Accurate density functional thermochemistry for larger molecules.
Raghavachari, K.; Stefanov, B. B.; Curtiss, L. A.; Lucent Tech.
1997-06-20
Density functional methods are combined with isodesmic bond separation reaction energies to yield accurate thermochemistry for larger molecules. Seven different density functionals are assessed for the evaluation of heats of formation, Delta H 0 (298 K), for a test set of 40 molecules composed of H, C, O and N. The use of bond separation energies results in a dramatic improvement in the accuracy of all the density functionals. The B3-LYP functional has the smallest mean absolute deviation from experiment (1.5 kcal mol/f).
Accurate ionization potential of semiconductors from efficient density functional calculations
NASA Astrophysics Data System (ADS)
Ye, Lin-Hui
2016-07-01
Despite its huge successes in total-energy-related applications, the Kohn-Sham scheme of density functional theory cannot get reliable single-particle excitation energies for solids. In particular, it has not been able to calculate the ionization potential (IP), one of the most important material parameters, for semiconductors. We illustrate that an approximate exact-exchange optimized effective potential (EXX-OEP), the Becke-Johnson exchange, can be used to largely solve this long-standing problem. For a group of 17 semiconductors, we have obtained the IPs to an accuracy similar to that of the much more sophisticated G W approximation (GWA), with the computational cost of only local-density approximation/generalized gradient approximation. The EXX-OEP, therefore, is likely as useful for solids as for finite systems. For solid surfaces, the asymptotic behavior of the vx c has effects similar to those of finite systems which, when neglected, typically cause the semiconductor IPs to be underestimated. This may partially explain why standard GWA systematically underestimates the IPs and why using the same GWA procedures has not been able to get an accurate IP and band gap at the same time.
An Accurate Density Functional from Exchange-Correlation Hole
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang
The exchange-correlation hole is most fundamentally important in the development and understanding of density functional theory (DFT). However, due to the nonlocal nature of the exchange-correlation hole, development of DFT from the underlying hole presents a great challenge, and the works along this direction are limited. Here I will discuss a novel nonempirical DFT based on a semilocal hole, which is obtained from the density matrix expansion. Extensive tests on molecules and solids show that this functional can achieve remarkable accuracy for wide-ranging properties in condensed matter physics and quantum chemistry. This work was supported by NSF under Grant No. CHE-1261918.
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. PMID:27563956
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. PMID:27240749
Accurate calculation and modeling of the adiabatic connection in density functional theory
NASA Astrophysics Data System (ADS)
Teale, A. M.; Coriani, S.; Helgaker, T.
2010-04-01
AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here.
Accurate ab Initio Spin Densities
2012-01-01
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]. PMID:22707921
NASA Astrophysics Data System (ADS)
Skone, Jonathan; Govoni, Marco; Galli, Giulia
Dielectric-dependent hybrid [DDH] functionals have recently been shown to yield highly accurate energy gaps and dielectric constants for a wide variety of solids, at a computational cost considerably less than standard GW calculations. The fraction of exact exchange included in the definition of DDH functionals depends (self-consistently) on the dielectric constant of the material. In the present talk we introduce a range-separated (RS) version of DDH functionals where short and long-range components are matched using material dependent, non-empirical parameters. Comparing with state of the art GW calculations and experiment, we show that such RS hybrids yield accurate electronic properties of both molecules and solids, including energy gaps, photoelectron spectra and absolute ionization potentials. This work was supported by NSF-CCI Grant Number NSF-CHE-0802907 and DOE-BES.
NASA Astrophysics Data System (ADS)
Balabin, Roman M.; Lomakina, Ekaterina I.
2009-08-01
Artificial neural network (ANN) approach has been applied to estimate the density functional theory (DFT) energy with large basis set using lower-level energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree-Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantum-chemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several low-level energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFT energies was 0.6±0.2 kcal mol-1. In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/6-311G(3df,3pd) and DFT/6-311G(2df,2pd) energy estimation was developed, and the benchmark results were provided.
Santiago, Régis Tadeu; Haiduke, Roberto Luiz Andrade
2015-10-30
This research provides a performance investigation of density functional theory and also proposes new functional parameterizations to deal with electric field gradient (EFG) calculations at nuclear positions. The entire procedure is conducted within the four-component formalism. First, we noticed that traditional hybrid and long-range corrected functionals are more efficient in the description of EFG variations for a set of elements (indium, antimony, iodine, lutetium, and hafnium) among linear molecules. Thus, we selected the PBE0, B3LYP, and CAM-B3LYP functionals and promoted a reoptimization of their parameters for a better description of these EFG changes. The PBE0q variant developed here showed an overall promising performance in a validation test conducted with potassium, iodine, copper, and gold. In general, the correlation coefficients found in linear regressions between experimental nuclear quadrupole coupling constants and calculated EFGs are improved while the systematic EFG errors also decrease as a result of this reparameterization. PMID:26284820
NASA Astrophysics Data System (ADS)
Małolepsza, Edyta; Witek, Henryk A.; Morokuma, Keiji
2005-09-01
An optimization technique for enhancing the quality of repulsive two-body potentials of the self-consistent-charge density-functional tight-binding (SCC-DFTB) method is presented and tested. The new, optimized potentials allow for significant improvement of calculated harmonic vibrational frequencies. Mean absolute deviation from experiment computed for a group of 14 hydrocarbons is reduced from 59.0 to 33.2 cm -1 and maximal absolute deviation, from 436.2 to 140.4 cm -1. A drawback of the new family of potentials is a lower quality of reproduced geometrical and energetic parameters.
Accurate hydrogen bond energies within the density functional tight binding method.
Domínguez, A; Niehaus, T A; Frauenheim, T
2015-04-01
The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water-containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expansion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB. PMID:25763597
Calbo, Joaquín; Ortí, Enrique; Sancho-García, Juan C; Aragó, Juan
2015-03-10
In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems. PMID:26579747
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.
Matanović, Ivana; Atanassov, Plamen; Kiefer, Boris; Garzon, Fernando H; Henson, Neil J
2014-10-01
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 -2.62 and -1.1% for the N-N stretching and Rh-H 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 Rh-H and N-N stretching modes from the bulk phonons and by solving one- and two-dimensional Schrödinger equation associated with the Rh-H, Rh-N, and N-N potential energy we calculated the anharmonic correction for N-N and Rh-H stretching modes as -31 cm(-1) and -77 cm(-1) at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. PMID:25164265
Jiang, Bin; Guo, Hua
2016-08-01
In search for an accurate description of the dissociative chemisorption of water on the Ni(111) surface, we report a new nine-dimensional potential energy surface (PES) based on a large number of density functional theory points using the RPBE functional. Seven-dimensional quantum dynamical calculations have been carried out on the RPBE PES, followed by site averaging and lattice effect corrections, yielding sticking probabilities that are compared with both the previous theoretical results based on a PW91 PES and experiment. It is shown that the RPBE functional increases the reaction barrier, but has otherwise a minor impact on the PES topography. Better agreement with experimental results is obtained with the new PES, but the agreement is still not quantitative. Possible sources of the remaining discrepancies are discussed. PMID:27436348
NASA Astrophysics Data System (ADS)
Zhao, P. W.; Song, L. S.; Sun, B.; Geissel, H.; Meng, J.
2012-12-01
The covariant density functional theory with the point-coupling interaction PC-PK1 is compared with new and accurate experimental masses in the element range from 50 to 91. The experimental data are from a mass measurement performed with the storage ring mass spectrometry at Gesellschaft für Schwerionenforschung (GSI) [Chen , Nucl. Phys. ANUPABL0375-947410.1016/j.nuclphysa.2012.03.002 882, 71 (2012)]. Although the microscopic theory contains only 11 parameters, it agrees well with the experimental data. The comparison is characterized by a rms deviation of 0.859 MeV. For even-even nuclei, the theory agrees within about 600 keV. Larger deviations are observed in this comparison for the odd-A and odd-odd nuclei. Improvements and possible reasons for the deviations are discussed in this contribution as well.
Sun, Y. Y.; Kim, Y. H.; Lee, K.; Zhang, S. B.
2008-01-01
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.
Sutton, Christopher; Gray, Matthew T.; Brunsfeld, Max; Parrish, Robert M.; Sherrill, C. David; Sears, John S.; Brédas, Jean-Luc E-mail: thomas.koerzdoerfer@uni-potsdam.de; Körzdörfer, Thomas E-mail: thomas.koerzdoerfer@uni-potsdam.de
2014-02-07
We investigate the torsion potentials in two prototypical π-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains.
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.
Kanai, Y; Takeuchi, N
2009-10-14
We revisit the molecular line growth mechanism of styrene on the hydrogenated Si(001) 2x1 surface. In particular, we investigate the energetics of the radical chain reaction mechanism by means of diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) calculations. For the exchange correlation (XC) functional we use the non-empirical generalized-gradient approximation (GGA) and meta-GGA. We find that the QMC result also predicts the intra dimer-row growth of the molecular line over the inter dimer-row growth, supporting the conclusion based on DFT results. However, the absolute magnitudes of the adsorption and reaction energies, and the heights of the energy barriers differ considerably between the QMC and DFT with the GGA/meta-GGA XC functionals.
Ratcliff, Laura E; Grisanti, Luca; Genovese, Luigi; Deutsch, Thierry; Neumann, Tobias; Danilov, Denis; Wenzel, Wolfgang; Beljonne, David; Cornil, Jérôme
2015-05-12
A fast and accurate scheme has been developed to evaluate two key molecular parameters (on-site energies and transfer integrals) that govern charge transport in organic supramolecular architecture devices. The scheme is based on a constrained density functional theory (CDFT) approach implemented in the linear-scaling BigDFT code that exploits a wavelet basis set. The method has been applied to model disordered structures generated by force-field simulations. The role of the environment on the transport parameters has been taken into account by building large clusters around the active molecules involved in the charge transfer. PMID:26574411
NASA Astrophysics Data System (ADS)
Wiktor, Julia; Jomard, Gérald; Torrent, Marc
2015-09-01
Many techniques have been developed in the past in order to compute positron lifetimes in materials from first principles. However, there is still a lack of a fast and accurate self-consistent scheme that could handle accurately the forces acting on the ions induced by the presence of the positron. We will show in this paper that we have reached this goal by developing the two-component density functional theory within the projector augmented-wave (PAW) method in the open-source code abinit. This tool offers the accuracy of the all-electron methods with the computational efficiency of the plane-wave ones. We can thus deal with supercells that contain few hundreds to thousands of atoms to study point defects as well as more extended defects clusters. Moreover, using the PAW basis set allows us to use techniques able to, for instance, treat strongly correlated systems or spin-orbit coupling, which are necessary to study heavy elements, such as the actinides or their compounds.
NASA Astrophysics Data System (ADS)
Teale, Andrew M.; Lutnæs, Ola B.; Helgaker, Trygve; Tozer, David J.; Gauss, Jürgen
2013-01-01
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)], 10.1063/1.3242081, 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.
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. PMID:19603962
Get accurate LNG densities with COSTALD
Hankinson, R.W.; Coker, T.A.; Thomson, G.H.
1982-04-01
A fine-tuned version of the COSTALD correlation predicts the densities for 40 LNG-type mixtures at an average absolute error of 0.078%. When tested against 285 points of low-temperature data collected by the US National Bureau of Standards, the average error was 0.199%, compared with a 0.227% error obtained with the NBS's McCarty-Klosek-McKinley technique. The COSTALD correlation relates the saturated molar volume of a liquid to a characteristic volume, the reduced temperature, and, a modified acentric factor for each stream component. The fine-tuning involved adding several interaction parameters dervied from binary density data.
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. PMID:27537680
Precise and Accurate Density Determination of Explosives Using Hydrostatic Weighing
B. Olinger
2005-07-01
Precise and accurate density determination requires weight measurements in air and water using sufficiently precise analytical balances, knowledge of the densities of air and water, knowledge of thermal expansions, availability of a density standard, and a method to estimate the time to achieve thermal equilibrium with water. Density distributions in pressed explosives are inferred from the densities of elements from a central slice.
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.
Chan, Bun; Radom, Leo
2016-08-01
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). PMID:27471908
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; 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. PMID:26851912
Partition density functional theory
NASA Astrophysics Data System (ADS)
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
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.
Molecular adsorption at Pt(111). How accurate are DFT functionals?
Gautier, Sarah; Steinmann, Stephan N; Michel, Carine; Fleurat-Lessard, Paul; Sautet, Philippe
2015-11-21
Molecular chemisorption at a metal surface is a key step for many processes, such as catalysis, electrochemistry, surface treatment, tribology and friction. Modeling with density functional theory is largely used on these systems. From a detailed comparison with accurate micro-calorimetric data on ten systems (involving ethylene, cyclohexene, benzene, naphthalene, CO, O2, H2, methane, ethane), we study the accuracy, for chemisorption on Pt(111), of five exchange-correlation functionals including one generalized gradient approximation functional (PBE) and four functionals that take into account van der Waals interactions (optPBE-vdW, optB86b-vdW, BEEF-vdW, PBE-dDsC). If the functionals used provide very similar geometries and electronic structures, as shown by projected density of states, they give strikingly different results for the adsorption energy of molecules on Pt(111). Among the set of chemisorption data, the lowest mean absolute deviations (MAD) are obtained with the optPBE-vdW and PBE-dDsC functionals (∼0.2 eV) while PBE and optB86b-vdW give twice larger MAD (∼0.45 eV). BEEF-vdW is intermediate with a MAD of 0.33 eV. For laterally π-bound unsaturated hydrocarbons (cyclohexene, benzene, naphthalene) the PBE and the BEEF-vdW functionals are severally under-bound, while optPBE-vdW and PBE-dDsC provide a good match with experiments. Hence both the incorporation of van der Waals dispersive forces and the choice of the exchange functional have a key influence on the chemisorption energy. Vertically bound ethylidyne and CO are in contrast over-bound with all functionals, the best agreement being obtained with BEEF-vdW. None of the selected functionals hence provides a universally accurate treatment of chemisorption energies. PMID:26455444
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: 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
Locality of correlation in density functional theory
NASA Astrophysics Data System (ADS)
Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano
2016-08-01
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.
Locality of correlation in density functional theory.
Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano
2016-08-01
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed. PMID:27497544
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.
Fast and accurate Coulomb calculation with Gaussian functions.
Füsti-Molnár, László; Kong, Jing
2005-02-15
Coulomb interaction is one of the major time-consuming components in a density functional theory (DFT) calculation. In the last decade, dramatic progresses have been made to improve the efficiency of Coulomb calculation, including continuous fast multipole method (CFMM) and J-engine method, all developed first inside Q-Chem. The most recent development is the advent of Fourier transform Coulomb method developed by Fusti-Molnar and Pulay, and an improved version of the method has been recently implemented in Q-Chem. It replaces the least efficient part of the previous Coulomb methods with an accurate numerical integration scheme that scales in O(N2) instead of O(N4) with the basis size. The result is a much smaller slope in the linear scaling with respect to the molecular size and we will demonstrate through a series of benchmark calculations that it speeds up the calculation of Coulomb energy by several folds over the efficient existing code, i.e., the combination of CFMM and J-engine, without loss of accuracy. Furthermore, we will show that it is complementary to the latter and together the three methods offer the best performance for Coulomb part of DFT calculations, making the DFT calculations affordable for very large systems involving thousands of basis functions. PMID:15743222
Density Functionals of Chemical Bonding
Putz, Mihai V.
2008-01-01
The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems. PMID:19325846
Rohmann, Kai; Hölscher, Markus; Leitner, Walter
2016-01-13
The catalytic hydrogenation of cyclohexene and 1-methylcyclohexene is investigated experimentally and by means of density functional theory (DFT) computations using novel ruthenium Xantphos(Ph) (4,5-bis(diphenylphosphino)-9,9-dimethylxanthene) and Xantphos(Cy) (4,5-bis(dicyclohexylphosphino)-9,9-dimethylxanthene) precatalysts [Ru(Xantphos(Ph))(PhCO2)(Cl)] (1) and [Ru(Xantphos(Cy))(PhCO2)(Cl)] (2), the synthesis, characterization, and crystal structures of which are reported. The intention of this work is to (i) understand the reaction mechanisms on the microscopic level and (ii) compare experimentally observed activation barriers with computed barriers. The Gibbs free activation energy ΔG(⧧) was obtained experimentally with precatalyst 1 from Eyring plots for the hydrogenation of cyclohexene (ΔG(⧧) = 17.2 ± 1.0 kcal/mol) and 1-methylcyclohexene (ΔG(⧧) = 18.8 ± 2.4 kcal/mol), while the Gibbs free activation energy ΔG(⧧) for the hydrogenation of cyclohexene with precatalyst 2 was determined to be 21.1 ± 2.3 kcal/mol. Plausible activation pathways and catalytic cycles were computed in the gas phase (M06-L/def2-SVP). A variety of popular density functionals (ωB97X-D, LC-ωPBE, CAM-B3LYP, B3LYP, B97-D3BJ, B3LYP-D3, BP86-D3, PBE0-D3, M06-L, MN12-L) were used to reoptimize the turnover determining states in the solvent phase (DF/def2-TZVP; IEF-PCM and/or SMD) to investigate how well the experimentally obtained activation barriers can be reproduced by the calculations. The density functionals B97-D3BJ, MN12-L, M06-L, B3LYP-D3, and CAM-B3LYP reproduce the experimentally observed activation barriers for both olefins very well with very small (0.1 kcal/mol) to moderate (3.0 kcal/mol) mean deviations from the experimental values indicating for the field of hydrogenation catalysis most of these functionals to be useful for in silico catalyst design prior to experimental work. PMID:26713773
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
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.
Semiclassical origins of density functionals
NASA Astrophysics Data System (ADS)
Burke, Kieron
By careful numerical analysis of non-relativistic atomic correlation energies, we show that (a) the local density approximation becomes relatively exact for the correlation energy as the atomic number approaches infinity, (b) we find the leading correction, which is about 38.5 milliHartrees per atom, (c) show how this correction dominates for larger atoms and (d) how to construct a generalized gradient approximation that respects this limit (See KB, A. Cancio, T. Gould, S. Pittalis, arXiv:1409.4834). The relevance to density functional calculations will also be explained. Support provided by NSF CHE-1464795.
Density Functional Theory Models for Radiation Damage
NASA Astrophysics Data System (ADS)
Dudarev, S. L.
2013-07-01
Density functional theory models developed over the past decade provide unique information about the structure of nanoscale defects produced by irradiation and about the nature of short-range interaction between radiation defects, clustering of defects, and their migration pathways. These ab initio models, involving no experimental input parameters, appear to be as quantitatively accurate and informative as the most advanced experimental techniques developed for the observation of radiation damage phenomena. Density functional theory models have effectively created a new paradigm for the scientific investigation and assessment of radiation damage effects, offering new insight into the origin of temperature- and dose-dependent response of materials to irradiation, a problem of pivotal significance for applications.
Teaching Density Functional Theory Through Experiential Learning
NASA Astrophysics Data System (ADS)
Narasimhan, Shobhana
2015-09-01
Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school.
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. PMID:24524947
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.
Ions in solution: Density corrected density functional theory (DC-DFT)
Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
2014-05-14
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl{sup −} and HO·H{sub 2}O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
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.
]: a density functional theory investigation
NASA Astrophysics Data System (ADS)
Ulian, Gianfranco; Tosoni, Sergio; Valdrè, Giovanni
2014-09-01
In this work, we modelled the structure, the compressional behaviour and the physical properties of talc over a wide range of pressure using a quantum mechanical approach based on periodic boundary conditions. We adopted the density functional theory using the B3LYP-D* functional, which includes a correction for the dispersive forces and all-electron Gaussian-type orbitals basis sets. An atomic level description of the athermal pressure-induced structural modification of talc is provided. From the compression results, we obtained the athermal ( T = 0 K) bulk modulus ( K T0), its first derivative ( K') and the athermal volume at zero pressure ( V 0) by a third-order Birch-Murnaghan equation with parameters K T0 = 56.25 GPa, K' = 5.66 and V 0 = 450.34 Å3. The mechanical behaviour is highly anisotropic, as observed by the axial compressibility. The presented data are in very good agreement with recent experimental results obtained by single-crystal neutron and X-ray diffraction experiments.
Accurate Relations Between the Neutron Current Densities and the Neutron Fluxes
Ronen, Yigal
2004-02-15
Accurate relations between neutron current densities and neutron flux are obtained using the integral transport equation. Using these relations and Fick's Law, diffusion constants can be calculated. These diffusion constants are better than those usually used for the cases in which {sigma}{sub a}/{sigma}{sub s} is not small.
NASA Astrophysics Data System (ADS)
Kasai, Hidetaka; Nishibori, Eiji
2016-04-01
In recent years multiple synchrotron radiation (SR) powder x-ray diffraction profiles have been successfully applied to advanced structural studies such as an accurate charge density study and a structure determination from powder diffraction. The results have been presented with several examples. Abilities and future prospects have been discussed using state of the art powder diffraction data.
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).
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.
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
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. Microsc. Res. Tech. 79:422-430, 2016. © 2016 Wiley Periodicals, Inc. PMID:26920339
Accurate and fast DFT calculations with the AM05 functional
NASA Astrophysics Data System (ADS)
Mattsson, Ann E.
2008-03-01
The AM05 functional [1] has the same excellent performance for solids as the hybrid density functionals tested in Paier et. al. (J. Chem. Phys 124, 154709 (2006); ibid 125, 249901 (2006)). This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. While hybrid functionals are computationally expensive, preveting them from being used in large systems and/or long molecular dynamics simulations, the AM05 functional is on a regular semi-local GGA form with corresponding computational cost. The performance of AM05 is even superior to an `informed choice' between LDA and PBE. By comparing data from different electronic-structure codes we have determined that the numerical errors in this study are equal to or smaller than corresponding experimental uncertainties. Results for other systems will also be presented. 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-AC04-94AL85000. [1] R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005).
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.
Unexpected properties of a density functional
Karwowski, J.; Stanke, M.
2005-02-01
An observation on a pathological behavior of an exact density functional derived from either relativistic (Dirac) or nonrelativistic (Levy-Leblond) quantum-mechanical equation is reported. As expected, in the case of a one-electron atom the variational minimum of this functional is equal to the exact ground-state energy. However, apart from the correct density, this minimum is reached also by an infinite set of densities which do not correspond to the exact wave function. This paradoxical property of the functional is related to the multicomponent structure of both Dirac and Levy-Leblond wave functions. In particular, imposing the correct boundary conditions upon the trial densities removes only a part of the fake solutions. The results of this study demonstrate that in density-functional theories derived from models based on multicomponent wave functions, one should not expect any simple relation between the accuracy of the energy and the correctness of the corresponding density.
NASA Astrophysics Data System (ADS)
Bochevarov, Arteum D.; Friesner, Richard A.
2008-01-01
We investigate one of the fundamental observables, electronic charge density, as produced by a number of popular functionals of the density functional theory (DFT): SVWN5, B3LYP, B3LYP, OLYP, O3LYP, BP86, B3P86, O3P86, and PBE using restricted and unrestricted orbitals. Measuring and comparing the quality of the densities could tell us more about the physical soundness of the functional models. The study is performed on the small molecules He, H2, LiH, H4 in an extensive range of correlation-consistent basis sets. We compare DFT densities to those of full configuration interaction (FCI) under the assumption that the FCI density in the largest employed basis set is sufficiently close to the exact one. For LiH and H4, we also compare the DFT densities to those of CCSD. The SVWN5 functional consistently shows the worst performance. The OPTX exchange functional regularly beats the Becke exchange. Among the best performers are all the hybrid functionals, the novel O3P86 being the most accurate in most cases. The popular functional B3LYP was consistently outmatched by O3LYP, and produced, in fact, some of the poorest densities among the hybrids. CCSD was found to produce much more accurate densities than any DFT functional in the case of LiH in equilibrium geometry, but was sometimes outperformed by DFT in the case of slightly stretched H4, where CCSD theory itself starts to break down. Surprisingly, as one stretches the H2 molecule, BP86 and PBE improve the description of density although such behavior is not observed in other systems. We conclude by reasoning how functionals such as B3LYP, despite being quite average for density, could still be very successful in predicting thermodynamic properties.
Surface electron density models for accurate ab initio molecular dynamics with electronic friction
NASA Astrophysics Data System (ADS)
Novko, D.; Blanco-Rey, M.; Alducin, M.; Juaristi, J. I.
2016-06-01
Ab initio molecular dynamics with electronic friction (AIMDEF) is a valuable methodology to study the interaction of atomic particles with metal surfaces. This method, in which the effect of low-energy electron-hole (e-h) pair excitations is treated within the local density friction approximation (LDFA) [Juaristi et al., Phys. Rev. Lett. 100, 116102 (2008), 10.1103/PhysRevLett.100.116102], can provide an accurate description of both e-h pair and phonon excitations. In practice, its applicability becomes a complicated task in those situations of substantial surface atoms displacements because the LDFA requires the knowledge at each integration step of the bare surface electron density. In this work, we propose three different methods of calculating on-the-fly the electron density of the distorted surface and we discuss their suitability under typical surface distortions. The investigated methods are used in AIMDEF simulations for three illustrative adsorption cases, namely, dissociated H2 on Pd(100), N on Ag(111), and N2 on Fe(110). Our AIMDEF calculations performed with the three approaches highlight the importance of going beyond the frozen surface density to accurately describe the energy released into e-h pair excitations in case of large surface atom displacements.
Density-functional theory of superconductivity
NASA Astrophysics Data System (ADS)
Gross, E. K. U.
2008-03-01
A prominent challenge of modern condensed-matter theory is to predict reliably material-specific properties of superconductors, such as the critical temperature. The traditional model of Bardeen, Cooper and Schrieffer (BCS) properly describes the universal features that all conventional superconductors have in common, but it is not able to make accurate predictions of material-specific properties. To tackle this problem, a density-functional formalism has been developed [1] which describes superconductors in thermal equilibrium in terms of three quantities: the ordinary density, the superconducting order parameter, and the nuclear N-body density. These three ``densities'' are determined self-consistently through a set of Kohn-Sham equations. Approximations of the universal exchange-correlation functional are derived on the basis of many-body perturbation theory. In this way, a true ab-initio description is achieved which does not contain any adjustable parameters such as the μ* of Eliashberg theory. Numerical results for the critical temperature, the isotope effect, the gap function and the jump of the specific heat will be presented for simple metals, for MgB2 [2] and CaBeSi, and for calcium intercalated graphite (CaC6) [3]. Furthermore, results for Li, Al, K, and H under pressure will be discussed. The calculations explain why Li and Al behave very differently, leading to a strong enhancement of superconductivity for Li and to a clear suppression for Al with increasing pressure [4]. For K we predict a behavior similar to Li, i.e. a strong increase of Tc with increasing pressure. Finally, hydrogen is found to be a three-gap superconductor whose critical temperature increases with increasing pressure until about 100K (at 500 GPa). [1] M. Lüders, M.A.L. Marques, N.N. Lathiotakis, A. Floris,G. Profeta, L. Fast, A.Continenza, S. Massidda, E.K.U. Gross, PRB 72, 024545 (2005). [2] A. Floris, G. Profeta, N.N. Lathiotakis, M. Lüders, M.A.L. Marques, C. Franchini, E
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.
Semiclassical origins of density functional theory
NASA Astrophysics Data System (ADS)
Burke, Kieron
2009-03-01
Until the seminal work of Hohenberg, Kohn, and Sham of the mid 60's, most density functional theory (DFT) was derived from semiclassical approximations. This non-empirical approach shows an intrinsic difference between solids (for which DFT was originally developed) and molecules, and explains many of its more mysterious manifestations. For example, the success of DFT for molecules has nothing to do with the uniform gas. Results include [1] a derivation of the empirical parameter in the B88 exchange functional, [2] PBEsol, a new GGA that restores the exchange gradient expansion and improves lattice constants in solids, [3] a novel approach to ``orbital-free'' DFT that, in preliminary tests, is 40 times more accurate than its DFT counterpart. The talk is aimed at a general theoretical audience. Detailed technical knowledge of DFT is neither needed, nor desirable. [4pt] [1] J.P. Perdew, L.A. Constantin, E. Sagvolden, and KB, Phys. Rev. Lett. 97, 223002 (2006). [0pt] [2] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and KB, Phys. Rev. Lett. 100, 136406 (2008). [0pt] [3] Peter Elliott, Donghyung Lee, Attila Cangi, KB, Phys. Rev. Lett. 100, 256406 (2008).
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.
Rationale for switching to nonlocal functionals in density functional theory
NASA Astrophysics Data System (ADS)
Lazić, P.; Atodiresei, N.; Caciuc, V.; Brako, R.; Gumhalter, B.; Blügel, S.
2012-10-01
Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.
A Safari Through Density Functional Theory
NASA Astrophysics Data System (ADS)
Dreizler, Reiner M.; Lüdde, Cora S.
Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.
Density functional theory for Yukawa fluids
NASA Astrophysics Data System (ADS)
Hatlo, Marius M.; Banerjee, Priyanka; Forsman, Jan; Lue, Leo
2012-08-01
We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.
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.
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.
iTagPlot: an accurate computation and interactive drawing tool for tag density plot
Kim, Sung-Hwan; Ezenwoye, Onyeka; Cho, Hwan-Gue; Robertson, Keith D.; Choi, Jeong-Hyeon
2015-01-01
Motivation: Tag density plots are very important to intuitively reveal biological phenomena from capture-based sequencing data by visualizing the normalized read depth in a region. Results: We have developed iTagPlot to compute tag density across functional features in parallel using multicores and a grid engine and to interactively explore it in a graphical user interface. It allows us to stratify features by defining groups based on biological function and measurement, summary statistics and unsupervised clustering. Availability and implementation: http://sourceforge.net/projects/itagplot/. Contact: jechoi@gru.edu and jeochoi@gmail.com Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25792550
Fluctuation-dissipation theorem density-functional theory
NASA Astrophysics Data System (ADS)
Furche, Filipp; Van Voorhis, Troy
2005-04-01
Using the fluctuation-dissipation theorem (FDT) in the context of density-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent density response function. When combined with time-dependent density-functional theory, a new class of density functionals results that use approximations to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDT-DFT beyond the random-phase approximation (RPA)—that is, the first such results with fxc≠0. We show that kernels derived from the adiabatic local-density approximation and other semilocal functionals suffer from an "ultraviolet catastrophe," producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approximations to fxc should satisfy and discuss the prospects of FDT-DFT.
Van der Waals density functional applied to adsorption systems
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2013-03-01
The van der Waals density functional (vdW-DF) is a promising density functional to describe the van der Waals forces within density functional theory. However, despite the recent efforts, there is still room for further improvement, especially for describing molecular adsorption on metal surfaces. I will show that by choosing appropriate exchange and nonlocal correlation functionals, it is possible to calculate geometries and electronic structures for adsorption systems accurately within the framework of vdW-DF. Applicability of the present approach will be illustrated with its applications to graphene/metal, fullerene/metal, and water/graphene interfaces. This work is partly supported by a Grant-in-Aid for Scientific Research on Innovative Area (No. 23104501). AIMR was established by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
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.
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. PMID:24697459
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.
Procedure for accurate fabrication of tissue compensators with high-density material
NASA Astrophysics Data System (ADS)
Mejaddem, Younes; Lax, Ingmar; Adakkai K, Shamsuddin
1997-02-01
An accurate method for producing compensating filters using high-density material (Cerrobend) is described. The procedure consists of two cutting steps in a Styrofoam block: (i) levelling a surface of the block to a reference level; (ii) depth-modulated milling of the levelled block in accordance with pre-calculated thickness profiles of the compensator. The calculated thickness (generated by a dose planning system) can be reproduced within acceptable accuracy. The desired compensator thickness manufactured according to this procedure is reproduced to within 0.1 mm, corresponding to a 0.5% change in dose at a beam quality of 6 MV. The results of our quality control checks performed with the technique of stylus profiling measurements show an accuracy of 0.04 mm in the milling process over an arbitrary profile along the milled-out Styrofoam block.
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
Particle conservation in dynamical density functional theory
NASA Astrophysics Data System (ADS)
de las Heras, Daniel; Brader, Joseph M.; Fortini, Andrea; Schmidt, Matthias
2016-06-01
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.
Particle conservation in dynamical density functional theory.
de Las Heras, Daniel; Brader, Joseph M; Fortini, Andrea; Schmidt, Matthias
2016-06-22
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium. PMID:27115673
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.}
Hutchins, Patrick M.; Ronsein, Graziella E.; Monette, Jeffrey S.; Pamir, Nathalie; Wimberger, Jake; He, Yi; Anantharamaiah, G.M.; Kim, Daniel Seung; Ranchalis, Jane E.; Jarvik, Gail P.; Vaisar, Tomas; Heinecke, Jay W.
2015-01-01
Background It is critical to develop new metrics to determine whether high density lipoprotein (HDL) is cardioprotective in humans. One promising approach is HDL particle concentration (HDL-P) – the size and concentration of HDL in plasma or serum. However, the two methods currently used to determine HDL-P yield concentrations that differ more than 5-fold. We therefore developed and validated an improved approach to quantify HDL-P, termed calibrated ion mobility analysis (calibrated IMA). Methods HDL was isolated from plasma by ultracentrifugation, introduced into the gas phase with electrospray ionization, separated by size, and quantified by particle counting. A calibration curve constructed with purified proteins was used to correct for the ionization efficiency of HDL particles. Results The concentrations of gold nanoparticles and reconstituted HDLs measured by calibrated IMA were indistinguishable from concentrations determined by orthogonal methods. In plasma of control (n=40) and cerebrovascular disease (n=40) subjects, three subspecies of HDL were reproducibility measured, with an estimated total HDL-P of 13.4±2.4 µM (mean±SD). HDL-C accounted for 48% of the variance in HDL-P. HDL-P was significantly lower in subjects with cerebrovascular disease, and this difference remained significant after adjustment for HDL cholesterol levels. Conclusions Calibrated IMA accurately and reproducibly determined the concentration of gold nanoparticles and synthetic HDL, strongly suggesting the method could accurately quantify HDL particle concentration. Importantly, the estimated stoichiometry of apoA-I determined by calibrated IMA was 3–4 per HDL particle, in excellent agreement with current structural models. Furthermore, HDL-P associated with cardiovascular disease status in a clinical population independently of HDL cholesterol. PMID:25225166
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.
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.
Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio
2015-04-21
We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method. PMID:25903880
Connection formulas for thermal density functional theory
NASA Astrophysics Data System (ADS)
Pribram-Jones, A.; Burke, K.
2016-05-01
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. We illustrate our results on the uniform electron gas.
External orthogonality in subsystem time-dependent density functional theory.
Chulhai, Dhabih V; Jensen, Lasse
2016-08-01
Subsystem density functional theory (subsystem DFT) is a DFT partitioning method that is exact in principle, but depends on approximations to the kinetic energy density functional (KEDF). One may avoid the use of approximate KEDFs by ensuring that the inter-subsystem molecular orbitals are orthogonal, termed external orthogonality (EO). We present a method that extends a subsystem DFT method, that includes EO, into the time-dependent DFT (TDDFT) regime. This method therefore removes the need for approximations to the kinetic energy potential and kernel, and we show that it can accurately reproduce the supermolecular TDDFT results for weakly and strongly coupled subsystems, and for systems with strongly overlapping densities (where KEDF approximations traditionally fail). PMID:26932176
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.
Generalized local-spin-density-functional theory
NASA Astrophysics Data System (ADS)
Guo, Yufei; Whitehead, M. A.
1991-01-01
An alternative density-functional theory, the generalized local-spin-density-functional (G-LSD) theory, is proposed based on the boundary conditions and sum rule of the Fermi-correlation factor in the Hartree-Fock (HF) limit. It avoids the physical restrictions to the boundary conditions and the sum rule used in the generalized exchange local-spin-density-functional (GX-LSD) theory completely, the homogeneous electron-density approximation in the Hartree-Fock-Slater (HFS) theory and in the Gáspár-Kohn-Sham (GKS) theory partly, and the time-consuming step to search for the optimal exchange parameter for each atom or ion in the Xα and Ξa theories. The alternative G-LSD theory generates the GX-LSD, HFS, GKS, Xα, and Ξa theories, when additional approximations or certain Fermi-hole shapes or high electron-density limit in a system are used. Theoretically, the G-LSD theory is more rigorous than the GX-LSD, HFS, GKS, and Ξa theories. Numerically, the statistical total energies for atoms in the G-LSD theory are in excellent agreement with the HF results, when the Gopinathan, Whitehead, and Bogdanovic [Phys. Rev. A 14, 1 (1976)] Fermi-hole parameters are used.
Density-functional expansion methods: Grand challenges
Giese, Timothy J.; York, Darrin M.
2016-01-01
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian. PMID:27293378
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.
NASA Astrophysics Data System (ADS)
Brawand, Nicholas; Vörös, Márton; Govoni, Marco; Galli, Giulia
The accurate prediction of optoelectronic properties of molecules and solids is a persisting challenge for current density functional theory (DFT) based methods. We propose a hybrid functional where the mixing fraction of exact and local exchange is determined by a non-empirical, system dependent function. This functional yields ionization potentials, fundamental and optical gaps of many, diverse systems in excellent agreement with experiments, including organic and inorganic molecules and nanocrystals. We further demonstrate that the newly defined hybrid functional gives the correct alignment between the energy level of the exemplary TTF-TCNQ donor-acceptor system. DOE-BES: DE-FG02-06ER46262.
Nuclear moments in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, J.; Zhao, P. W.; Zhang, S. Q.; Hu, J. N.; Li, J.
2014-05-01
Recent progresses on microscopic and self-consistent description of the nuclear moments in covariant density functional theory based on a point-coupling interaction are briefly reviewed. In particular, the electric quadrupole moments of Cd isotopes and the magnetic moments of Pb isotopes are discussed.
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.
Probability density function learning by unsupervised neurons.
Fiori, S
2001-10-01
In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals. PMID:11709808
Differentiability of Lieb functional in electronic density functional theory
NASA Astrophysics Data System (ADS)
Lammert, Paul E.
A solid understanding of the Lieb functional FL is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of FL at an ensemble-V-representable density are given by (minus) the potential. A widely accepted purported proof that FL is Gâteaux differentiable at EV-representable densities would say, ?yes.? But that proof is fallacious, as shown here. FL is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of FL at an EV-representable density ?0 in the direction of ?1 is given by the potential if ?0 and ?1 are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order.
The exact density functional for two electrons in one dimension
NASA Astrophysics Data System (ADS)
Cohen, Aron; Mori-Sanchez, Paula
The exact universal density functional F [ ρ ] is calculated for real space two-electron densities in one dimension ρ (x) with a soft-Coulomb interaction. It is calculated by the Levy constrained search F [ ρ ] =minΨ-->ρ < Ψ | \\Tcirc +\\Vcircee | Ψ > over wavefunctions of a two-dimensional Hilbert space Ψ (x1 ,x2) --> ρ (x1) and can be directly visualized. We do an approximate constrained search via density matrices and a direct approximation to natural orbitals. This allows us to make an accurate approximation to the exact functional that is calculated using a search over potentials. We investigate the exact functional and the performance of many approximations on some of the most challenging electronic structure in two-electron systems, from strongly-correlated electron transfer to the description of a localized-delocalized transition. The exact Kohn-Sham potential, vs (x) , and exact Kohn-Sham eigenvalues, ɛi, are calculated and this allows us to discuss the band-gap problem versus the perspective of the exact density functional F [ ρ ] for all numbers of electrons. We calculate the derivative discontinuity of the exact functional in an example of a Mott-Insulator, one-dimensional stretched H2.
Density gradient expansion of correlation functions
NASA Astrophysics Data System (ADS)
van Leeuwen, Robert
2013-04-01
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of density derivatives of arbitrary order. We further derive a consistency condition that is necessary for the existence of the gradient expansion. This condition is used to carry out an infinite summation of terms involving response functions up to infinite order from which it follows that the coefficient functions of the gradient expansion can be expressed in terms of the local density profile rather than the background density around which the expansion is carried out. We apply the method to the calculation of the gradient expansion of the one-particle density matrix to second order in the density gradients and recover in an alternative manner the result of Gross and Dreizler [Gross and Dreizler, Z. Phys. AZPAADB0340-219310.1007/BF01413038 302, 103 (1981)], which was derived using the Kirzhnits method. The nonlinear response method is more general and avoids the turning point problem of the Kirzhnits expansion. We further give a description of the exchange hole in momentum space and confirm the wave vector analysis of Langreth and Perdew [Langreth and Perdew, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.21.5469 21, 5469 (1980)] for this case. This is used to derive that the second-order gradient expansion of the system averaged exchange hole satisfies the hole sum rule and to calculate the gradient coefficient of the exchange energy without the need to regularize divergent integrals.
Density-Functional Theory of Thermal Transport
NASA Astrophysics Data System (ADS)
Eich, F. G.; Principi, A.; di Ventra, M.; Vignale, G.
2014-03-01
We have recently introduced a non-equilibrium density-functional theory of local temperature and associated energy density that is suitable for the study of thermoelectric phenomena from first principles. This theory rests on a local temperature field coupled to the energy-density operator. Here we apply the theory to a simple two-terminal setup, in which the terminals are held at different temperatures. We show that our treatment becomes equivalent to the standard Landauer-Büttiker formulation of thermal transport in the non-interacting limit. We gratefully acknowledge support from DOE under Grant No. DE-FG02-05ER46203 (FGE, AP, GV) and DE-FG02-05ER46204 (MD).
Jankowski, K; Nowakowski, K; Grabowski, I; Wasilewski, J
2009-04-28
The problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory (DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A density-based approach directly hinged on difference radial-density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basis-set incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)]. For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy- and density-based perspectives. They indicate the usefulness of density-based criteria for developing new exchange-correlation functionals. PMID:19405556
NASA Astrophysics Data System (ADS)
Jankowski, K.; Nowakowski, K.; Grabowski, I.; Wasilewski, J.
2009-04-01
The problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory (DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A density-based approach directly hinged on difference radial-density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basis-set incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)]. For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy- and density-based perspectives. They indicate the usefulness of density-based criteria for developing new exchange-correlation functionals.
Density functional calculations on model tyrosyl radicals.
Himo, F; Gräslund, A; Eriksson, L A
1997-01-01
A gradient-corrected density functional theory approach (PWP86) has been applied, together with large basis sets (IGLO-III), to investigate the structure and hyperfine properties of model tyrosyl free radicals. In nature, these radicals are observed in, e.g., the charge transfer pathways in photosystem II (PSII) and in ribonucleotide reductases (RNRs). By comparing spin density distributions and proton hyperfine couplings with experimental data, it is confirmed that the tyrosyl radicals present in the proteins are neutral. It is shown that hydrogen bonding to the phenoxyl oxygen atom, when present, causes a reduction in spin density on O and a corresponding increase on C4. Calculated proton hyperfine coupling constants for the beta-protons show that the alpha-carbon is rotated 75-80 degrees out of the plane of the ring in PSII and Salmonella typhimurium RNR, but only 20-30 degrees in, e.g., Escherichia coli, mouse, herpes simplex, and bacteriophage T4-induced RNRs. Furthermore, based on the present calculations, we have revised the empirical parameters used in the experimental determination of the oxygen spin density in the tyrosyl radical in E. coli RNR and of the ring carbon spin densities, from measured hyperfine coupling constants. Images FIGURE 1 FIGURE 5 PMID:9083661
Orbital-optimized density cumulant functional theory
Sokolov, Alexander Yu. Schaefer, Henry F.
2013-11-28
In density cumulant functional theory (DCFT) the electronic energy is evaluated from the one-particle density matrix and two-particle density cumulant, circumventing the computation of the wavefunction. To achieve this, the one-particle density matrix is decomposed exactly into the mean-field (idempotent) and correlation components. While the latter can be entirely derived from the density cumulant, the former must be obtained by choosing a specific set of orbitals. In the original DCFT formulation [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] the orbitals were determined by diagonalizing the effective Fock operator, which introduces partial orbital relaxation. Here we present a new orbital-optimized formulation of DCFT where the energy is variationally minimized with respect to orbital rotations. This introduces important energy contributions and significantly improves the description of the dynamic correlation. In addition, it greatly simplifies the computation of analytic gradients, for which expressions are also presented. We offer a perturbative analysis of the new orbital stationarity conditions and benchmark their performance for a variety of chemical systems.
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…
Electrochemical phase diagrams for Ti oxides from density functional calculations
NASA Astrophysics Data System (ADS)
Huang, Liang-Feng; Rondinelli, James M.
2015-12-01
Developing an accurate simulation method for the electrochemical stability of solids, as well as understanding the physics related with its accuracy, is critically important for improving the performance of compounds and predicting the stability of new materials in aqueous environments. Herein we propose a workflow for the accurate calculation of first-principles electrochemical phase (Pourbaix) diagrams. With this scheme, we study the electrochemical stabilities of Ti and Ti oxides using density-functional theory. First, we find the accuracy of an exchange-correlation functional in predicting formation energies and electrochemical stabilities is closely related with the electronic exchange interaction therein. Second, the metaGGA and hybrid functionals with a more precise description of the electronic exchange interaction lead to a systematic improvement in the accuracy of the Pourbaix diagrams. Furthermore, we show that accurate Ti Pourbaix diagrams also require that thermal effects are included through vibrational contributions to the free energy. We then use these diagrams to explain various experimental electrochemical phenomena for the Ti-O system, and show that if experimental formation energies for Ti oxides, which contain contributions from defects owing to their generation at high (combustion) temperatures, are directly used to predict room temperature Pourbaix diagrams then significant inaccuracies result. In contrast, the formation energies from accurate first-principles calculations, e.g., using metaGGA and hybrid functionals, are found to be more reliable. Finally, to facilitate the future application of our accurate electrochemical phase equilibria diagrams, the variation of the Ti Pourbaix diagrams with aqueous ion concentration is also provided.
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.
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.
Properties of the cosmological density distribution function
NASA Astrophysics Data System (ADS)
Bernardeau, Francis; Kofman, Lev
1995-04-01
The properties of the probability distribution function (PDF) of the cosmological continuous density field are studied. We focus our analysis on the quasi-linear regime where various calculations, based on dynamically motivated methods, have been presented: either by using the Zel'dovich approximation (ZA) or by using the perturbation theory to evaluate the behavior of the moments of the distribution function. We show how these two approaches are related to each other and that they can be used in a complementary way. For that respect, the one-dimensional dynamics, where the ZA is exact solution, has first been used as a testing ground. In particular, we show that, when the density PDF obtained with the ZA is regularized, its various moments exhibit the behavior expected by the perturbation theory applied to the ZA. We show that ZA approach can be used for arbitrary initial conditions (not only Gaussian) and that the nonlinear evolution of the moments can be obtained. The perturbation theory can be used for the exact dynamics. We take into account the final filtering of the density field both for ZA and perturbation theory. Applying these techniques, we got the generating function of the moments for the one-dimensional dynamics, the three-dimensional ZA, with and without smoothing effects. We also suggest methods to build PDFs. One is based on the Laplace inverse transform of the moment generating function. The other, the Edgeworth expansion, is obtained when the previous generating function is truncated at a given order and allows evaluation of the PDF out of limited number of moments. It provides insight on the relationship between the moments and the shape of the density PDF. In particular, it provides an alternative method to evaluate the skewness and kurtosis by measuring the PDF around its maximum. Eventually, results obtained from a numerical simulation with cold dark matter initial conditions have been used to validate the accuracy of the considered
Momentum distribution function of the electron gas at metallic densities
NASA Astrophysics Data System (ADS)
Takada, Yasutami; Yasuhara, H.
1991-10-01
The momentum distribution function n(k) of the electron gas is calculated in the effective-potential-expansion method at metallic densities. The recently established self-consistency relation between n(k) and the correlation energy [Y. Takada and T. Kita, J. Phys. Soc. Jpn. 60, 25 (1991)] is employed to check the accuracy of our results. This check shows that the effective-potential-expansion method provides probably the exact and at least more accurate results of n(k) than all the other methods that have given n(k) thus far.
Density functional theory for strongly-correlated ultracold dipolar gases
NASA Astrophysics Data System (ADS)
Malet Giralt, Francesc; Reimann, Stephanie; Gori-Giorgi, Paola; Lund University Collaboration
2014-03-01
We address quasi-one-dimensional strongly-correlated dipolar ultracold gases by means of density functional theory. We make use of an approximation for the Hartree-exchange-correlation that has been shown to be very accurate for electronic systems with coulombic interactions. We show that this approach allows to treat systems with very large particle numbers at relatively low computational cost. This work has been supported by a VIDI grant of the NWO and a Marie Curie grant within the FP7 programme.
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.
Analysis of the local-density approximation of density-functional theory
NASA Astrophysics Data System (ADS)
Sahni, Viraht; Bohnen, K.-P.; Harbola, Manoj K.
1988-03-01
In this paper we perform a configuration-space analysis of the local-density approximation (LDA) for the exchange-correlation energy functional of Kohn-Sham density-functional theory in terms of the corresponding average exchange-correlation charge (hole) and energy densities. According to our analysis, the explanation for the quantitative success of the LDA based on the hole charge-conservation sum rule and the assumed consequent cancellation of errors in the spherical averages of the hole is inadequate. The principal conclusion of our work is that the constraint of charge neutrality is a necessary but not sufficient condition for an approximate energy functional to lead to accurate ground-state energies and ionization potentials. The significant additional requirement for the functional is that it must, at least qualitatively, reproduce correctly the structure of the hole as a function of electron position. We perform our calculations within the exchange-only approximation as applied to atoms and jellium metal surfaces. In atoms the Fermi hole is localized about the nucleus; as a consequence the LDA Fermi hole is accurate only for electron positions close to it. However, we show that the spherically averaged LDA hole is accurate for electron positions in the shell regions; it is substantially in error in the intershell and classically forbidden regions. The fact that the principal contribution to the exchange energy comes from the inner-shell region of the atom, where the LDA hole is accurate, explains why the errors in the LDA ground-state energies are small. However, the ionization potential, which depends on the structure of the hole in the outer regions of the atom, is substantially in error in the LDA since here the LDA hole differs significantly from the exact one. For metallic surfaces, on the other hand, as an electron is pulled from within the metal to infinity outside, the Fermi hole is delocalized and spread throughout the crystal. As a consequence
Pseudospectral time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Ko, Chaehyuk; Malick, David K.; Braden, Dale A.; Friesner, Richard A.; Martínez, Todd J.
2008-03-01
Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.
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.
Fundamental gap of molecular crystals via constrained density functional theory
NASA Astrophysics Data System (ADS)
Droghetti, Andrea; Rungger, Ivan; Das Pemmaraju, Chaitanya; Sanvito, Stefano
2016-05-01
The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.
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.
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.
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.
Adiabatic corrections to density functional theory energies and wave functions.
Mohallem, José R; Coura, Thiago de O; Diniz, Leonardo G; de Castro, Gustavo; Assafrão, Denise; Heine, Thomas
2008-09-25
The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT. PMID:18537228
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-01
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. PMID:27059181
Van der Waals Interactions in Density Functional Theory: Intermolecular Complexes
NASA Astrophysics Data System (ADS)
Kannemann, Felix; Becke, Axel
2010-03-01
Conventional density functional theory (GGA and hybrid functionals) fails to account for dispersion interactions and is therefore not applicable to systems where van der Waals interactions play a dominant role, such as intermolecular complexes and biomolecules. The exchange-hole dipole moment (XDM) dispersion model of Becke and Johnson [A. D. Becke and E. R. Johnson, J. Chem. Phys. 127, 154108 (2007)] corrects for this deficiency. We have previously shown that the XDM dispersion model can be combined with standard GGA functionals (PW86 for exchange and PBE for correlation) to give accurate binding energy curves for rare-gas diatomics [F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput. 5, 719 (2009)]. Here we present further tests of the GGA-XDM method using benchmark sets including hydrogen bonding, electrostatic, dispersion and stacking interactions, and systems ranging from rare-gas diatomics to biomolecular complexes.
Local spin analyses using density functional theory
NASA Astrophysics Data System (ADS)
Abate, Bayileyegn; Peralta, Juan
Local spin analysis is a valuable technique in computational investigations magnetic interactions on mono- and polynuclear transition metal complexes, which play vital roles in catalysis, molecular magnetism, artificial photosynthesis, and several other commercially important materials. The relative size and complex electronic structure of transition metal complexes often prohibits the use of multi-determinant approaches, and hence, practical calculations are often limited to single-determinant methods. Density functional theory (DFT) has become one of the most successful and widely used computational tools for the electronic structure study of complex chemical systems; transition metal complexes in particular. Within the DFT formalism, a more flexible and complete theoretical modeling of transition metal complexes can be achieved by considering noncollinear spins, in which the spin density is 'allowed to' adopt noncollinear structures in stead of being constrained to align parallel/antiparallel to a universal axis of magnetization. In this meeting, I will present local spin analyses results obtained using different DFT functionals. Local projection operators are used to decompose the expectation value
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.
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.
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.
Density functional studies of representative pericyclic reactions
NASA Astrophysics Data System (ADS)
Carpenter, John E.; Sosa, Carlos P.
1994-07-01
Density functional theory (DFT) has traditionally been shunned by computational chemists, but has long seen widespread use in the physics community. Recently, however, DFT has been adopted by the ab initio quantum chemistry community and much activity has been devoted to refining the methodology and exploring the range of its applicability. We investigate the use of DFT (both local (LDF) and non-local (NLDF) spin density approximations) to calculate transition and equilibrium structures for three representative pericyclic reactions: the electrocyclic ring opening reaction of cyclobutene, the [1,5] sigmatropic hydrogen shift reaction in (Z)-1,3-pentadiene, and the Diels-Alder cycloaddition reaction between ethylene and butadiene. LDF theory tends to overemphasize the stability of the ringed structures in each of these reactions. For example, LDF predicts a very low (6 kcal mol -1) barrier to reaction for the Deils-Alder reaction. NLDF theory substantially improves the calculated reaction barrier (20 kcal mol -1), but it is still low with respect to experiment.
Semiconductor Thermochemistry in Density Functional Calculations
Lany, S.
2008-01-01
The local-density and generalized gradient approximations (LDA and GGA) to density functional theory (DFT) exhibit incomplete error cancellation when energy differences are taken between chemically dissimilar systems. This energy inconsistency is manifested, e.g., in the tendency to underestimate the heat (enthalpy) of formation of semiconducting and insulating compounds in LDA and, even more so, in GGA. Considering a set of 61 compounds that can be formed from 14 elements (cations: Cu, Mg, Ca, Zn, Cd, Al, Ga, and In; anions: N, P, As, O, S, and Se), optimized elemental reference energies are determined by least-squares error minimization of an overdetermined set of linear equations. These elemental energies are 'optimally consistent' with the DFT energies of the semiconductor compounds and imply corrections of up to 1 eV compared to the respective LDA or GGA energies. While these 'corrections' are not to be understood to yield the correct absolute total energies of the elements, they are proposed to give appropriate bounds for the chemical potentials for thermodynamic processes in semiconductors and insulators, such as, e.g., defect formation, surface reconstruction, or catalytic processes. The present model allows to evaluate thermodynamic processes using DFT energy differences taken only between systems that are expected to show good error cancellation.
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.
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.
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.
Effective potential in density matrix functional theory.
Nagy, A; Amovilli, C
2004-10-01
In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established. PMID:15473719
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.
Kohn-Sham density-functional theory and renormalization of many-body perturbation expansions
NASA Astrophysics Data System (ADS)
Valiev, Marat
1998-03-01
Numerous practical applications provide strong evidence that despite its simplicity and crude approximations, density-functional theory leads to a rather accurate description of ground state properties of various condensed matter systems. Although well documented numerically, to our knowledge a theoretical explanation of the accuracy of density-functional theory has not been given. This issue is clarified in this work by demonstrating that density-functional theory represents a particular renormalization procedure of a many-body perturbation expansion. In other words, it is shown that density-functional theory is a many-body perturbation theory whose convergence properties have been optimized. The realization of this fact brings new meaning into density-functional theory and explains the success of density-functional based calculations. For more information go to http://alchemy.ucsd.edu/marat/ .
A method to measure the density of seawater accurately to the level of 10-6
NASA Astrophysics Data System (ADS)
Schmidt, Hannes; Wolf, Henning; Hassel, Egon
2016-04-01
A substitution method to measure seawater density relative to pure water density using vibrating tube densimeters was realized and validated. Standard uncertainties of 1 g m-3 at atmospheric pressure, 10 g m-3 up to 10 MPa, and 20 g m-3 to 65 MPa in the temperature range of 5 °C to 35 °C and for salt contents up to 35 g kg-1 were achieved. The realization was validated by comparison measurements with a hydrostatic weighing apparatus for atmospheric pressure. For high pressures, literature values of seawater compressibility were compared with substitution measurements of the realized apparatus.
Accurate definition of brain regions position through the functional landmark approach.
Thirion, Bertrand; Varoquaux, Gaël; Poline, Jean-Baptiste
2010-01-01
In many application of functional Magnetic Resonance Imaging (fMRI), including clinical or pharmacological studies, the definition of the location of the functional activity between subjects is crucial. While current acquisition and normalization procedures improve the accuracy of the functional signal localization, it is also important to ensure that functional foci detection yields accurate results, and reflects between-subject variability. Here we introduce a fast functional landmark detection procedure, that explicitly models the spatial variability of activation foci in the observed population. We compare this detection approach to standard statistical maps peak extraction procedures: we show that it yields more accurate results on simulations, and more reproducible results on a large cohort of subjects. These results demonstrate that explicit functional landmark modeling approaches are more effective than standard statistical mapping for brain functional focus detection. PMID:20879321
Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.
Neuhauser, Daniel; Rabani, Eran; Cytter, Yael; Baer, Roi
2016-05-19
We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe-Salpeter approach. PMID:26651840
A density functional for sparse matter
NASA Astrophysics Data System (ADS)
Langreth, D. C.; Lundqvist, B. I.; Chakarova-Käck, S. D.; Cooper, V. R.; Dion, M.; Hyldgaard, P.; Kelkkanen, A.; Kleis, J.; Kong, Lingzhu; Li, Shen; Moses, P. G.; Murray, E.; Puzder, A.; Rydberg, H.; Schröder, E.; Thonhauser, T.
2009-02-01
Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed for the nonlocal correlations between electrons and applied to various relevant molecules and materials, including to those layered systems like graphite, boron nitride and molybdenum sulfide, to dimers of benzene, polycyclic aromatic hydrocarbons (PAHs), doped benzene, cytosine and DNA base pairs, to nonbonding forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators. Comparison with results from wavefunction calculations for the smaller systems and with experimental data for the extended ones show the vdW-DF path to be promising. This could have great ramifications.
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.
Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation
NASA Astrophysics Data System (ADS)
Chung, Haejun; Ha, Sang-Gyu; Choi, Jaehoon; Jung, Kyung-Young
2015-07-01
This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model.
Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.
Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-09-01
We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations. PMID:26575912
Density Functional Theory study of the equilibrium density of water at normal conditions
NASA Astrophysics Data System (ADS)
Wang, Jue; Roman-Perez, Guillermo; Soler, Jose M.; Artacho, Emilio; Fernandez-Serra, Marivi
2010-03-01
Ab initio molecular dynamics of liquid water with the use of density functional theory (DFT) currently underperform experimental equilibrium density 1g/cm^3 under room temperature. At constant density, not much is known about the equilibrium density of commonly used GGA functionals in liquid water simulations. We present a DFT-based AIMD study of liquid water at different densities and analyze the structure and diffusivity of water with different exchange and correlation functionals. We show that all current GGA functionals fail to reproduce experimental density, however, the explicit description of long range correlations through a Van der Walls density functional (DRSLL)footnotetextM. Dion, H. Rydberg, E. Schr"oder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004) can potentially transform our current understanding of the structure of liquid water. Our results shows that this new functional improves density, with only 2% error to experiment. But it underperforms GGA functionals in terms of structure.
Flexoelectricity from density-functional perturbation theory
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2013-11-01
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.
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
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
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
Photostriction in Ferroelectrics from Density Functional Theory
NASA Astrophysics Data System (ADS)
Paillard, Charles; Xu, Bin; Dkhil, Brahim; Geneste, Grégory; Bellaiche, L.
2016-06-01
An ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed ne concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of ne. This method is applied to bulk multiferroic BiFeO3 and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect.
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.
Photostriction in Ferroelectrics from Density Functional Theory.
Paillard, Charles; Xu, Bin; Dkhil, Brahim; Geneste, Grégory; Bellaiche, L
2016-06-17
An ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed n_{e} concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of n_{e}. This method is applied to bulk multiferroic BiFeO_{3} and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect. PMID:27367406
NASA Astrophysics Data System (ADS)
Roquet, F.; Madec, G.; McDougall, Trevor J.; Barker, Paul M.
2015-06-01
A new set of approximations to the standard TEOS-10 equation of state are presented. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first being a fit of density for Boussinesq ocean models, and the second fitting specific volume which is more suitable for compressible models. Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of ∼0.1% on the thermal expansion coefficients. A 75-term polynomial expression is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed, and it is suggested that this expression represents a valuable approximation of the TEOS-10 equation of state for hydrographic data analysis. In the last section, practical aspects about the implementation of TEOS-10 in ocean models are discussed.
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.
Woods: A fast and accurate functional annotator and classifier of genomic and metagenomic sequences.
Sharma, Ashok K; Gupta, Ankit; Kumar, Sanjiv; Dhakan, Darshan B; Sharma, Vineet K
2015-07-01
Functional annotation of the gigantic metagenomic data is one of the major time-consuming and computationally demanding tasks, which is currently a bottleneck for the efficient analysis. The commonly used homology-based methods to functionally annotate and classify proteins are extremely slow. Therefore, to achieve faster and accurate functional annotation, we have developed an orthology-based functional classifier 'Woods' by using a combination of machine learning and similarity-based approaches. Woods displayed a precision of 98.79% on independent genomic dataset, 96.66% on simulated metagenomic dataset and >97% on two real metagenomic datasets. In addition, it performed >87 times faster than BLAST on the two real metagenomic datasets. Woods can be used as a highly efficient and accurate classifier with high-throughput capability which facilitates its usability on large metagenomic datasets. PMID:25863333
The Nuclear Energy Density Functional Formalism
NASA Astrophysics Data System (ADS)
Duguet, T.
The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a Hamiltonian-based picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel E[g',g] at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a mathematically meaningful fashion even if E[g',g] does not derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making any reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a physical standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.
Steele, Mark A.; Forrester, Graham E.
2005-01-01
Field experiments provide rigorous tests of ecological hypotheses but are usually limited to small spatial scales. It is thus unclear whether these findings extrapolate to larger scales relevant to conservation and management. We show that the results of experiments detecting density-dependent mortality of reef fish on small habitat patches scale up to have similar effects on much larger entire reefs that are the size of small marine reserves and approach the scale at which some reef fisheries operate. We suggest that accurate scaling is due to the type of species interaction causing local density dependence and the fact that localized events can be aggregated to describe larger-scale interactions with minimal distortion. Careful extrapolation from small-scale experiments identifying species interactions and their effects should improve our ability to predict the outcomes of alternative management strategies for coral reef fishes and their habitats. PMID:16150721
Steele, Mark A; Forrester, Graham E
2005-09-20
Field experiments provide rigorous tests of ecological hypotheses but are usually limited to small spatial scales. It is thus unclear whether these findings extrapolate to larger scales relevant to conservation and management. We show that the results of experiments detecting density-dependent mortality of reef fish on small habitat patches scale up to have similar effects on much larger entire reefs that are the size of small marine reserves and approach the scale at which some reef fisheries operate. We suggest that accurate scaling is due to the type of species interaction causing local density dependence and the fact that localized events can be aggregated to describe larger-scale interactions with minimal distortion. Careful extrapolation from small-scale experiments identifying species interactions and their effects should improve our ability to predict the outcomes of alternative management strategies for coral reef fishes and their habitats. PMID:16150721
LETTER TO THE EDITOR: Mean-field dynamical density functional theory
NASA Astrophysics Data System (ADS)
Dzubiella, J.; Likos, C. N.
2003-02-01
We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini, Bettolo, Marconi and Tarazona (1999 J. Chem. Phys. 110 8032), supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed.
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.
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. PMID:26574206
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
A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies.
Truchon, Jean-François; Pettitt, B Montgomery; Labute, Paul
2014-03-11
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
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.
Fattebert, J.-L.
2010-01-20
An Accelerated Block Preconditioned Gradient (ABPG) method is proposed to solve electronic structure problems in Density Functional Theory. This iterative algorithm is designed to solve directly the non-linear Kohn-Sham equations for accurate discretization schemes involving a large number of degrees of freedom. It makes use of an acceleration scheme similar to what is known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of convergence for large scale applications using a finite difference discretization and multigrid preconditioning.
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.
Goel, Himanshu; Butler, Charles L; Windom, Zachary W; Rai, Neeraj
2016-07-12
Recent developments in dispersion corrected and nonlocal density functionals are aimed at accurately capturing dispersion interactions, a key shortcoming of local and semilocal approximations of density functional theory. These functionals have shown significant promise for dimers and small clusters of molecules as well as crystalline materials. However, their efficacy for predicting vapor liquid equilibria is largely unexplored. In this work, we examine the accuracy of dispersion-corrected and nonlocal van der Waals functionals by computing the vapor liquid coexistence curves (VLCCs) of hydrofluoromethanes. Our results indicate that the PBE-D3 functional performs significantly better in predicting saturated liquid densities than the rVV10 functional. With the PBE-D3 functional, we also find that as the number of fluorine atoms increase in the molecule, the accuracy of saturated liquid density prediction improves as well. All the functionals significantly underpredict the saturated vapor densities, which also result in an underprediction of saturated vapor pressure of all compounds. Despite the differences in the bulk liquid densities, the local microstructures of the liquid CFH3 and CF2H2 are relatively insensitive to the density functional employed. For CF3H, however, rVV10 predicts slightly more structured liquid than the PBE-D3 functional. PMID:27295451
Peverati, Roberto; Truhlar, Donald G.
2012-01-01
The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps. PMID:22482577
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)
Peng, Liang-You; Gong, Qihuang
2010-12-01
The accurate computations of hydrogenic continuum wave functions are very important in many branches of physics such as electron-atom collisions, cold atom physics, and atomic ionization in strong laser fields, etc. Although there already exist various algorithms and codes, most of them are only reliable in a certain ranges of parameters. In some practical applications, accurate continuum wave functions need to be calculated at extremely low energies, large radial distances and/or large angular momentum number. Here we provide such a code, which can generate accurate hydrogenic continuum wave functions and corresponding Coulomb phase shifts at a wide range of parameters. Without any essential restrict to angular momentum number, the present code is able to give reliable results at the electron energy range [10,10] eV for radial distances of [10,10] a.u. We also find the present code is very efficient, which should find numerous applications in many fields such as strong field physics. Program summaryProgram title: HContinuumGautchi Catalogue identifier: AEHD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHD_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.: 1233 No. of bytes in distributed program, including test data, etc.: 7405 Distribution format: tar.gz Programming language: Fortran90 in fixed format Computer: AMD Processors Operating system: Linux RAM: 20 MBytes Classification: 2.7, 4.5 Nature of problem: The accurate computation of atomic continuum wave functions is very important in many research fields such as strong field physics and cold atom physics. Although there have already existed various algorithms and codes, most of them can only be applicable and reliable in a certain range of parameters. We present here an accurate FORTRAN program for
Assumed Probability Density Functions for Shallow and Deep Convection
NASA Astrophysics Data System (ADS)
Bogenschutz, Peter A.; Krueger, Steven K.; Khairoutdinov, Marat
2010-04-01
The assumed joint probability density function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PDF families are based on the double Gaussian form and the remaining two are the single Gaussian and a Double Delta Function (analogous to a mass flux model). The assumed PDF method is tested for grid sizes as small as 0.4 km to as large as 204.8 km. In addition, studies are performed for PDF sensitivity to errors in the input moments and for how well the PDFs diagnose some higher-order moments. In general, the double Gaussian PDFs more accurately represent SGS cloud structure and turbulence moments in the boundary layer compared to the single Gaussian and Double Delta Function PDFs for the range of grid sizes tested. This is especially true for small SGS cloud fractions. While the most complex PDF, Lewellen-Yoh, better represents shallow convective cloud properties (cloud fraction and liquid water mixing ratio) compared to the less complex Analytic Double Gaussian 1 PDF, there appears to be no advantage in implementing Lewellen-Yoh for deep convection. However, the Analytic Double Gaussian 1 PDF better represents the liquid water flux, is less sensitive to errors in the input moments, and diagnoses higher order moments more accurately. Between the Lewellen-Yoh and Analytic Double Gaussian 1 PDFs, it appears that neither family is distinctly better at representing cloudy layers. However, due to the reduced computational cost and fairly robust results, it appears that the Analytic Double Gaussian 1 PDF could be an ideal family for SGS cloud and turbulence representation in coarse
Fermionic density functional at a Feshbach resonance
Seidl, Michael; Bhaduri, Rajat K.
2007-05-15
We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature. The atoms interact via a short-range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second-order perturbation theory, has the same density dependence as the first-order exchange energy, and the two almost exactly cancel each other at a Feshbach resonance irrespective of the shape of the potential, provided ({mu}r{sub s})>>1. Here ({mu}){sup -1} is the range of the two-body potential, and r{sub s} is defined through the number density, n=3/(4{pi}r{sub s}{sup 3}). The implications of this result for universality are discussed.
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. PMID:26026447
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.
Designing Meaningful Density Functional Theory Calculations in Materials Science
NASA Astrophysics Data System (ADS)
Mattsson, A. E.
2005-07-01
Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. These methods are also increasingly used in Equation of State work, in particular in the warm dense matter regime. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms, and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary to investigate a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We give an overview of DFT and discuss several of the most important issues that go into designing a meaningful DFT calculation. 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-AC04-94AL85000.
Phonons in nonlocal van der Waals density functional theory
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Küçükbenli, Emine; Pham, Cong Huy; de Gironcoli, Stefano
2016-06-01
We extend the formulation of density functional perturbation theory to treat nonlocal density functionals, accounting for van der Waals interactions, in a rigorous and efficient way. We provide a general formalism, suitable for any functional in this family, and give specific equations for the most widely used ones. We then study the lattice dynamics of graphite, comparing several nonlocal functionals and the local density approximation, showing that our recent revision of the VV10 functional [R. Sabatini et al., Phys. Rev. B 87, 041108(R) (2013), 10.1103/PhysRevB.87.041108] gives the best comparison with experiments.
Exact conditions on the temperature dependence of density functionals
NASA Astrophysics Data System (ADS)
Burke, K.; Smith, J. C.; Grabowski, P. E.; Pribram-Jones, A.
2016-05-01
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
Density-potential mapping in time-dependent density-functional theory
Maitra, N. T.; Todorov, T. N.; Woodward, C.; Burke, K.
2010-04-15
The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.
Spin constraints on nuclear energy density functionals
NASA Astrophysics Data System (ADS)
Robledo, L. M.; Bernard, R. N.; Bertsch, G. F.
2014-02-01
The Gallagher-Moszkowski rule in the spectroscopy of odd-odd nuclei imposes a new spin constraint on the energy functionals for self-consistent mean field theory. The commonly used parametrization of the effective three-body interaction in the Gogny and Skyrme families of energy functionals is ill suited to satisfy the spin constraint. In particular, the Gogny parametrization of the three-body interaction has the spin dependence opposite to that required by the observed spectra. The two-body part has a correct sign, but in combination the rule is violated as often as not. We conclude that a new functional form is needed for the effective three-body interaction that can take into better account the different spin-isospin channels of the interaction.
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…
Double-hybrid density-functional theory with meta-generalized-gradient approximations
Souvi, Sidi M. O. Sharkas, Kamal; Toulouse, Julien; CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris
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.
NASA Astrophysics Data System (ADS)
Skone, Jonathan; Govoni, Marco; Galli, Giulia
2015-03-01
Building upon a recently proposed self-consistent hybrid (sc-hybrid) functional, where the optimal dielectric screening is included self-consistently, we propose an improved form by incorporating range-separation of the exchange part. We discuss the choice of the non-empirical parameters defining range separation, and we present results for condensed media including semiconductors, amorphous insulators, and molecular crystals. We find that the range-separated sc-hybrid functional further improves upon the electronic gaps obtained with full-range sc-hybrids, thus providing an accurate functional for high throughput band gap engineering. This work was supported by NSF-CCI Grant Number NSF-CHE-0802907 and ARL Grant Number W911NF-12-2-0023.
Nuclear collective excitations: A relativistic density functional approach
NASA Astrophysics Data System (ADS)
Piekarewicz, J.
2015-08-01
Density functional theory provides the most promising, and likely unique, microscopic framework to describe nuclear systems ranging from finite nuclei to neutron stars. Properly optimized energy density functionals define a new paradigm in nuclear theory where predictive capability is possible and uncertainty quantification is demanded. Moreover, density functional theory offers a consistent approach to the linear response of the nuclear ground state. In this paper, we review the fundamental role played by nuclear collective modes in uncovering novel excitations and in guiding the optimization of the density functional. Indeed, without collective excitations the determination of the density functional remains incomplete. Without collective excitations, the equation of state of neutron-rich matter continues to be poorly constrained. We conclude with a discussion of some of the remaining challenges in this field and propose a path forward to address these challenges.
Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer.
Hunter, Brian; Guo, Zhixiong
2012-04-20
The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux. PMID:22534933
NASA Astrophysics Data System (ADS)
Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Miguel A.
2016-01-01
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 density-functional-theory-based first-principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo (QMC) -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 insight into how well the local liquid structure is captured by different density functionals. We find 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 differences exhibited by the major classes of functionals, and we estimate the magnitudes of these effects when possible.
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.
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
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
Density Functional Approximation for Non-Hard Sphere Fluids Subjected to External Fields
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard-Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.
Turesson, Martin; Szparaga, Ryan; Ma, Ke; Woodward, Clifford E; Forsman, Jan
2014-05-14
A new classical density functional approach is developed to accurately treat a coarse-grained model of room temperature aromatic ionic liquids. Our major innovation is the introduction of charge-charge correlations, which are treated in a simple phenomenological way. We test this theory on a generic coarse-grained model for aromatic RTILs with oligomeric forms for both cations and anions, approximating 1-alkyl-3-methyl imidazoliums and BF₄⁻, respectively. We find that predictions by the new density functional theory for fluid structures at charged surfaces are very accurate, as compared with molecular dynamics simulations, across a range of surface charge densities and lengths of the alkyl chain. Predictions of interactions between charged surfaces are also presented. PMID:24718295
Structures and vibrational frequencies of FOOF and FONO using density functional theory
NASA Astrophysics Data System (ADS)
Amos, Roger D.; Murray, Christopher W.; Handy, Nicholas C.
1993-02-01
Calculations of the equilibrium structure and vibrational frequencies of FOOF using the local density approximation are in good agreement with experimental results. However using a theoretically more accurate gradient corrected (non-local) density functional produces a worse structure. Three isomers of FONO are also studied. The geometry of C 2v isomer FNO 2 is predicted accurately by the local density approximation, with gradient corrected functions again giving a poorer structure, but better vibrational frequencies. The structure of the trans-isomer of FONO is in agreement with recent coupled cluster studies, however calculations on cis-FONO disagree with the coupled cluster results, but may be in better agreement with the experimental geometry.
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
Efficiency issues related to probability density function comparison
Kelly, P.M.; Cannon, M.; Barros, J.E.
1996-03-01
The CANDID project (Comparison Algorithm for Navigating Digital Image Databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some efficiency considerations when working with PDFS. Since PDFs can take on many forms, we look into tradeoffs between accurate representation and efficiency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We find that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simplified. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoffs encountered when using these constraints.
Predicting stability constants for uranyl complexes using density functional theory.
Vukovic, Sinisa; Hay, Benjamin P; Bryantsev, Vyacheslav S
2015-04-20
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 use density functional theory (B3LYP) and the integral equation formalism polarizable continuum model (IEF-PCM) to compute aqueous stability constants for UO2(2+) 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 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 chelating capability to uranyl. PMID:25835578
A probability density function method for acoustic field uncertainty analysis
NASA Astrophysics Data System (ADS)
James, Kevin R.; Dowling, David R.
2005-11-01
Acoustic field predictions, whether analytical or computational, rely on knowledge of the environmental, boundary, and initial conditions. When knowledge of these conditions is uncertain, acoustic field predictions will also be uncertain, even if the techniques for field prediction are perfect. Quantifying acoustic field uncertainty is important for applications that require accurate field amplitude and phase predictions, like matched-field techniques for sonar, nondestructive evaluation, bio-medical ultrasound, and atmospheric remote sensing. Drawing on prior turbulence research, this paper describes how an evolution equation for the probability density function (PDF) of the predicted acoustic field can be derived and used to quantify predicted-acoustic-field uncertainties arising from uncertain environmental, boundary, or initial conditions. Example calculations are presented in one and two spatial dimensions for the one-point PDF for the real and imaginary parts of a harmonic field, and show that predicted field uncertainty increases with increasing range and frequency. In particular, at 500 Hz in an ideal 100 m deep underwater sound channel with a 1 m root-mean-square depth uncertainty, the PDF results presented here indicate that at a range of 5 km, all phases and a 10 dB range of amplitudes will have non-negligible probability. Evolution equations for the two-point PDF are also derived.
Many-electron expansion: A density functional hierarchy for strongly correlated systems
NASA Astrophysics Data System (ADS)
Zhu, Tianyu; de Silva, Piotr; van Aggelen, Helen; Van Voorhis, Troy
2016-05-01
Density functional theory (DFT) is the de facto method for the electronic structure of weakly correlated systems. But for strongly correlated materials, common density functional approximations break down. Here, we derive a many-electron expansion (MEE) in DFT that accounts for successive one-, two-, three-, ... particle interactions within the system. To compute the correction terms, the density is first decomposed into a sum of localized, nodeless one-electron densities (ρi). These one-electron densities are used to construct relevant two- (ρi+ρj ), three- (ρi+ρj+ρk ), ... electron densities. Numerically exact results for these few-particle densities can then be used to correct an approximate density functional via any of several many-body expansions. We show that the resulting hierarchy gives accurate results for several important model systems: the Hubbard and Peierls-Hubbard models in 1D and the pure Hubbard model in 2D. We further show that the method is numerically convergent for strongly correlated systems: applying successively higher order corrections leads to systematic improvement of the results. MEE thus provides a hierarchy of density functional approximations that applies to both weakly and strongly correlated systems.
Molecular density functional theory of water including density-polarization coupling.
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2016-06-22
We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities. PMID:27116250
The benchmark of gutzwiller density functional theory in hydrogen systems
Yao, Y.; Wang, Cai-Zhuang; Ho, Kai-Ming
2012-02-23
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures.
The Benchmark of Gutzwiller Density Functional Theory in Hydrogen Systems
Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2011-01-13
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
Generalized van der Waals density functional theory for nonuniform polymers
Patra, Chandra N.; Yethiraj, Arun
2000-01-15
A density functional theory is presented for the effect of attractions on the structure of polymers at surfaces. The theory treats the ideal gas functional exactly, and uses a weighted density approximation for the hard chain contribution to the excess free energy functional. The attractive interactions are treated using a van der Waals approximation. The theory is in good agreement with computer simulations for the density profiles at surfaces for a wide range of densities and temperatures, except for low polymer densities at low temperatures where it overestimates the depletion of chains from the surface. This deficiency is attributed to the neglect of liquid state correlations in the van der Waals term of the free energy functional. (c) 2000 American Institute of Physics.
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.
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. PMID:26001454
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.
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg–Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
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.
Integration, Continuity and a Connection with Probability Density Functions
ERIC Educational Resources Information Center
Samuels, M.
2006-01-01
This note considers functions of two variables which are continuous on a possibly unbounded closed region in [vertical bar]R[squared], and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is investigated, as are connections with joint density and marginal…
SIFTER search: a web server for accurate phylogeny-based protein function prediction.
Sahraeian, Sayed M; Luo, Kevin R; Brenner, Steven E
2015-07-01
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
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. PMID:27013261
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
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.
NASA Astrophysics Data System (ADS)
Jolivet, L.; Cohen, M.; Ruas, A.
2015-08-01
Landscape influences fauna movement at different levels, from habitat selection to choices of movements' direction. Our goal is to provide a development frame in order to test simulation functions for animal's movement. We describe our approach for such simulations and we compare two types of functions to calculate trajectories. To do so, we first modelled the role of landscape elements to differentiate between elements that facilitate movements and the ones being hindrances. Different influences are identified depending on landscape elements and on animal species. Knowledge were gathered from ecologists, literature and observation datasets. Second, we analysed the description of animal movement recorded with GPS at fine scale, corresponding to high temporal frequency and good location accuracy. Analysing this type of data provides information on the relation between landscape features and movements. We implemented an agent-based simulation approach to calculate potential trajectories constrained by the spatial environment and individual's behaviour. We tested two functions that consider space differently: one function takes into account the geometry and the types of landscape elements and one cost function sums up the spatial surroundings of an individual. Results highlight the fact that the cost function exaggerates the distances travelled by an individual and simplifies movement patterns. The geometry accurate function represents a good bottom-up approach for discovering interesting areas or obstacles for movements.
Charge and spin fluctuations in the density functional theory
Gyoerffy, B.L.; Barbieri, A. . H.H. Wills Physics Lab.); Staunton, J.B. . Dept. of Physics); Shelton, W.A.; Stocks, G.M. )
1990-01-01
We introduce a conceptual framework which allow us to treat charge and spin fluctuations about the Local density Approximation (LDA) to the Density Functional Theory (DFT). We illustrate the approach by explicit study of the Disordered Local Moment (DLM) state in Fe above the Curie Temperature {Tc} and the Mott insulating state in MnO. 27 refs., 6 figs.
Density Functional Model for Nondynamic and Strong Correlation.
Kong, Jing; Proynov, Emil
2016-01-12
A single-term density functional model for the left-right nondynamic/strong electron correlation is presented based on single-determinant Kohn-Sham density functional theory. It is derived from modeling the adiabatic connection for kinetic correlation energy based on physical arguments, with the correlation potential energy based on the Becke'13 model ( Becke, A.D. J. Chem. Phys . 2013 , 138 , 074109 ). This functional satisfies some known scaling relationships for correlation functionals. The fractional spin error is further reduced substantially with a new density-functional correction. Preliminary tests with self-consistent-field implementation show that the model, with only three empirical parameters, recovers the majority of left-right nondynamic/strong correlation upon bond dissociation and performs reasonably well for atomization energies and singlet-triplet energy splittings. This study also demonstrates the feasibility of developing DFT functionals for nondynamic and strong correlation within the single-determinant KS scheme. PMID:26636190
Density and Spin Response Functions in Ultracold Fermionic Atom Gases
Mihaila, Bogdan; Blagoev, Krastan B.; Balatsky, Alexander V.; Smith, Darryl L.; Gaudio, Sergio; Littlewood, Peter B.
2005-08-26
We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin-response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the normal-ordered part of the density response function signals the transition between a BEC and a BCS regime, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC-to-BCS crossover. Spin rotational symmetry breaking due to the magnetic field, if observed, can be used to validate the one-channel model.
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.
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.
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.
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. PMID:24832306
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.
Shells of charge: a density functional theory for charged hard spheres.
Roth, Roland; Gillespie, Dirk
2016-06-22
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. PMID:27116385
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-28
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH(+) ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations. PMID:24697449
NASA Astrophysics Data System (ADS)
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-01
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH+ ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations.
Energy Densities in the Strong-Interaction Limit of Density Functional Theory.
Mirtschink, André; Seidl, Michael; Gori-Giorgi, Paola
2012-09-11
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots (Hooke's atoms) are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals. PMID:26605721
Comments on the locality in density-functional theory
Lindgren, Ingvar; Salomonson, Sten
2003-05-01
The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress.
Density functional theory for polymeric systems in 2D
NASA Astrophysics Data System (ADS)
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-01
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.
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. PMID:27115343
Franca, Vivian V.; D'Amico, Irene
2011-04-15
We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local-density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations--which includes reproducing subtle signatures of the particle density stages--shows that our density functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, in contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.
Reactivity of Graphene Investigated by Density-Functional Theory
NASA Astrophysics Data System (ADS)
Soni, Himadri; Gebhardt, Julian; Görling, Andreas; Chair of Theoretical Chemistry Team
Using spin-polarized density-functional theory, we study the adsorption and reaction of hydrogen and fluorine with graphene. Graphene has a bipartite lattice with two different sublattices and hence, due to Lieb's theorem, the inequality between two sublattices should lead to a net magnetic moment upon adsorption of hydrogen or fluorine. Our calculations using density-functional theory with the generalized gradient approximation predict a magnetic moment of 1 µB for a single hydrogen adsorbed on graphene but not for a single fluorine atom adsorbed on graphene. Switching to hybrid density-functional theory with the HSE functional, we obtain a magnetic moment of 1 µB for of a single fluorine atom adsorption on graphene. This is in line with work of Kim et al., who also found in density-functional theory calculations with the HSE exchange-correlation functional spin-polarization for a fluorine adatom on graphene. Here, we present a systematic study of the reactivity and relevant adsorption mechanism for single-sided graphene, i.e., a graphene sheet which is accessible by an adsorbate from only one side with hydrogen and fluorine using hybrid density-functional theory. German Research Council (DFG) by the Collaborative Research Center 953.
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
Optimal-transport formulation of electronic density-functional theory
NASA Astrophysics Data System (ADS)
Buttazzo, Giuseppe; De Pascale, Luigi; Gori-Giorgi, Paola
2012-06-01
The most challenging scenario for Kohn-Sham density-functional theory, that is, when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well-established field of mathematics and economics. In practice, we show that to solve the problem of finding the minimum possible internal repulsion energy for N electrons in a given density ρ(r) is equivalent to find the optimal way of transporting N-1 times the density ρ into itself, with the cost function given by the Coulomb repulsion. We use this link to set the strong-interaction limit of density-functional theory on firm ground and to discuss the potential practical aspects of this reformulation.
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 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
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.
Optimization of an exchange-correlation density functional for water.
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M
2016-06-14
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. PMID:27305990
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.
Michalopoulou, Zoi-Heleni; Pole, Andrew
2016-07-01
The dispersion pattern of a received signal is critical for understanding physical properties of the propagation medium. The objective of this work is to estimate accurately sediment sound speed using modal arrival times obtained from dispersion curves extracted via time-frequency analysis of acoustic signals. A particle filter is used that estimates probability density functions of modal frequencies arriving at specific times. Employing this information, probability density functions of arrival times for modal frequencies are constructed. Samples of arrival time differences are then obtained and are propagated backwards through an inverse acoustic model. As a result, probability density functions of sediment sound speed are estimated. Maximum a posteriori estimates indicate that inversion is successful. It is also demonstrated that multiple frequency processing offers an advantage over inversion at a single frequency, producing results with reduced variance. PMID:27475202
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
Modal density function and number of propagating modes in ducts
NASA Technical Reports Server (NTRS)
Rice, E. J.
1976-01-01
Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.
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
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.
Methane dissociation on Pt(111): Searching for a specific reaction parameter density functional
NASA Astrophysics Data System (ADS)
Nattino, Francesco; Migliorini, Davide; Bonfanti, Matteo; Kroes, Geert-Jan
2016-01-01
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 CHD3 + 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.
Density functional theory modeling of multilayer "epitaxial" graphene oxide.
Zhou, Si; Bongiorno, Angelo
2014-11-18
CONSPECTUS: Graphene oxide (GO) is a complex material of both fundamental and applied interest. Elucidating the structure of GO is crucial to achieve control over its properties and technological applications. GO is a nonstoichiometric and hygroscopic material with a lamellar structure, and its physical chemical properties depend critically on synthesis procedures and postsynthesis treatments. Numerous efforts are in place to both understand and exploit this versatile layered carbon material. This Account reports on recent density functional theory (DFT) studies of "epitaxial" graphene oxide (hereafter EGO), a type of GO obtained by oxidation of graphene films grown epitaxially on silicon carbide. Here, we rely on selected X-ray photoelectron spectroscopy (XPS), infrared spectroscopy (IR), and X-ray diffraction (XRD) measurements of EGO, and we discuss in great detail how we utilized DFT-based techniques to project out from the experimental data basic atomistic information about the chemistry and structure of these films. This Account provides an example as to how DFT modeling can be used to elucidate complex materials such as GO from a limited set of experimental information. EGO exhibits a uniform layered structure, consisting of a stack of graphene planes hosting predominantly epoxide and hydroxyl groups, and water molecules intercalated between the oxidized carbon layers. Here, we first focus on XPS measurements of EGO, and we use DFT to generate realistic model structures, calculate core-level chemical shifts, and through the comparison with experiment, gain insight on the chemical composition and metastability characteristics of EGO. DFT calculations are then used to devise a simplistic but accurate simulation scheme to study thermodynamic and kinetic stability and to predict the intralayer structure of EGO films aged at room temperature. Our simulations show that aged EGO encompasses layers with nanosized oxidized domains presenting a high concentration of
Addressing spectroscopic quality of covariant density functional theory
NASA Astrophysics Data System (ADS)
Afanasjev, A. V.
2015-03-01
The spectroscopic quality of covariant density functional theory has been accessed by analyzing the accuracy and theoretical uncertainties in the description of spectroscopic observables. Such analysis is first presented for the energies of the single-particle states in spherical and deformed nuclei. It is also shown that the inclusion of particle-vibration coupling improves the description of the energies of predominantly single-particle states in medium and heavy-mass spherical nuclei. However, the remaining differences between theory and experiment clearly indicate missing physics and missing terms in covariant energy density functionals. The uncertainties in the predictions of the position of two-neutron drip line sensitively depend on the uncertainties in the prediction of the energies of the single-particle states. On the other hand, many spectroscopic observables in well deformed nuclei at ground state and finite spin only weakly depend on the choice of covariant energy density functional.
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.
Ruggiero, Michael T; Gooch, Jonathan; Zubieta, Jon; Korter, Timothy M
2016-02-18
The problem of nonlocal interactions in density functional theory calculations has in part been mitigated by the introduction of range-corrected functional methods. While promising solutions, the continued evaluation of range corrections in the structural simulations of complex molecular crystals is required to judge their efficacy in challenging chemical environments. Here, three pyridinium-based crystals, exhibiting a wide range of intramolecular and intermolecular interactions, are used as benchmark systems for gauging the accuracy of several range-corrected density functional techniques. The computational results are compared to low-temperature experimental single-crystal X-ray diffraction and terahertz spectroscopic measurements, enabling the direct assessment of range correction in the accurate simulation of the potential energy surface minima and curvatures. Ultimately, the simultaneous treatment of both short- and long-range effects by the ωB97-X functional was found to be central to its rank as the top performer in reproducing the complex array of forces that occur in the studied pyridinium solids. These results demonstrate that while long-range corrections are the most commonly implemented range-dependent improvements to density functionals, short-range corrections are vital for the accurate reproduction of forces that rapidly diminish with distance, such as quadrupole-quadrupole interactions. PMID:26814572
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.