. (in press). which hopefully will be published before the present talk, and include applications by other groups not listed below. If possible, I will also review results from a more recent collaboration to study nucleosomal DNA and beyond.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Hoft, Jan; Weber, J. K.; Raut, E.; Larson, Vincent E.; Wang, Minghuai; Rasch, Philip J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection.These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2014-06-11
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Density functional theory investigation of sodium azide at high pressure
NASA Astrophysics Data System (ADS)
Steele, B. A.; Landerville, A. C.; Oleynik, I. I.
2014-05-01
High pressure experiments utilizing Raman spectroscopy indicate that the a phase of sodium azide undergoes a polymeric phase transition at high pressure. In this work, the structural and vibrational properties, including the first order Raman and infrared spectra, of the a phase of sodium azide are calculated using first-principles density functional theory up to 92 GPa. The equation of state of α NaN3 is obtained within the quasi-harmonic approximation at various temperatures. Each Raman-active mode blue shifts under compression whereas the doubly degenerate IR-active azide bending mode red-shifts under compression. However, at 70 GPa, the intensity of the Bu IR-active bending mode decreases substantially, and a new distorted azide bending lattice mode appears in the IR spectrum. In contrast to the bending mode, this new mode blue-shifts under compression. No new modes appear in the Raman spectra at high pressure, indicating that the changes in the Raman spectrum seen in experiment at high pressure are signs of new high nitrogen content structures, but not due to sodium azide.
Density functional theory study of phase IV of solid hydrogen
NASA Astrophysics Data System (ADS)
Pickard, Chris J.; Martinez-Canales, Miguel; Needs, Richard J.
2012-06-01
We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using density functional theory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250-295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater.1476-112210.1038/nmat3175 10, 927 (2011) and R. T. Howie , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.125501 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.
DENSITY-FUNCTIONAL STUDY OF THE U-ZR SYSTEM
Landa, A; Soderlind, P; Turchi, P
2008-06-25
Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the {gamma} (bcc) and {delta} (C32) phases are in good agreement with experimental data. The decomposition curve for the {gamma}-based U-Zr solutions is calculated. Our calculations confirm that experimentally observed 'partial' ordering of the alloy components in the {delta}-UZr{sub 2} (AlB{sub 2}) phase, in which Zr atoms occupy the 'Al' position and the two 'B' sites are randomly shared by the U and Zr atoms, is the most energetically favorable within the C32 structure. We argue that stabilization of the {delta}-UZr{sub 2} phase relative to the {alpha}-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr. A comparison with stabilization of the {omega}-phase (also C32) in Zr under compression is made.
Density functional and neutron diffraction studies of lithium polymer electrolytes.
Baboul, A. G.
1998-06-26
The structure of PEO doped with lithium perchlorate has been determined using neutron diffraction on protonated and deuterated samples. The experiments were done in the liquid state. Preliminary analysis indicates the Li-O distance is about 2.0 {angstrom}. The geometries of a series of gas phase lithium salts [LiCF{sub 3}SO{sub 3}, Li(CF{sub 3}SO{sub 2}){sub 2}N, Li(CF{sub 3}SO{sub 2}){sub 2}CH, LiClO{sub 4}, LiPF{sub 6}, LiAsF{sub 6}] used in polymer electrolytes have been optimized at B3LYP/6-31G(d) density functional level of theory. All local minima have been identified. For the triflate, imide, methanide, and perchlorate anions, the lithium cation is coordinated to two oxygens and have binding energies of ca 141 kcal/mol at the B3LYP/6-311+G(3df,2p)/B3LYP/6-31G* level of theory. For the hexafluoroarsenate and hexafluorophosphate the lithium cation is coordinated to three oxygens and have binding energies of ca. 136 kcal/mol.
Excess electrons in ice: a density functional theory study.
Bhattacharya, Somesh Kr; Inam, Fakharul; Scandolo, Sandro
2014-02-21
We present a density functional theory study of the localization of excess electrons in the bulk and on the surface of crystalline and amorphous water ice. We analyze the initial stages of electron solvation in crystalline and amorphous ice. In the case of crystalline ice we find that excess electrons favor surface states over bulk states, even when the latter are localized at defect sites. In contrast, in amorphous ice excess electrons find it equally favorable to localize in bulk and in surface states which we attribute to the preexisting precursor states in the disordered structure. In all cases excess electrons are found to occupy the vacuum regions of the molecular network. The electron localization in the bulk of amorphous ice is assisted by its distorted hydrogen bonding network as opposed to the crystalline phase. Although qualitative, our results provide a simple interpretation of the large differences observed in the dynamics and localization of excess electrons in crystalline and amorphous ice films on metals.
Probability Density Function Analysis of Turbulent Condensation Using GPU Hardware
NASA Astrophysics Data System (ADS)
Keedy, Ryan; Riley, James; Aliseda, Alberto
2014-11-01
Growth of liquid droplets by condensation is an important phenomenon in many environmental and industrial applications. In a homogenous, supersaturated environment, condensation will tend to narrow the diameter distribution of a poly-disperse collection of droplets. However, free shear turbulence can broaden the diameter distribution due to intermittency in the mixing and by subjecting droplets to non-Gaussian supersaturation statistics. In order to understand the condensation behavior of water droplets in a turbulent flow, it is necessary to understand the dispersion of the droplets and transported scalars. We describe a hybrid approach for predicting droplet growth and dispersion in a turbulent mixing layer and compare our computational predictions to experimental data. The approach utilizes a finite-volume code to calculate the fluid velocity field and a particle-mesh Monte Carlo method to track the locations and thermodynamics of the large number of stochastic particles throughout the domain required to resolve the Probability Density Function of the water vapor and droplets. The particle tracking algorithm is designed to take advantage of the computational power of a large number of GPU cores, with significant speed-up when compared against a baseline CPU configuration.
Density Functional Theory for Phase-Ordering Transitions
Wu, Jianzhong
2016-03-30
Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic density functional theory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.
Density functional theory study of oxygen migration in molten carbonate
NASA Astrophysics Data System (ADS)
Lei, Xueling; Haines, Kahla; Huang, Kevin; Qin, Changyong
2016-02-01
The process of oxygen migration in alkali molten carbonate salts has been examined using density functional theory method. All geometries were optimized at the B3LYP/6-31G(d) level, while single point energy corrections were performed using MP4 and CCSD(T). At TS, a O-O-O linkage is formed and O-O bond forming and breaking is concerted. A cooperative "cogwheel" mechanism as described in the equation of CO42- + CO32- → CO32- ⋯O ⋯ CO32- → CO32- + CO42- is involved. The energy barrier is calculated to be 103.0, 136.3 and 127.9 kJ/mol through an intra-carbonate pathway in lithium, sodium and potassium carbonate, respectively. The reliability and accuracy of B3LYP/6-31G(d) were confirmed by CCSD(T). The calculated low values of activation energy indicate that the oxygen transfer in molten carbonate salts is fairly easy. In addition, it is found that lithium carbonate is not only a favorable molten carbonate salt for better cathode kinetics, but also it is widely used for reducing the melting point of Li/Na and Li/K eutectic MC mixtures. The current results imply that the process of oxygen reduction in MC modified cathodes is facilitated by the presence of MC, resulting in an enhancement of cell performance at low operating temperatures.
Density functional studies of model cerium oxide nanoparticles.
Loschen, Christoph; Migani, Annapaola; Bromley, Stefan T; Illas, Francesc; Neyman, Konstantin M
2008-10-01
Density functional plane-wave calculations have been performed to investigate a series of ceria nanoparticles (CeO2-x)(n), n
Embedding germanium in graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Xu, Zhuo; Li, Yangping; Tan, Tingting; Liu, Zhengtang
2017-03-01
Based on the density functional theory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 μB is observed in single Ge-chain incorporated 4 × 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices.
Communication: Dynamical density functional theory for dense suspensions of colloidal hard spheres
NASA Astrophysics Data System (ADS)
Stopper, Daniel; Roth, Roland; Hansen-Goos, Hendrik
2015-11-01
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [D. Stopper et al., Phys. Rev. E 92, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function G(r, t), we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for G(r, t) are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.
Probabilistic density function method for nonlinear dynamical systems driven by colored noise
Barajas-Solano, David A.; Tartakovsky, Alexandre M.
2016-05-01
We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time. We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.
An efficient state-specific scheme of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Chiba, Mahito; Tsuneda, Takao; Hirao, Kimihiko
2006-03-01
A state-specific scheme for time-dependent density functional theory (SS-TDDFT) based on the Davidson algorithm is presented. SS-TDDFT is a method devised for speeding up TDDFT calculations by screening transitions that contribute to a specific excitation. By applying this method to calculations of the low-lying excitation energies of test molecules (N 2, CO, H 2CO, C 2H 4 and C 6H 6), water clusters and polyenes, we found that SS-TDDFT accurately reproduced the excitation energies of standard TDDFT while drastically reducing the rank of the TDDFT response matrix without loss of accuracy. We have thus formulated TDDFT that works more efficiently and economically for memory storage.
NASA Astrophysics Data System (ADS)
Müller, M.; MacDowell, L. G.; Yethiraj, A.
2003-02-01
The surface and interfacial properties of a molecular liquid composed of short linear chains are investigated using molecular density-functional theories. The molecules are modeled as spherical sites connected by springs, and each site interacts with other sites and the surfaces with a modified Lennard-Jones interaction. In the density-functional theories, the ideal gas free energy functional is treated exactly (using a partial enumeration scheme) and the excess (over ideal gas) free energy functional is treated using a weighted density approximation (WDA). The latter requires the thermodynamic properties of the homogeneous fluid and a prescription for the weighting function. The thermodynamics of the homogeneous system is described via Wertheim's perturbation theory, and various approximations for the weighting function in the WDA are tested. We find that for the theory to be accurate, it is important to decompose the excess free energy function into a repulsive and an attractive part, with different approximations for the two parts. Results from several approximations are in good agreement with Monte Carlo simulations for the chain conformations, density oscillations (packing) in the vicinity of surfaces, and the surface tension, for both liquid-vapor interfaces and attractive surfaces.
NASA Astrophysics Data System (ADS)
Zucca, E.; Zamorani, G.; Vettolani, G.; Cappi, A.; Merighi, R.; Mignoli, M.; Stirpe, G. M.; MacGillivray, H.; Collins, C.; Balkowski, C.; Cayatte, V.; Maurogordato, S.; Proust, D.; Chincarini, G.; Guzzo, L.; Maccagni, D.; Scaramella, R.; Blanchard, A.; Ramella, M.
1997-10-01
The ESO Slice Project (ESP) is a galaxy redshift survey we have recently completed as an ESO Key-Project over about 23 square degrees, in a region near the South Galactic Pole. The survey is nearly complete to the limiting magnitude b_J_=19.4 and consists of 3342 galaxies with reliable redshift determination. The ESP survey is intermediate between shallow, wide angle samples and very deep, one-dimensional pencil beams: spanning a volume of ~5x10^4^h^-3^Mpc^3^ at the sensitivity peak (z~0.1), it provides an accurate determination of the "local" luminosity function and the mean galaxy density. We find that, although a Schechter function (with α=-1.22, M^*^_bJ_=-19.61+5logh and φ^*^=0.020h^3^/Mpc^3^) is an acceptable representation of the luminosity function over the entire range of magnitudes (M_bJ_<=-12.4+5logh), our data suggest the presence of a steepening of the luminosity function for M_bJ_>=-17+5logh. Such a steepening at the faint end of the luminosity function, well fitted by a power law with slope β~-1.6, is almost completely due to galaxies with emission lines: in fact, dividing our galaxies into two samples, i.e. galaxies with and without emission lines, we find significant differences in their luminosity functions. In particular, galaxies with emission lines show a significantly steeper slope and a fainter M^*^. The amplitude and the α and M^*^ parameters of our luminosity function are in good agreement with those of the AUTOFIB redshift survey (Ellis et al. 1996). Vice-versa, our amplitude is significantly higher, by a factor ~1.6 at M~M^*^, than that found for both the Stromlo-APM (Loveday et al. 1992) and the Las Campanas (Lin et al. 1996) redshift surveys. Also the faint end slope of our luminosity function is significantly steeper than that found in these two surveys. The galaxy number density for M_bJ_<=-16+5logh is well determined (n{bar}=0.08+/-0.015h^3^/Mpc^3^). Its estimate for M_bJ_<=-12.4+5logh is more uncertain, ranging from n{bar}=0.28h
On Predicting Mössbauer Parameters of Iron-Containing Molecules with Density-Functional Theory
2014-01-01
The performance of six frequently used density functional theory (DFT) methods (RPBE, OLYP, TPSS, B3LYP, B3LYP*, and TPSSh) in the prediction of Mössbauer isomer shifts(δ) and quadrupole splittings (ΔEQ) is studied for an extended and diverse set of Fe complexes. In addition to the influence of the applied density functional and the type of the basis set, the effect of the environment of the molecule, approximated with the conducting-like screening solvation model (COSMO) on the computed Mössbauer parameters, is also investigated. For the isomer shifts the COSMO-B3LYP method is found to provide accurate δ values for all 66 investigated complexes, with a mean absolute error (MAE) of 0.05 mm s–1 and a maximum deviation of 0.12 mm s–1. Obtaining accurate ΔEQ values presents a bigger challenge; however, with the selection of an appropriate DFT method, a reasonable agreement can be achieved between experiment and theory. Identifying the various chemical classes of compounds that need different treatment allowed us to construct a recipe for ΔEQ calculations; the application of this approach yields a MAE of 0.12 mm s–1 (7% error) and a maximum deviation of 0.55 mm s–1 (17% error). This accuracy should be sufficient for most chemical problems that concern Fe complexes. Furthermore, the reliability of the DFT approach is verified by extending the investigation to chemically relevant case studies which include geometric isomerism, phase transitions induced by variations of the electronic structure (e.g., spin crossover and inversion of the orbital ground state), and the description of electronically degenerate triplet and quintet states. Finally, the immense and often unexploited potential of utilizing the sign of the ΔEQ in characterizing distortions or in identifying the appropriate electronic state at the assignment of the spectral lines is also shown. PMID:25821417
Huang, Ying; Rong, Chunying; Zhang, Ruiqin; Liu, Shubin
2017-01-01
Wave function theory (WFT) and density functional theory (DFT)-the two most popular solutions to electronic structure problems of atoms and molecules-share the same origin, dealing with the same subject yet using distinct methodologies. For example, molecular orbitals are artifacts in WFT, whereas in DFT, electron density plays the dominant role. One question that needs to be addressed when using these approaches to appreciate properties related to molecular structure and reactivity is if there is any link between the two. In this work, we present a piece of strong evidence addressing that very question. Using five polymeric systems as illustrative examples, we reveal that using quantities from DFT such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, Onicescu information energy, Rényi entropy, etc., one is able to accurately evaluate orbital-related properties in WFT like frontier orbital energies and the HOMO (highest occupied molecular orbital)/LUMO (lowest unoccupied molecular orbital) gap. We verified these results at both the whole molecule level and the atoms-in-molecules level. These results provide compelling evidence suggesting that WFT and DFT are complementary to each other, both trying to comprehend the same properties of the electronic structure and molecular reactivity from different perspectives using their own characteristic vocabulary. Hence, there should be a bridge or bridges between the two approaches.
Hlushak, S. P.; Cummings, P. T.; McCabe, C.
2013-12-21
Adsorption of flexible oligomers into narrow cylindrical pores has been studied by means of several versions of classical density functional theory (CDFT) and Monte Carlo simulation. The adsorption process is interesting to study due to the competition between the entropic depletion of oligomers from the pores and the wall–oligomer attraction. It is also challenging to describe using current CDFTs, which tend to overestimate the amount of the adsorbed fluid. From a comparison of several different CDFT approaches, we find that this is due to the assumption of ideal or freely jointed chain conformations. Moreover, it is demonstrated that it is impossible to obtain a reasonable description of the adsorption isotherms without taking into account accurate contact values in the distribution functions describing the structure of the reference monomer fluid. At low densities, more accurate result are obtained in comparison with Monte Carlo simulation data when accurate contact values are incorporated into the theory rather than the more commonly used hard-sphere contact value. However, even the CDFT with accurate contact values still overestimates the amount of the adsorbed fluid due to the ideal or freely jointed chain approximation, used for the description of chain conformations in most CDFT approaches. We find that significant improvement can achieved by employing self-consistent field theory, which samples self-avoiding chain conformations and decreases the number of possible chain conformations, and, consequently, the amount of the adsorbed fluid.
Symmetry Energy as a Function of Density and Mass
Danielewicz, Pawel; Lee, Jenny
2007-10-26
Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the symmetry energy at subnormal densities produces mass dependence of nuclear symmetry coefficient and, thus, can be constrained by that latter dependence. We deduce values of the mass dependent symmetry coefficients, by using excitation energies to isobaric analog states. The coefficient systematic, for intermediate and high masses, is well described in terms of the symmetry coefficient values of a{sub a}{sup V} = (31.5-33.5) MeV for the volume coefficient and a{sub a}{sup S} = (9-12) MeV for the surface coefficient. These two further correspond to the parameter values describing density dependence of symmetry energy, of L{approx}95 MeV and K{sub sym}{approx}25 MeV.
Density functional study of condensation in capped capillaries
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Savva, N.; Kalliadasis, S.
2015-07-01
We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤slant {{T}\\text{cw}} ) or continuous (at T\\gt {{T}\\text{cw}} ), where {{T}\\text{cw}} is the capillary wetting temperature. At T \\gt {{T}\\text{cw}} , the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.
Antioxidant Properties of Kynurenines: Density Functional Theory Calculations
2016-01-01
Kynurenines, the main products of tryptophan catabolism, possess both prooxidant and anioxidant effects. Having multiple neuroactive properties, kynurenines are implicated in the development of neurological and cognitive disorders, such as Alzheimer's, Parkinson's, and Huntington's diseases. Autoxidation of 3-hydroxykynurenine (3HOK) and its derivatives, 3-hydroxyanthranilic acid (3HAA) and xanthommatin (XAN), leads to the hyperproduction of reactive oxygen species (ROS) which damage cell structures. At the same time, 3HOK and 3HAA have been shown to be powerful ROS scavengers. Their ability to quench free radicals is believed to result from the presence of the aromatic hydroxyl group which is able to easily abstract an electron and H-atom. In this study, the redox properties for kynurenines and several natural and synthetic antioxidants have been calculated at different levels of density functional theory in the gas phase and water solution. Hydroxyl bond dissociation enthalpy (BDE) and ionization potential (IP) for 3HOK and 3HAA appear to be lower than for xanthurenic acid (XAA), several phenolic antioxidants, and ascorbic acid. BDE and IP for the compounds with aromatic hydroxyl group are lower than for their precursors without hydroxyl group. The reaction rate for H donation to *O-atom of phenoxyl radical (Ph-O*) and methyl peroxy radical (Met-OO*) decreases in the following rankings: 3HOK ~ 3HAA > XAAOXO > XAAENOL. The enthalpy absolute value for Met-OO* addition to the aromatic ring of the antioxidant radical increases in the following rankings: 3HAA* < 3HOK* < XAAOXO* < XAAENOL*. Thus, the high free radical scavenging activity of 3HAA and 3HOK can be explained by the easiness of H-atom abstraction and transfer to O-atom of the free radical, rather than by Met-OO* addition to the kynurenine radical. PMID:27861556
Laser Spectroscopy and Density Functional Study on Niobium Dimer Cation
NASA Astrophysics Data System (ADS)
Aydin, Metin; Lombardi, John R.
2009-06-01
Resonant multiphoton fragmentation spectra of niobium dimer cation (Nb2+) have been obtained by utilizing laser vaporization of a Nb metal target. Ions are mass-selected with a time-of-flight mass spectrometer followed by a mass gate, then fragmented with a pulsed dye laser, and the resulting fragment ions are detected with a second time-of-flight reflectron mass spectrometer and multichannel plate. Photon resonances are detected by monitoring ion current as a function of fragmentation laser wavelength. A rich, but complex spectrum of the cation is obtained. The bands display a characteristic multiplet structure that may be interpreted as due to transitions from the ground state X^{4}{Σ}^{-}({Ω}g) to several excited states, X^{4}{Π}({Ω}u) and X^{4}{Σ}(^{-}{Ω}u). The ground state X^{4}{Σ}^{-}({Ω}g) is derived from the electron configuration ({π}{_u})^{4} (1{σ}{_g})^{2}(2{σ}{_g})^{1} ({δ}{_g})^{2}. The two spin-orbit components are split by 145 cm^{-1} due to a strong second-order isoconfigurational spin-orbit interaction with the low-lying ^{2}{Σ}^{+}({Ω}g) state. The vibrational frequencies of the ground sate and the excited state of Nb2+ are identified as well as molecular spin-orbit constants (A{_S}{_O}) in the excited state. The electronic structure of niobium dimer cation was investigated using density functional theory. For the electronic ground state, the predicted spectroscopic properties were in good agreement with experiment. Calculations on excited states reveal congested manifolds of quartet and doublet electronic states in the range 0-30,000 cm^{-1}, reflecting the multitude of possible electronic promotions among the 4d- and 5s-based molecular orbitals. Comparisons are drawn between Nb^{+}{_2} and the prevalent isoelectronic molecules V^{+}{_2}/NbV^{+}/Nb{_2}/V{_2}/NbV. M. Aydin and John R. Lombardi J. Phys. Chem. A. xx XXXX 2009.
Pavelcík, Frantisek; Václavík, Jirí
2010-09-01
The automatic building of protein structures with tripeptidic and tetrapeptidic fragments was investigated. The oligopeptidic conformers were positioned in the electron-density map by a phased rotation, conformation and translation function and refined by a real-space refinement. The number of successfully located fragments lay within the interval 75-95% depending on the resolution and phase quality. The overlaps of partially located fragments were analyzed. The correctly positioned fragments were connected into chains. Chains formed in this way were extended directly into the electron density and a sequence was assigned. In the initial stage of the model building the number of located fragments was between 60% and 95%, but this number could be increased by several cycles of reciprocal-space refinement and automatic model rebuilding. A nearly complete structure can be obtained on the condition that the resolution is reasonable. Computer graphics will only be needed for a final check and small corrections.
Stoitsov, M.; Kortelainen, M.; Schunck, N.; Bogner, S. K.; Gebremariam, B.; Duguet, T.
2010-11-15
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
Nishimoto, Yoshio
2015-09-07
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
A comparative density functional study on electrical properties of layered penta-graphene
Yu, Zhi Gen Zhang, Yong-Wei
2015-10-28
We present a comparative study of the influence of the number of layers, the biaxial strain in the range of −3% to 3%, and the stacking misalignments on the electronic properties of a new 2D carbon allotrope, penta-graphene (PG), based on hybrid-functional method within the density functional theory (DFT). In comparison with local exchange-correlation approximation in the DFT, the hybrid-functional provides an accurate description on the degree of p{sub z} orbitals localization and bandgap. Importantly, the predicted bandgap of few-layer PG has a weak layer dependence. The bandgap of monolayer PG is 3.27 eV, approximately equal to those of GaN and ZnO; and the bandgap of few-layer PG decreases slowly with the number of layers (N) and converge to 2.57 eV when N ≥ 4. Our calculations using HSE06 functional on few-layer PG reveal that bandgap engineering by stacking misalignment can further tune the bandgap down to 1.37 eV. Importantly, there is no direct-to-indirect bandgap transition in PG by varying strain, layer number, and stacking misalignment. Owing to its tunable, robustly direct, and wide bandgap characteristics, few-layer PG is promising for optoelectronic and photovoltaic applications.