First-principles derivation of density-functional formalism for quenched-annealed systems.
Lafuente, Luis; Cuesta, José A
2006-10-01
We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.
First-principles derivation of density-functional formalism for quenched-annealed systems
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2006-10-01
We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.
Seo, Dong-Kyun
2006-10-21
A perturbational approach is presented for the general analysis of spin-polarization effect on electronic structures and energies within spin-density functional formalism. Explicit expressions for the changes in Kohn-Sham [Phys. Rev. 140, 1133 (1965)] orbital energies and coefficients as well as for the change in total electronic energy are derived upon using the local spin density and self-interaction-corrected exchange-correlation functionals. The application of the method for atoms provides analytical expressions for the exchange splitting energy and spin-polarization energy. The atomic exchange parameters are obtained from the expressions for the elements with Z=1-92 and they match well with Stoner exchange parameters for 3d metal elements.
Weatherbee, Andrew; Sugita, Mitsuro; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex
2016-06-15
The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.
Janetzko, Florian; Köster, Andreas M; Salahub, Dennis R
2008-01-14
The development of the cyclic cluster model (CCM) formalism for Kohn-Sham auxiliary density functional theory (KS-ADFT) methods is presented. The CCM is a direct space approach for the calculation of perfect and defective systems under periodic boundary conditions. Translational symmetry is introduced in the CCM by integral weighting. A consistent weighting scheme for all two-center and three-center interactions appearing in the KS-ADFT method is presented. For the first time, an approach for the numerical integration of the exchange-correlation potential within the cyclic cluster formalism is derived. The presented KS-ADFT CCM implementation was applied to covalent periodic systems. The results of cyclic and molecular cluster model (MCM) calculations for trans-polyacetylene, graphene, and diamond are discussed as examples for systems periodic in one, two, and three dimensions, respectively. All structures were optimized. It is shown that the CCM results represent the results of MCM calculations in the limit of infinite molecular clusters. By analyzing the electronic structure, we demonstrate that the symmetry of the corresponding periodic systems is retained in CCM calculations. The obtained geometric and electronic structures are compared with available data from the literature.
Linear-scaling time-dependent density-functional theory in the linear response formalism.
Zuehlsdorff, T J; Hine, N D M; Spencer, J S; Harrison, N M; Riley, D J; Haynes, P D
2013-08-14
We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on (10,0) carbon nanotubes of different lengths.
Nagesh, Jayashree; Frisch, Michael J; Brumer, Paul; Izmaylov, Artur F
2016-12-28
We extend the localized operator partitioning method (LOPM) [J. Nagesh, A. F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Becke's atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1- naphthyl)- methyl)- anthracene and 4-((2- naphthyl)- methyl)- benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that is not accessible using a simple density difference analysis.
A fully consistent spin formalism for the nonempirical van der Waals density functional vdW-DF
NASA Astrophysics Data System (ADS)
Thonhauser, T.; Zuluaga, S.; Arter, C.; Berland, K.; Schröder, E.; Hyldgaard, P.
We present a proper nonempirical spin-density formalism for the van der Waals density functional (vdW-DF) method. We show that this generalization, termed svdW-DF, is firmly rooted in the single-particle nature of exchange and we test it on a range of spin systems. We investigate in detail the role of spin in the van der Waals driven adsorption of H2 and CO2 in the linear magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that spin plays a significant role during the adsorption process despite the general weakness of the molecular-magnetic responses. The case of CO2 adsorption in Ni-MOF74 is particularly interesting, as the inclusion of spin effects results in an increased attraction, opposite to what the diamagnetic nature of CO2 would suggest. We explain this counter-intuitive result, tracking the behavior to a coincidental hybridization of the O p states with the Ni d states in the down-spin channel. More generally, by providing insight on van der Waals interactions in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions. Work supported by DOE DE-FG02-08ER46491 and NSF DMR-1145968.
NASA Astrophysics Data System (ADS)
Liu, Jie; Liang, WanZhen
2011-11-01
The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.
Liu, Jie; Liang, WanZhen
2011-11-14
The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.
Send, Robert; Furche, Filipp
2010-01-28
First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn-Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernyak-Mukamel formula for first-order NACMEs in the complete basis-set limit, but greatly improves basis-set convergence in finite atom-centered basis sets due to additional Pulay type terms. The Chernyak-Mukamel formula is shown to be equivalent to the Hellmann-Feynman contribution in analytical gradient theory. Our formalism may be implemented in TDDFT analytical excited-state gradient codes with minor modifications. Tests for systems with up to 147 atoms show that evaluation of first-order NACMEs causes total computation times to increase by an insignificant 10% on average. The resolution-of-the-identity approximation for the Coulomb energy (RI-J) reduces the computational cost by an order of magnitude for nonhybrid functionals, while errors are insignificant with standard auxiliary basis sets. We compare the computed NACMEs to full configuration interaction (FCI) in benchmark results for diatomic molecules; hybrid TDDFT and FCI are found to be in agreement for
Prociuk, Alexander; Van Kuiken, Ben; Dunietz, Barry D
2006-11-28
Electronic transmission through a metal-molecule-metal system is calculated by employing a Green's function formalism in the scattering based scheme. Self-energy models representing the bulk and the potential bias are used to describe electron transport through the molecular system. Different self-energies can be defined by varying the partition between device and bulk regions of the metal-molecule-metal model system. In addition, the self-energies are calculated with different representations of the bulk through its Green's function. In this work, the dependence of the calculated transmission on varying the self-energy subspaces is benchmarked. The calculated transmission is monitored with respect to the different choices defining the self-energy model. In this report, we focus on one-dimensional model systems with electronic structures calculated at the density functional level of theory.
Qian, Zekan; Li, Rui; Hou, Shimin; Xue, Zengquan; Sanvito, Stefano
2007-11-21
An efficient self-consistent approach combining the nonequilibrium Green's function formalism with density functional theory is developed to calculate electron transport properties of molecular devices with quasi-one-dimensional (1D) electrodes. Two problems associated with the low dimensionality of the 1D electrodes, i.e., the nonequilibrium state and the uncertain boundary conditions for the electrostatic potential, are circumvented by introducing the reflectionless boundary conditions at the electrode-contact interfaces and the zero electric field boundary conditions at the electrode-molecule interfaces. Three prototypical systems, respectively, an ideal ballistic conductor, a high resistance tunnel junction, and a molecular device, are investigated to illustrate the accuracy and efficiency of our approach.
Wang, Fan; Ziegler, Tom
2005-10-15
In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.
Formalism and functionalism in linguistics.
Newmeyer, Frederick J
2010-05-01
Formalism and functionalism in linguistics are often taken to be diametrically opposed approaches. However, close examination of the relevant phenomena reveals that the two are complementary, rather than being irrevocably in opposition to each other. One can be a formal linguist and a functional linguist at the same time, without there being any contradiction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.
Alonso, J L; Andrade, X; Echenique, P; Falceto, F; Prada-Gracia, D; Rubio, A
2008-08-29
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast with other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large-scale AIMD simulations.
Hu, Chunping; Hirai, Hirotoshi; Sugino, Osamu
2007-08-14
We present an efficient method to compute nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, within the framework of time-dependent density functional theory (TDDFT) in frequency domain. Based on the comparison of dynamic polarizability formulated both in the many-body wave function form and the Casida formalism, a rigorous expression is established for NACs, which is similar to the calculation of oscillator strength in the Casida formalism. The adiabatic local density approximation (ALDA) gives results in reasonable accuracy as long as the conical intersection (ci) is not approached too closely, while its performance quickly degrades near the ci point. This behavior is consistent with the real-time TDDFT calculation. Through the use of modified linear response theory together with the ground-state-component separation scheme, the performance of ALDA can be greatly improved, not only in the vicinity of ci but also for Rydberg transitions and charge-transfer excitations. Several calculation examples, including the quantization of NACs from the Jahn-Teller effect in the H3 system, have been given to show that TDDFT can efficiently give NACs with an accuracy comparable to that of wave-function-based methods.
Huang, Zhi-Feng; Elder, K R; Provatas, Nikolas
2010-08-01
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.
Kitamura, Sota; Tsuji, Naoto; Aoki, Hideo
2015-07-24
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice; that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the interatom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator," has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large off-site interactions on top of a small on-site interaction. Here, we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in A and B sublattices makes the on-site interaction Pauli forbidden, while a sizeable intersite interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt density functional theory for cold atoms, here extended to accommodate noncollinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.
NASA Astrophysics Data System (ADS)
Klein, Roman
2016-06-01
Electron storage rings with appropriate design are primary source standards, the spectral radiant intensity of which can be calculated from measured parameters using the Schwinger equation. PTB uses the electron storage rings BESSY II and MLS for source-based radiometry in the spectral range from the near-infrared to the x-ray region. The uncertainty of the calculated radiant intensity depends on the uncertainty of the measured parameters used for the calculation. Up to now the procedure described in the guide to the expression of uncertainty in measurement (GUM), i.e. the law of propagation of uncertainty, assuming a linear measurement model, was used to determine the combined uncertainty of the calculated spectral intensity, and for the determination of the coverage interval as well. Now it has been tested with a Monte Carlo simulation, according to Supplement 1 to the GUM, whether this procedure is valid for the rather complicated calculation by means of the Schwinger formalism and for different probability distributions of the input parameters. It was found that for typical uncertainties of the input parameters both methods yield similar results.
Partition Density Functional Theory
NASA Astrophysics Data System (ADS)
Wasserman, Adam
2012-02-01
Partition Density Functional Theory (PDFT) is a formally exact method for obtaining molecular properties from self-consistent calculations on isolated fragments [1,2]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that sum to the correct molecular density. I describe our progress understanding the behavior of the fragment energies as a function of fragment occupations, derivative discontinuities, practical implementation, and applications of PDFT to small molecules. I also discuss implications for ground-state Density Functional Theory, such as the promise of PDFT to circumvent the delocalization error of approximate density functionals. [4pt] [1] M.H. Cohen and A. Wasserman, J. Phys. Chem. A, 111, 2229(2007).[0pt] [2] P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010).
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.
Santarossa, Gianluca; Vargas, Angelo; Iannuzzi, Marcella; Pignedoli, Carlo A; Passerone, Daniele; Baiker, Alfons
2008-12-21
We present a study on structural and electronic properties of bulk platinum and the two surfaces (111) and (100) comparing the Gaussian and plane wave method to standard plane wave schemes, normally employed for density functional theory calculations on metallic systems. The aim of this investigation is the assessment of methods based on the expansion of the Kohn-Sham orbitals into localized basis sets and on the supercell approach, in the description of the metallicity of Pt. Electronic structure calculations performed at Gamma-point only on supercells of different sizes, from 108 up to 864 atoms, are compared to the results obtained for the unit cell of four Pt atoms where the k-point expansion of the wave function over Monkhorst-Pack grids up to (10x10x10) has been employed. The evaluation of the two approaches with respect to bulk properties is done through the calculation of the equilibrium lattice constant, the bulk modulus, and the total and the d-projected density of states. For the Pt(111) and Pt(100) surfaces, we consider the relaxation of the first layers, the surface energies, the work function, the total density of states, as well as the center and filling of the d bands. Our results confirm that the accuracy of two approaches in the description of electronic and structural properties of Pt is equivalent, providing that consistent supercells and k-point meshes are used. Moreover, we estimate the supercell size that can be safely adopted in the Gaussian and plane wave method in order to obtain the same reliability of previous theoretical studies based on well converged plane wave calculations available in literature. The latter studies, in turn, set the level of agreement with experimental data. In particular, we obtain excellent agreement in the evaluation of the density of states for either bulk and surface systems, and our data are also in good agreement with previous works on Pt reported in literature. We conclude that Gaussian and plane wave
NASA Astrophysics Data System (ADS)
Kurita, Noriyuki; Araki, Masahiro; Nakao, Kenji; Kobayashi, Kinya
1999-11-01
We have developed a molecular-orbital (MO) method based on a Slater-type basis set and non-local density functional theory (DFT) for describing the DNA base stacking properties, and its efficiency has been confirmed by investigating the stacking energy of cytosine dimer. Our DFT method can reproduce the dependence of stacking energy on the stacking conformation obtained by the ab initio second-order Møller-Plesset (MP2) calculation. The stable structures of hydrogen-bonded Watson-Crick base pairs and (PO 4H 2) -1 ion have been investigated and the structures obtained by our DFT method are comparable with those from the MP2 and DFT methods in Gaussian94. Therefore, our DFT method may be applicable for investigating the stable structures of more realistic models for stacked DNA base pairs including backbones.
NASA Astrophysics Data System (ADS)
Zobač, Vladimír; Lewis, James P.; Abad, Enrique; Mendieta-Moreno, Jesús I.; Hapala, Prokop; Jelínek, Pavel; Ortega, José
2015-05-01
The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.
Zobač, Vladimír; Lewis, James P; Abad, Enrique; Mendieta-Moreno, Jesús I; Hapala, Prokop; Jelínek, Pavel; Ortega, José
2015-05-08
The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.
Green's function formalism for calculating spin-wave spectra
NASA Astrophysics Data System (ADS)
Aryasetiawan, F.; Karlsson, K.
1999-09-01
We propose a formalism for calculating ab initio spin-wave spectra which is based on the many-body temperature Green's function. The main quantity to be calculated is the linear magnetic susceptibility from which all magnetic excitations involving the creation of an additional spin in the system can formally be obtained. The Schwinger functional derivative technique is employed in calculating the self-energy. The approach avoids both the assumption of local spins (Heisenberg model) and the use of a local exchange and correlation interaction (local-density approximation). Starting from the GW approximation we obtain a Bethe-Salpeter equation for the kernel describing the interaction between electrons in both spin channels. However, this kernel exhibits a nonlocal screened interaction.
Modelling charge transfer reactions with the frozen density embedding formalism
Pavanello, Michele; Neugebauer, Johannes
2011-12-21
The frozen density embedding (FDE) subsystem formulation of density-functional theory is a useful tool for studying charge transfer reactions. In this work charge-localized, diabatic states are generated directly with FDE and used to calculate electronic couplings of hole transfer reactions in two {pi}-stacked nucleobase dimers of B-DNA: 5{sup '}-GG-3{sup '} and 5{sup '}-GT-3{sup '}. The calculations rely on two assumptions: the two-state model, and a small differential overlap between donor and acceptor subsystem densities. The resulting electronic couplings agree well with benchmark values for those exchange-correlation functionals that contain a high percentage of exact exchange. Instead, when semilocal GGA functionals are used the electronic couplings are grossly overestimated.
Modelling charge transfer reactions with the frozen density embedding formalism.
Pavanello, Michele; Neugebauer, Johannes
2011-12-21
The frozen density embedding (FDE) subsystem formulation of density-functional theory is a useful tool for studying charge transfer reactions. In this work charge-localized, diabatic states are generated directly with FDE and used to calculate electronic couplings of hole transfer reactions in two π-stacked nucleobase dimers of B-DNA: 5'-GG-3' and 5'-GT-3'. The calculations rely on two assumptions: the two-state model, and a small differential overlap between donor and acceptor subsystem densities. The resulting electronic couplings agree well with benchmark values for those exchange-correlation functionals that contain a high percentage of exact exchange. Instead, when semilocal GGA functionals are used the electronic couplings are grossly overestimated.
Zeng, Qiao; Liang, WanZhen; Liu, Jie
2014-05-14
This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.
Zeng, Qiao; Liu, Jie; Liang, WanZhen
2014-05-14
This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.
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.
General Green's function formalism for layered systems: Wave function approach
NASA Astrophysics Data System (ADS)
Zhang, Shu-Hui; Yang, Wen; Chang, Kai
2017-02-01
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency and is limited to relatively small systems. Here we present a numerically efficient and physically transparent GF formalism for a general layered structure. In contrast to the recursive GF that directly calculates the GF through the Dyson equations, our approach converts the calculation of the GF to the generation and subsequent propagation of a scattering wave function emanating from a local excitation. This viewpoint not only allows us to reproduce existing results in a concise and physically intuitive manner, but also provides analytical expressions of the GF in terms of a generalized scattering matrix. This identifies the contributions from each individual scattering channel to the GF and hence allows this information to be extracted quantitatively from dual-probe STM experiments. The simplicity and physical transparency of the formalism further allows us to treat the multiple reflection analytically and derive an analytical rule to construct the GF of a general layered system. This could significantly reduce the computational time and enable quantum transport calculations for large samples. We apply this formalism to perform both analytical analysis and numerical simulation for the two-dimensional conductance map of a realistic graphene p -n junction. The results demonstrate the possibility of observing the spatially resolved interference pattern caused by negative refraction and further reveal a few interesting features, such as the distance-independent conductance and its quadratic dependence on the carrier concentration, as opposed to the linear dependence in uniform graphene.
A logarithmic correction in the entropy functional formalism
NASA Astrophysics Data System (ADS)
Hammad, Fayçal; Faizal, Mir
2016-04-01
The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein-Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein-Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an ℱ(R)-gravity are the same as those obtained in the literature from cosmological considerations.
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.
Dominant partition method. [based on a wave function formalism
NASA Technical Reports Server (NTRS)
Dixon, R. M.; Redish, E. F.
1979-01-01
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.
Density functional theory of complex transition densities.
Ernzerhof, Matthias
2006-09-28
We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.
Combining Formal and Functional Approaches to Topic Structure
ERIC Educational Resources Information Center
Zellers, Margaret; Post, Brechtje
2012-01-01
Fragmentation between formal and functional approaches to prosodic variation is an ongoing problem in linguistic research. In particular, the frameworks of the Phonetics of Talk-in-Interaction (PTI) and Empirical Phonology (EP) take very different theoretical and methodological approaches to this kind of variation. We argue that it is fruitful to…
Formalization Studies in Functional Size Measurement: How Do They Help?
NASA Astrophysics Data System (ADS)
Ozkan, Baris; Demirors, Onur
Functional size has been favored as a software characteristic that can be measured early and independent of language, tools, techniques and technology; hence has many uses in software project management. It has been about three decades since Albrecht introduced the concept of functional size. However, Functional Size Measurement (FSM) has not been a common practice in the software community. The problems with FSM method structures and practices have been discussed to be the major factors to explain this situation. In this paper, we make a review of formalization proposals to the problems in Functional Size Measurement (FSM). We analyze the works included in the papers and we explore the extent of their contributions.
General performance of density functionals.
Sousa, Sérgio Filipe; Fernandes, Pedro Alexandrino; Ramos, Maria João
2007-10-25
The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
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.
Partitioned density functional approach for a Lennard-Jones fluid.
Zhou, Shiqi
2003-12-01
The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature T(*)=1.35 and a density point for reduced temperature T(*)=1. The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
Wave-function functionals for the density
Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht
2011-11-15
We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.
NASA Astrophysics Data System (ADS)
Teichert, Fabian; Zienert, Andreas; Schuster, Jörg; Schreiber, Michael
2017-04-01
We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computational complexity scales linearly with the number of defects, instead of linearly with the total system length for the conventional approach. We show that the scaling of the calculation time of the Green's function depends on the defect density of a random test system. Furthermore, we discuss the calculation time and the memory requirement of the whole transport formalism applied to defective carbon nanotubes.
Studies in Density Functional Theory
NASA Astrophysics Data System (ADS)
Lee, Hsing
The first chapter begins with reviews of density -functional theory and Green's function method. The connections between these two theories are emphasized. Then we present an approximate model of kinetic energy functional and a possible form of the universal functional is given through an equality obeyed by true ground state densities. Chapter two is aimed at developing a general formulation of the response function in density-functional theory. We first give our definition of response functions in the context of functional derivative. The parameter-differentiation technique employed greatly reduces the efforts for computations. The advantage of this method is its numerical simplicity. It is also the aim of this chapter to elucidate the connections between exchange-correlation potential and the response functions. We show that the computations of response functions in the Kohn-Sham formulation will be exact if the so-called uniqueness assumption we present here is true. Various integral formulas for nonlinear response functions are derived here for the first time. In the third chapter we demonstrate that the exchange -correlation functional given in the form of Pade approximation to gradient expansion approximation, yields excellent results when applied to atoms. The coefficients for the Pade approximation are derived by numerical fits to the exchange and exchange -correlation energies of the atoms He through Ar. The fitted non-local gradient corrections are used in the minimization of the Kohn-Sham functional to solve for the exchange and exchange-correlation total energies. The resulting standard deviations in the calculated total energies are 0.0043 for exchange only and 0.0014 for exchange-correlation. The conjoint relation of kinetic and exchange energy functionals is proposed in the fourth chapter. Supportive evidence is given numerically and theoretically. Test cases are the second-row atoms and a group of small molecules with Becke equivalent form, and
Functional Lagrange formalism for time-non-local Lagrangians
NASA Astrophysics Data System (ADS)
Ferialdi, L.; Bassi, A.
2012-05-01
We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.
Density functional theory: Foundations reviewed
NASA Astrophysics Data System (ADS)
Kryachko, Eugene S.; Ludeña, Eduardo V.
2014-11-01
Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg-Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb's comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn-Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn-Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn-Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem
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
Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Wigner function in Liouville space: A canonical formalism
NASA Astrophysics Data System (ADS)
Royer, Antoine
1991-01-01
The Wigner-Weyl (WW) phase-space formulation of quantum mechanics is discussed within the Liouville-space formalism, where quantum operators A^ are viewed as vectors, represented by L kets ||A^>>, on which act ``superoperators'' the scalar product is <>=TrA^°B^. With every operator A^, we associate commutation and anticommutation superoperators A^- and A^+, defined by their actions on any operator B^ as A^-B^=ħ-1[A^,B^], A^+B^=1/2(AB^+BÂ^). The WW representation corresponds to the choice of a special basis in Liouville space, namely, the eigenbasis of the position and momentum anticommutation superoperators q^+ and p^+ (where [q^,p^]=iħ). These, together with the commutation superoperators q^- and p^-, form a canonical set of superoperators, [q^+,p^-]=[q^-,p^+]=i (the other commutators vanishing), as functions of which all other super- operators can be expressed. Weyl ordering is expressed as f(q^,p^)Weyl ordering=f(q^+,p^+)1^. A generalization of Ehrenfest's theorem is obtained.
Combining formal and functional approaches to topic structure.
Zellers, Margaret; Post, Brechtje
2012-03-01
Fragmentation between formal and functional approaches to prosodic variation is an ongoing problem in linguistic research. In particular, the frameworks of the Phonetics of Talk-in-Interaction (PTI) and Empirical Phonology (EP) take very different theoretical and methodological approaches to this kind of variation. We argue that it is fruitful to adopt the insights of both PTI's qualitative analysis and EP's quantitative analysis and combine them into a multiple-methods approach. One realm in which it is possible to combine these frameworks is in the analysis of discourse topic structure and the prosodic cues relevant to it. By combining a quantitative and a qualitative approach to discourse topic structure, it is possible to give a better account of the observed variation in prosody, for example in the case of fundamental frequency (F0) peak timing, which can be explained in terms of pitch accent distribution over different topic structure categories. Similarly, local and global patterns in speech rate variation can be better explained and motivated by adopting insights from both PTI and EP in the study of topic structure. Combining PTI and EP can provide better accounts of speech data as well as opening up new avenues of investigation which would not have been possible in either approach alone.
Density functional theory with fractional orbital occupations.
Chai, Jeng-Da
2012-04-21
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.
Multifractal formalism by enforcing the universal behavior of scaling functions
NASA Astrophysics Data System (ADS)
Mukli, Peter; Nagy, Zoltan; Eke, Andras
2015-01-01
Despite its solid foundations, multifractal analysis is still a challenging task. The 'inversed' singularity spectrum is a major pitfall in standard multifractal analyses especially for empirical signals. To resolve this issue, we identified the fan-like convergent geometry of scaling functions yielding a limit value (termed focus) for all moments at the largest scale. Building on this behavior of scaling, we introduce the novel concept of focus-based multifractal formalism. It relies on enforcing this universal behavior when the moment-wise scaling exponents are assessed for the scaling functions. Besides developing focus-based variants of the established multifractal detrended fluctuation analysis and the wavelet leader method, we present a novel analytical tool of multifractal signal summation conversion. All methods are extensively tested on exact multifractal signals synthesized by the generalized binomial multifractal model in terms of precision and incidence of 'inversed' singularity spectra. Our focus-based variants never yielded 'inversed' spectra and their precision was found similar to that of standard methods. Our approach allowed computing a moment-wise and a global error parameter describing the impact of finite size effect and degree of multifractality as compared to that of the fitted exact multifractal model. We demonstrate that the standard approach to multifractal analyses contains a central element that is essentially monofractal due to its regression scheme assessing the scaling exponents for each and every moment, separately. Hence these methods can yield reliable estimates only for ideally behaving multifractal signals. In contrast, our focus-based variants due to their genuine multifractal model fitting always yield reliable estimates accompanied by goodness-of-fit statistics. The presented novel multifractal tools offer means of dealing with the consequences of endogenous impurities of potentially multifractal empirical signals.
Formal functional test designs with a test representation language
NASA Technical Reports Server (NTRS)
Hops, J. M.
1993-01-01
The application of the category-partition method to the test design phase of hardware, software, or system test development is discussed. The method provides a formal framework for reducing the total number of possible test cases to a minimum logical subset for effective testing. An automatic tool and a formal language were developed to implement the method and produce the specification of test cases.
Trovato, M.; Reggiani, L.
2011-12-15
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ({h_bar}/2{pi}){sup 2}. In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when ({h_bar}/2{pi}){yields}0.
Trovato, M; Reggiani, L
2011-12-01
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of h(2). In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when h → 0.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-09
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
Internal density functional theory of molecular systems
NASA Astrophysics Data System (ADS)
Nalewajski, Roman F.
1984-08-01
A thermodynamiclike theory of internal equilibrium and constrained equilibrium states of individual molecular systems is formulated, based on the Legendre transformed density functional theory (LT DFT). The molecular system (nonrelativistic, field free, Born-Oppenheimer or non-Born-Oppenheimer) is treated as the closed composite thermodynamic system, consisting of very small, rigid (open) subsystems (simple systems) containing a multi-(m)-component charged fluid in the presence of an external field. The generalized Levy constrained search construction of various ``thermodynamic'' potentials of LT DFT is given and the local Maxwell relations are derived. The reduction of various second-order partial functional derivatives (system sensitivities) in terms of few independent, basic kernels is described, using the Jacobian determinants technique. The qualitative implications for the basic kernels of the theory, from the Maxwell relations and stability criteria (generalized Le Châtelier and Le Châtelier-Braun principles) are systematically examined. Finally, possible applications of the general formalism in the thermodynamic analysis of the chemical bond, molecular stability, and chemical reactivity are identified.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; Nicholson, D. M.
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; ...
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of themore » density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.« less
NASA Astrophysics Data System (ADS)
Hassaninia, Iman; Ghayour, Rahim; Abiri, Habib; Sheikhi, Mohammad
2009-12-01
The effect of noise on the performance of Schottky Barrier Carbon Nanotube Field Effect Transistors (SB-CNTFETs) has been investigated under various bias conditions. In order to calculate the noise power spectral density, the Non-Equilibrium Green's Function formalism (NEGF) is used to obtain the transmission coefficient and the number of carriers inside the channel. Results are presented in two sections: In the first section the Hooge's empirical rule is used to investigate the flicker noise properties of SB-CNTFETs with defects in the gate oxide region, while in the second section the thermal and shot noise properties of SB-CNTFETs are studied. Finally, the best bias points in the ON and OFF states have been suggested according to the total noise power spectral density and the device signal to noise ratio.
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.
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.
Excitons in Time-Dependent Density-Functional Theory.
Ullrich, Carsten A; Yang, Zeng-hui
2016-01-01
This chapter gives an overview of the description of the optical and dielectric properties of bulk insulators and semiconductors in time-dependent density-functional theory (TDDFT), with an emphasis on excitons. We review the linear-response formalism for periodic solids, discuss excitonic exchange-correlation kernels, calculate exciton binding energies for various materials, and compare the treatment of excitons with TDDFT and with the Bethe-Salpeter equation.
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Green's-function formalism for waveguide QED applications
NASA Astrophysics Data System (ADS)
Schneider, Michael P.; Sproll, Tobias; Stawiarski, Christina; Schmitteckert, Peter; Busch, Kurt
2016-01-01
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations both in the time and the frequency domains. In the single-excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cutoff frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent T -matrix equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the few-photon nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping, the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and nonequilibrium effects.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
NASA Astrophysics Data System (ADS)
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-01
The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_{max} = (l,m)_{max}, while scattering matrices, which determine spectral properties, are truncated at L_{tr} = (l,m)_{tr} where phase shifts δl>l_{tr} are negligible. Historically, L_{max} is set equal to L_{tr}, which is correct for large enough L_{max} but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_{max} > L_{tr} with δl>l_{tr} set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R^{3} process with rank N(l_{tr} + 1)^{2}] and includes higher-L contributions via linear algebra [R^{2} process with rank N(l_{max} +1)^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1_{0} CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L_{max} for a given L_{tr}.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; ...
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang andmore » Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.« less
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Wave function of the universe from a matrix-valued first-order formalism
NASA Astrophysics Data System (ADS)
Kruglov, Sergey I.; Faizal, Mir
2015-03-01
In this paper, the Wheeler-DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler-DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler-DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler-DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.
Maps of current density using density-functional methods
NASA Astrophysics Data System (ADS)
Soncini, A.; Teale, A. M.; Helgaker, T.; de Proft, F.; Tozer, D. J.
2008-08-01
The performance of several density-functional theory (DFT) methods for the calculation of current densities induced by a uniform magnetic field is examined. Calculations are performed using the BLYP and KT3 generalized-gradient approximations, together with the B3LYP hybrid functional. For the latter, both conventional and optimized effective potential (OEP) approaches are used. Results are also determined from coupled-cluster singles-and-doubles (CCSD) electron densities by a DFT constrained search procedure using the approach of Wu and Yang (WY). The current densities are calculated within the CTOCD-DZ2 distributed origin approach. Comparisons are made with results from Hartree-Fock (HF) theory. Several small molecules for which correlation is known to be especially important in the calculation of magnetic response properties are considered-namely, O3, CO, PN, and H2CO. As examples of aromatic and antiaromatic systems, benzene and planarized cyclooctatetraene molecules are considered, with specific attention paid to the ring current phenomenon and its Kohn-Sham orbital origin. Finally, the o-benzyne molecule is considered as a computationally challenging case. The HF and DFT induced current maps show qualitative differences, while among the DFT methods the maps show a similar qualitative structure. To assess quantitative differences in the calculated current densities with different methods, the maximal moduli of the induced current densities are compared and integration of the current densities to yield shielding constants is performed. In general, the maximal modulus is reduced in moving from HF to B3LYP and BLYP, and further reduced in moving to KT3, OEP(B3LYP), and WY(CCSD). The latter three methods offer the most accurate shielding constants in comparison with both experimental and ab initio data and hence the more reliable route to DFT calculation of induced current density in molecules.
Numerical Density-to-Potential Inversions in Time-dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Jensen, Daniel; Inchaustegui, Jean Pierre; Wasserman, Adam
2014-03-01
Time-dependent Density Functional Theory (TDDFT) is a formally exact method for solving the quantum many-body problem. In Kohn-Sham TDDFT, a fictitious noninteracting system is defined that exactly reproduces the time-dependent density of the interacting system. The potential that determines this noninteracting system (the time-dependent Kohn-Sham potential) has been proven to exist under certain restrictions, but finding the exact Kohn-Sham potential for a given density remains challenging. We show that this ill-posed inverse problem requires some form of regularization to produce realistic Kohn-Sham potentials. We explore various forms of regularization and illustrate how they work on simple one-dimensional model systems. We also show how our method can be applied to problems with both particle-in-a-box and periodic boundary conditions subject to oscillating electric fields.
Minh, David D L; Vaikuntanathan, Suriyanarayanan
2011-01-21
The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism.
Density-matrix formalism for the photoion-electron entanglement in atomic photoionization
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2006-09-15
The density-matrix theory, based on Dirac's relativistic equation, is applied for studying the entanglement between the photoelectron and residual ion in the course of the photoionization of atoms and ions. In particular, emphasis is placed on deriving the final-state density matrix of the overall system 'photoion+electron', including interelectronic effects and the higher multipoles of the radiation field. This final-state density matrix enables one immediately to analyze the change of entanglement as a function of the energy, angle and the polarization of the incoming light. Detailed computations have been carried out for the 5s photoionization of neutral strontium, leading to a photoion in a 5s {sup 2}S J{sub f}=1/2 level. It is found that the photoion-electron entanglement decreases significantly near the ionization threshold and that, in general, it depends on both the photon energy and angle. The possibility to extract photoion-electron pairs with a well-defined degree of entanglement may have far-reaching consequences for quantum information and elsewhere.
Dynamical density functional theory with hydrodynamic interactions in confined geometries
NASA Astrophysics Data System (ADS)
Goddard, B. D.; Nold, A.; Kalliadasis, S.
2016-12-01
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Probability Density Function at the 3D Anderson Transition
NASA Astrophysics Data System (ADS)
Rodriguez, Alberto; Vasquez, Louella J.; Roemer, Rudolf
2009-03-01
The probability density function (PDF) for the wavefunction amplitudes is studied at the metal-insulator transition of the 3D Anderson model, for very large systems up to L^3=240^3. The implications of the multifractal nature of the state upon the PDF are presented in detail. A formal expression between the PDF and the singularity spectrum f(α) is given. The PDF can be easily used to carry out a numerical multifractal analysis and it appears as a valid alternative to the more usual approach based on the scaling law of the general inverse participation rations.
Spin Density Matrices for Nuclear Density Functionals with Parity Violation
NASA Astrophysics Data System (ADS)
Barrett, Bruce; Giraud, Bertrand
2010-11-01
Within the context of the radial density functional [1], we apply the spin density matrix (SDM) used in atomic and molecular physics [2] to nuclear physics. The vector part of the SDM defines a ``hedgehog'' situation, which exists only if nuclear states contain some amount of parity violation. Thus, looking for the vector profile of the SDM could be used as a test for parity violation in nuclei. The difference between the scalar profile and the vector profile of the SDM will be illustrated by a toy model. [4pt] [1] B. G. Giraud, Phys. Rev. C 78, 014307 (2008).[0pt] [2] A. Goerling, Phys. Rev. A 47, 2783 (1993).
Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn
2016-08-15
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
Nagy, A.
2011-09-15
A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).
Density Scaling of Noninteracting Kinetic Energy Functionals.
Borgoo, Alex; Tozer, David J
2013-05-14
The influence of imposing an approximate density scaling condition on a noninteracting kinetic energy functional is investigated. A simple generalized gradient approximation (GGA) is presented, which satisfies both the density scaling condition and the usual coordinate scaling condition; the remaining multiplicative constant is determined from an energy criterion. In post-Kohn-Sham calculations, noninteracting kinetic energies of the closed-shell molecules of the G1 set determined using the GGA are a modest improvement over those determined using the corresponding local functional, which does not satisfy the density scaling condition. Potential energy curves of CO, F2, and P2 exhibit binding with the GGA, compared to purely repulsive curves with the local functional. Adjusting the exponent in the GGA form in order to optimize energy accuracy violates the density scaling condition, and two of the diatomics no longer exhibit binding. Results are compared with those from other local/GGA functionals in the literature.
Many-body theory and Energy Density Functionals
NASA Astrophysics Data System (ADS)
Baldo, M.
2016-07-01
In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach.
Implementation Strategies for Orbital-dependent Density Functionals
NASA Astrophysics Data System (ADS)
Bento, Marsal E.; Vieira, Daniel
2016-12-01
The development of density functional theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems. Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.
Whitenack, Daniel L; Wasserman, Adam
2012-04-28
Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.
NASA Astrophysics Data System (ADS)
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-07
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The
Nuclear chiral and magnetic rotation in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Zhao, Pengwei
2016-05-01
Excitations of chiral rotation observed in triaxial nuclei and magnetic and/or antimagnetic rotations (AMR) seen in near-spherical nuclei have attracted a lot of attention. Unlike conventional rotation in well-deformed or superdeformed nuclei, here the rotational axis is not necessary coinciding with any principal axis of the nuclear density distribution. Thus, tilted axis cranking (TAC) is mandatory to describe these excitations self-consistently in the framework of covariant density functional theory (CDFT). We will briefly introduce the formalism of TAC-CDFT and its application for magnetic and AMR phenomena. Configuration-fixed CDFT and its predictions for nuclear chiral configurations and for favorable triaxial deformation parameters are also presented, and the discoveries of the multiple chiral doublets in 133Ce and 103Rh are discussed.
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.}
Full canonical information from grand-potential density-functional theory.
de Las Heras, Daniel; Schmidt, Matthias
2014-12-05
We present a general and formally exact method to obtain the canonical one-body density distribution and the canonical free energy from direct decomposition of classical density functional results in the grand ensemble. We test the method for confined one-dimensional hard-core particles for which the exact grand potential density functional is explicitly known. The results agree to within high accuracy with those from exact methods and our Monte Carlo many-body simulations. The method is relevant for treating finite systems and for dynamical density functional theory.
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.
Bloomfield, Philip E
2005-05-01
The pulse-echo impulse-response format in the Field II formalism is generalized to separately located transmitter and receiver. To first order in sound velocity and density perturbations, identical results for the scattering-object function are obtained for the Morse-Ingard and the Chernov formulation in both the temporal and frequency domains: f(s)=-[2Delta(c/c)+(Delta(rho/rho))(1-cos(theta))] where for ultrasonic pulse-echo or transmission modality, cos(theta) approximately -1 or +1, respectively.
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
Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
Van der Waals density functional: An appropriate exchange functional
NASA Astrophysics Data System (ADS)
Cooper, Valentino R.
2010-04-01
In this Rapid Communication, an exchange functional which is compatible with the nonlocal Rutgers-Chalmers correlation functional [van der Waals density functional (vdW-DF)] is presented. This functional, when employed with vdW-DF, demonstrates remarkable improvements on intermolecular separation distances while further improving the accuracy of vdW-DF interaction energies. The key to the success of this three-parameter functional is its reduction in short-range exchange repulsion through matching to the gradient expansion approximation in the slowly varying/high-density limit while recovering the large reduced gradient, s , limit set in the revised Perdew-Burke-Ernzerhof (revPBE) exchange functional. This augmented exchange functional could be a solution to long-standing issues of vdW-DF lending to further applicability of density-functional theory to the study of relatively large, dispersion bound (van der Waals) complexes.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.
Putz, Mihai V.
2009-01-01
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Error analysis in nuclear density functional theory
NASA Astrophysics Data System (ADS)
Schunck, Nicolas; McDonnell, Jordan D.; Sarich, Jason; Wild, Stefan M.; Higdon, Dave
2015-03-01
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the Universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew J.; Marianetti, Chris A.
2015-07-01
Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the "plus U" extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare-earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.
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.
Density functional calculation of intermolecular potentials.
Nyeland, Carl
2011-06-30
Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.
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.
Radiative Strength Functions and Level Densities
Schiller, A; Becker, J A; Bernstein, L A; Voinov, A; Guttormsen, M; Hjorth-Jensen, M; Rekstad, J; Siem, S; Mitchell, G E; Tavukcu, E
2002-08-28
Radiative strength functions and level densities have been extracted from primary {gamma}-ray spectra for {sup 27,28}Si, {sup 56,57}Fe, {sup 96,97}Mo, and several rare earth nuclei. An unexpectedly strong ({approx} 1 mb MeV) resonance at 3 MeV in the radiative strength function has been observed for well-deformed rare earth nuclei. The physical origin of this resonance and its connection to the scissors mode is discussed.
Density functional theory studies of etoricoxib
NASA Astrophysics Data System (ADS)
Sachdeva, Ritika; Kaur, Prabhjot; Singh, V. P.; Saini, G. S. S.
2016-05-01
Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of density functional theory calculations using 6-311++ g (d, p) basis set and B3LYP functional.
Density functional theory: Fixing Jacob's ladder
NASA Astrophysics Data System (ADS)
Car, Roberto
2016-09-01
Density functional theory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.
Uncertainty Quantification for Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
McDonnell, Jordan; Schunck, Nicolas; Nazarewicz, Witold; Higdon, Dave; Sarich, Jason; Wild, Stefan
2014-09-01
Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. Nuclear density functional theory exhibits good overall agreement with measured nuclear masses for medium-mass to heavy nuclei. But the predictions of various models diverge substantially near the neutron and proton drip lines. Quantifying the theory's inherent uncertainty is essential for making reliable predictions. Through a Bayesian analysis, we calculate the theoretical uncertainty for nuclear masses obtained with a Skyrme-class energy density functional. We also assess whether a recent set of mass measurements of neutron-rich nuclei reduces the uncertainty in this model's predictions near the neutron drip line. This work was supported by the US Department of Energy under Contracts No. DE-SC0008499 and No. DE-AC52-07NA27344.
Differentiable but exact formulation of density-functional theory.
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M; Helgaker, Trygve
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
NASA Technical Reports Server (NTRS)
Hummer, D. G.; Mihalas, Dimitri
1988-01-01
An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.
Stochastic Time-Dependent Current-Density Functional Theory
NASA Astrophysics Data System (ADS)
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Dane, Markus; Gonis, Antonios
2016-07-05
Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.
Density Functional Approach and Random Matrix Theory in Proteogenesis
NASA Astrophysics Data System (ADS)
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Density functional theory for inhomogeneous associating chain fluids.
Bryk, P; Sokołowski, S; Pizio, O
2006-07-14
We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.
Reproducibility in density functional theory calculations of solids.
Lejaeghere, Kurt; Bihlmayer, Gustav; Björkman, Torbjörn; Blaha, Peter; Blügel, Stefan; Blum, Volker; Caliste, Damien; Castelli, Ivano E; Clark, Stewart J; Dal Corso, Andrea; de Gironcoli, Stefano; Deutsch, Thierry; Dewhurst, John Kay; Di Marco, Igor; Draxl, Claudia; Dułak, Marcin; Eriksson, Olle; Flores-Livas, José A; Garrity, Kevin F; Genovese, Luigi; Giannozzi, Paolo; Giantomassi, Matteo; Goedecker, Stefan; Gonze, Xavier; Grånäs, Oscar; Gross, E K U; Gulans, Andris; Gygi, François; Hamann, D R; Hasnip, Phil J; Holzwarth, N A W; Iuşan, Diana; Jochym, Dominik B; Jollet, François; Jones, Daniel; Kresse, Georg; Koepernik, Klaus; Küçükbenli, Emine; Kvashnin, Yaroslav O; Locht, Inka L M; Lubeck, Sven; Marsman, Martijn; Marzari, Nicola; Nitzsche, Ulrike; Nordström, Lars; Ozaki, Taisuke; Paulatto, Lorenzo; Pickard, Chris J; Poelmans, Ward; Probert, Matt I J; Refson, Keith; Richter, Manuel; Rignanese, Gian-Marco; Saha, Santanu; Scheffler, Matthias; Schlipf, Martin; Schwarz, Karlheinz; Sharma, Sangeeta; Tavazza, Francesca; Thunström, Patrik; Tkatchenko, Alexandre; Torrent, Marc; Vanderbilt, David; van Setten, Michiel J; Van Speybroeck, Veronique; Wills, John M; Yates, Jonathan R; Zhang, Guo-Xu; Cottenier, Stefaan
2016-03-25
The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.
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.
Computing dispersion interactions in density functional theory
NASA Astrophysics Data System (ADS)
Cooper, V. R.; Kong, L.; Langreth, D. C.
2010-02-01
In this article techniques for including dispersion interactions within density functional theory are examined. In particular comparisons are made between four popular methods: dispersion corrected DFT, pseudopotential correction schemes, symmetry adapted perturbation theory, and a non-local density functional - the so called Rutgers-Chalmers van der Waals density functional (vdW-DF). The S22 benchmark data set is used to evaluate the relative accuracy of these methods and factors such as scalability and transferability are also discussed. We demonstrate that vdW-DF presents an excellent compromise between computational speed and accuracy and lends most easily to full scale application in solid materials. This claim is supported through a brief discussion of a recent large scale application to H2 in a prototype metal organic framework material (MOF), Zn2BDC2TED. The vdW-DF shows overwhelming promise for first-principles studies of physisorbed molecules in porous extended systems; thereby having broad applicability for studies as diverse as molecular adsorption and storage, battery technology, catalysis and gas separations.
Tabacchi, G; Hutter, J; Mundy, C
2005-04-07
A combined linear response--frozen electron density model has been implemented in a molecular dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory, and a response contribution determined by the instaneous ionic configuration of the system. The method is free from empirical pair-potentials and the parameterization protocol involves only calculations on properly chosen subsystems. They apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparable to Kohn-Sham density functional calculations.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
NASA Technical Reports Server (NTRS)
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Differentiable but exact formulation of density-functional theory
Kvaal, Simen Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M.
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.
Differentiable but exact formulation of density-functional theory
NASA Astrophysics Data System (ADS)
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M.; Helgaker, Trygve
2014-05-01
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ɛ > 0, pairs of conjugate functionals (ɛE, ɛF) that converge to (E, F) pointwise everywhere as ɛ → 0+, and such that ɛF is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy ɛE(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for (ɛE, ɛF). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of ɛF, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Density-functional calculations of the surface tension of liquid Al and Na
NASA Technical Reports Server (NTRS)
Stroud, D.; Grimson, M. J.
1984-01-01
Calculations of the surface tensions of liquid Al and Na are described using the full ionic density functional formalism of Wood and Stroud (1983). Surface tensions are in good agreement with experiment in both cases, with results substantially better for Al than those found previously in the gradient approximation. Preliminary minimization with respect to surface profile leads to an oscillatory profile superimposed on a nearly steplike ionic density disribution; the oscillations have a wavellength of about a hardsphere diameter.
Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints
NASA Astrophysics Data System (ADS)
Woodward, Clifford E.; Forsman, Jan
2008-08-01
We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of ``site functions'' for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.
β-function formalism for inflationary models with a non minimal coupling with gravity
Pieroni, M.
2016-02-01
We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of our recently proposed β-function formalism for inflation. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.
Density functional theory for atomic Fermi gases
NASA Astrophysics Data System (ADS)
Ma, Ping Nang; Pilati, Sebastiano; Troyer, Matthias; Dai, Xi
2012-08-01
The interplay between interaction and inhomogeneity for electrons in solids generates many interesting phenomena, including insulating and metallic behaviour, magnetism, superconductivity, quantum criticality and more exotic phases. Many of the same phenomena appear in ultracold fermionic atoms in optical lattices, which provide clean, controlled and tunable `quantum simulators' to explore the intriguing physics of fermionic systems. Although density functional theory (DFT) is widely used to calculate material properties, it has not yet been applied to cold atomic gases in optical lattices. Here we present a new density functional for short-range interactions (as opposed to Coulomb interactions of electrons), which renders DFT suitable for atomic Fermi gases. This grants us access to an extensive toolset, previously developed for materials simulations, to calculate the static and dynamic properties of atomic Fermi gases in optical lattices and external potentials. Ultracold atom quantum simulators can in turn be used to explore limitations of DFT functionals, and to further improve hybrid functionals, thus forming a bridge between materials simulations and atomic physics.
NASA Astrophysics Data System (ADS)
Calzetta, E.; Hu, B. L.
1987-01-01
We discuss the generalization to curved spacetime of a path-integral formalism of quantum field theory based on the sum over paths first going forward in time in the presence of one external source from an in vacuum to a state defined on a hypersurface of constant time in the future, and then backwards in time in the presence of a different source to the same in vacuum. This closed-time-path formalism which generalizes the conventional method based on in-out vacuum persistence amplitudes yields real and causal effective actions, field equations, and expectation values. We apply this method to two problems in semiclassical cosmology. First we study the back reaction of particle production in a radiation-filled Bianchi type-I universe with a conformal scalar field. Unlike the in-out formalism which yields complex geometries the real and causal effective action here yields equations for real effective geometries, with more readily interpretable results. It also provides a clear identification of particle production as a dissipative process in semiclassical theories. In the second problem we calculate the vacuum expectation value of the stress-energy tensor for a nonconformal massive λφ4 theory in a Robertson-Walker universe. This study serves to illustrate the use of Feynman diagrams and higher-loop calculations in this formalism. It also demonstrates the economy of this method in the calculation of expectation values over the mode-sum Bogolubov transformation methods ordinarily applied to matrix elements calculated in the conventional in-out approach. The capability of the closed-time-path formalism of dealing with Feynman, causal, and correlation functions on the same footing makes it a potentially powerful and versatile technique for treating nonequilibrium statistical properties of dynamical systems as in early-Universe quantum processes.
Recent progress in density functional theory
NASA Astrophysics Data System (ADS)
Truhlar, Donald
2014-03-01
Ongoing work involves several areas of density functional theory: new methods for computing electronic excitation energies, including a new way to remove spin contamination in the spin-flip Tamm-Dancoff approximation and a configuration-interaction-corrected Tamm-Dancoff Approximation for treating conical intersections; new ways to treat open-shell states, including a reinterpreted broken-symmetry method and multi-configuration Kohn-Sham theory; a new exchange-correlation functional; new tests of density functional theory against databases for electronic transition energies and molecules and solids containing metal atoms; and applications. A selection of results will be presented. I am grateful to the following collaborators for contributions to the ongoing work: Boris Averkiev, Rebecca Carlson, Laura Fernandez, Laura Gagliardi, Chad Hoyer, Francesc Illas, Miho Isegawa, Shaohong Li, Giovanni Li Manni, Sijie Luo, Dongxia Ma, Remi Maurice, Rubén Means-Pañeda, Roberto Peverati, Nora Planas, Prasenjit Seal, Pragya Verma, Bo Wang, Xuefei Xu, Ke R. Yang, Haoyu Yu, Wenjing Zhang, and Jingjing Zheng. Supported in part by the AFOSR and U.S. DOE.
Optimization of constrained density functional theory
NASA Astrophysics Data System (ADS)
O'Regan, David D.; Teobaldi, Gilberto
2016-07-01
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.
Insight and progress in density functional theory
NASA Astrophysics Data System (ADS)
Yang, Weitao; Mori-Sanchez, Paula; Cohen, Aron J.
2012-12-01
Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties. The errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These errors can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently.
Modulation Based on Probability Density Functions
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Probability density functions in turbulent channel flow
NASA Technical Reports Server (NTRS)
Dinavahi, Surya P. G.
1992-01-01
The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.
Gross-Pitaevskii Approximation for the Bose-Einstein Condensation: Green Function Formalism.
NASA Astrophysics Data System (ADS)
Trallero-Giner, Carlos; Trallero-Herrero, Carlos; Birman, Joseph L.
2003-03-01
Using the Green function method we solved the time-independent, T=O K, one-dimension, Gross-Pitaevskii equation (G-PE) for the Bose-Einstein condensation in dilute atomic alkali gases. We are able to formally obtain an analytical solution for the order parameter Ψ (x) and for the chemical potential μ as a function of the trapping frequency ω and the effective interaction constant \\overlineΛ . A Bonn-Neuman iterative procedure is implemented for solving the non-linear system of equations obtained from the G-PE equations into the formalism. Also, we compare the G.f. formalism and two other method of solution: variational (soliton solution) and perturbation theory for the universal parameter, \\overlineΛ /(lhbar ω ) (l is the magnetic length), which characterize the atomic gas condensation. Generalization of the above mentioned methods for two order parameter Ψ _i(x); i=1,2 (i.e. two species of alkali atoms) is also presented.
Constrained density functional for noncollinear magnetism
NASA Astrophysics Data System (ADS)
Ma, Pui-Wai; Dudarev, S. L.
2015-02-01
Energies of arbitrary small- and large-angle noncollinear excited magnetic configurations are computed using a highly accurate constrained density functional theory approach. Numerical convergence and accuracy are controlled by the choice of Lagrange multipliers λI entering the constraining conditions. The penalty part Ep of the constrained energy functional at its minimum is shown to be inversely proportional to λI, enabling a simple, robust, and accurate iterative procedure to be followed to find a convergent solution. The method is implemented as a part of ab initio vasp package, and applied to the investigation of noncollinear B2-like and <001 > double-layer antiferromagnetic configurations of bcc iron, Fe2 dimer, and amorphous iron. Forces acting on atoms depend on the orientations of magnetic moments, and the proposed approach enables constrained self-consistent noncollinear magnetic and structural relaxation of large atomic systems to be carried out.
Band terminations in density functional theory
Afanasjev, A. V.
2008-11-15
The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its maximum exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields provided that other effects can be reliably isolated. Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion [H. Zdunczuk, W. Satula, and R. A. Wyss, Phys. Rev. C 71, 024305 (2005)] that the relative energies of the terminating states in the N{ne}Z,A{approx}44 mass region given by {delta}E provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction in density functional theories has been reanalyzed. The current investigation shows that the {delta}E value is affected also by the relative placement of the states with different orbital angular momentum l, namely, the placement of the d (l=2) and f (l=3) states. This indicates the dependence of the {delta}E value on the properties of the central potential.
Nishimoto, Yoshio
2015-09-07
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
Nitrogenase structure and function relationships by density functional theory.
Harris, Travis V; Szilagyi, Robert K
2011-01-01
Modern density functional theory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic density functional theory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.
Dispersion interactions in Density Functional Theory
NASA Astrophysics Data System (ADS)
Andrinopoulos, Lampros; Hine, Nicholas; Mostofi, Arash
2012-02-01
Semilocal functionals in Density Functional Theory (DFT) achieve high accuracy simulating a wide range of systems, but miss the effect of dispersion (vdW) interactions, important in weakly bound systems. We study two different methods to include vdW in DFT: First, we investigate a recent approach [1] to evaluate the vdW contribution to the total energy using maximally-localized Wannier functions. Using a set of simple dimers, we show that it has a number of shortcomings that hamper its predictive power; we then develop and implement a series of improvements [2] and obtain binding energies and equilibrium geometries in closer agreement to quantum-chemical coupled-cluster calculations. Second, we implement the vdW-DF functional [3], using Soler's method [4], within ONETEP [5], a linear-scaling DFT code, and apply it to a range of systems. This method within a linear-scaling DFT code allows the simulation of weakly bound systems of larger scale, such as organic/inorganic interfaces, biological systems and implicit solvation models. [1] P. Silvestrelli, JPC A 113, 5224 (2009). [2] L. Andrinopoulos et al, JCP 135, 154105 (2011). [3] M. Dion et al, PRL 92, 246401 (2004). [4] G. Rom'an-P'erez, J.M. Soler, PRL 103, 096102 (2009). [5] C. Skylaris et al, JCP 122, 084119 (2005).
Cuny, Jerome; Korchagina, Kseniia; Menakbi, Chemseddine; Mineva, Tzonka
2017-03-01
Application of ab initio molecular dynamics to study free energy surfaces (FES) is still not commonly performed because of the extensive sampling required. Indeed, it generally necessitates computationally costly simulations of more than several hundreds of picoseconds. To achieve such studies, efficient density functional theory (DFT) formalisms, based on various levels of approximate computational schemes, have been developed, and provide a good alternative to commonly used DFT implementations. We report benchmark results on the conformational change FES of alanine dipeptide obtained with auxiliary density functional theory (ADFT) and second- and third-order density functional tight-binding (DFTB) methods coupled to metadynamics simulations. The influence of an explicit water solvent is also studied with DFTB, which was made possible by its lower computational cost compared to ADFT. Simulations lengths of 2.1 and 15 ns were achieved with ADFT and DFTB, respectively, in a reasonably short computational time. ADFT leads to a free energy difference (ΔF eq-ax) of ∼ -3 kcal mol(-1) between the two low energy conformers, C7eq and C7ax, which is lower by only 1.5 kcal mol(-1) than the ΔF eq-ax computed with DFTB. The two minima in ADFT FES are separated by an energy barrier of 9 kcal mol(-1), which is higher than the DFTB barriers by 2-4 kcal mol(-1). Despite these small quantitative differences, the DFTB method reveals FES shapes, confor-mation geometries and energies of the stationary points in good agreement with these found with ADFT. This validates the promising applicability of DFTB to FES of reactions occurring in larger-size systems placed in complex environments.
Nuclear structure and dynamics with density functional theory
NASA Astrophysics Data System (ADS)
Stetcu, Ionel
2015-10-01
Even in the absence of ab initio methods capable of tackling heavy nuclei without restrictions, one can obtain an ab initio description of ground-state properties by means of the density functional theory (DFT), and its extension to superfluid systems in its local variant, the superfluid local density approximation (SLDA). Information about the properties of excited states can be obtained in the same framework by using an extension to the time-dependent (TD) phenomena. Unlike other approaches in which the nuclear structure information is used as a separate input into reaction models, the TD approach treats on the same footing the nuclear structure and dynamics, and is well suited to provide more reliable description for a large number of processes involving heavy nuclei, from the nuclear response to electroweak probes, to nuclear reactions, such as neutron-induced reactions, or nuclear fusion and fission. Such processes, sometimes part of integrated nuclear systems, have important applications in astrophysics, energy production, global security, etc. In this talk, I will present the simulation of a simple reaction, that is the Coulomb excitation of a 238U nucleus, and discuss the application of the TD-DFT formalism to the description of induced fission. I gratefully acknowledge partial support of the U.S. Department of Energy through an Early Career Award of the LANL/LDRD Program.
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.
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe2O3, Fe3O4, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
Phases of Polonium via Density Functional Theory
NASA Astrophysics Data System (ADS)
Verstraete, Matthieu J.
2010-01-01
The thermodynamical properties of the main phases of metallic polonium are examined using density functional theory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.
Modeling NMR lineshapes using logspline density functions.
Raz, J; Fernandez, E J; Gillespie, J
1997-08-01
Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An algorithm for fitting the model is described, the performance of the model and algorithm is investigated in applications to real and simulated data sets, and the logspline approach is compared to a previous Hermitian spline approach and to the Lorentzian model. The logspline model is more parsimonious than the Hermitian spline model, provides a better fit to real data, and is much less biased than the Lorentzian model.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2006-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2004-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Density-functional study of paramagnetic iron
NASA Astrophysics Data System (ADS)
Zhang, Hualei; Johansson, Börje; Vitos, Levente
2011-10-01
By using density-functional theory in combination with the coherent-potential approximation and the disordered local magnetic moment picture, we demonstrate that the competing high-temperature cubic phases of paramagnetic Fe correspond to two distinct total energy minima in the tetragonal (Bain) configurational space. Both the face-centered-cubic (fcc) and the body-centered-cubic (bcc) lattices are dynamically stable, and at static conditions the fcc structure is found to be the thermodynamically stable phase. The theoretical bcc and fcc bulk parameters are in agreement with the experimental data. Due to the shallow energy minimum around the bcc structure, increasing temperature is predicted to stabilize the bcc (δ) phase against the fcc (γ) one.
Unified Description of Electron-Nucleus Scattering within the Spectral Function Formalism.
Rocco, Noemi; Lovato, Alessandro; Benhar, Omar
2016-05-13
The formalism based on factorization and nuclear spectral functions has been generalized to treat transition matrix elements involving two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasielastic and Δ-production peaks. The relation to approaches based on the independent particle of the nucleus and the implications for the analysis of flux-integrated neutrino-nucleus cross sections are discussed.
Density Functional O(N) Calculations
NASA Astrophysics Data System (ADS)
Ordejón, Pablo
1998-03-01
We have developed a scheme for performing Density Functional Theory calculations with O(N) scaling.(P. Ordejón, E. Artacho and J. M. Soler, Phys. Rev. B, 53), 10441 (1996) The method uses arbitrarily flexible and complete Atomic Orbitals (AO) basis sets. This gives a wide range of choice, from extremely fast calculations with minimal basis sets, to greatly accurate calculations with complete sets. The size-efficiency of AO bases, together with the O(N) scaling of the algorithm, allow the application of the method to systems with many hundreds of atoms, in single processor workstations. I will present the SIESTA code,(D. Sanchez-Portal, P. Ordejón, E. Artacho and J. M. Soler, Int. J. Quantum Chem., 65), 453 (1997) in which the method is implemented, with several LDA, LSD and GGA functionals available, and using norm-conserving, non-local pseudopotentials (in the Kleinman-Bylander form) to eliminate the core electrons. The calculation of static properties such as energies, forces, pressure, stress and magnetic moments, as well as molecular dynamics (MD) simulations capabilities (including variable cell shape, constant temperature and constant pressure MD) are fully implemented. I will also show examples of the accuracy of the method, and applications to large-scale materials and biomolecular systems.
Building a Universal Nuclear Energy Density Functional
Carlson, Joe A.; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
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).
Pederson, Mark R.
2015-02-14
A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeit slightly too low.
Pederson, Mark R
2015-02-14
A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeit slightly too low.
Monte Carlo Green's function formalism for the propagation of partially coherent light.
Prahl, Scott A; Fischer, David G; Duncan, Donald D
2009-07-01
We present a Monte Carlo-derived Green's function for the propagation of partially spatially coherent fields. This Green's function, which is derived by sampling Huygens-Fresnel wavelets, can be used to propagate fields through an optical system and to compute first- and second-order field statistics directly. The concept is illustrated for a cylindrical f/1 imaging system. A Gaussian copula is used to synthesize realizations of a Gaussian Schell-model field in the pupil plane. Physical optics and Monte Carlo predictions are made for the first- and second-order statistics of the field in the vicinity of the focal plane for a variety of source coherence conditions. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. This formalism can be generally employed to treat the interaction of partially coherent fields with diffracting structures.
Filatov, Michael; Zou, Wenli; Cremer, Dieter
2012-03-13
The analytic linear response formalism for the calculation of the effective contact densities ρ̅ in the context of the normalized elimination of the small component (NESC) method is developed and implemented. The formalism is tested for the calculation of contact densities and contact density differences in a series of mercury cations and mercury-containing molecules. The calculations carried out at the NESC/SCF, NESC/MP2, and NESC/CCSD levels of theory demonstrate high sensitivity of the contact density to the local coordination environment and the oxidation state of mercury. The NESC/MP2 results are in a very good agreement with the NESC/CCSD ones, which suggests that the former method can be used as a cost-effective alternative to high-level ab initio calculations.
Density functional theory in the solid state.
Hasnip, Philip J; Refson, Keith; Probert, Matt I J; Yates, Jonathan R; Clark, Stewart J; Pickard, Chris J
2014-03-13
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.
Density functional theory in the solid state
Hasnip, Philip J.; Refson, Keith; Probert, Matt I. J.; Yates, Jonathan R.; Clark, Stewart J.; Pickard, Chris J.
2014-01-01
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure–property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program. PMID:24516184
Dynamical density functional theory for microswimmers.
Menzel, Andreas M; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-14
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Dynamical density functional theory for microswimmers
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-01
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Bone mineral density, adiposity, and cognitive functions
Sohrabi, Hamid R.; Bates, Kristyn A.; Weinborn, Michael; Bucks, Romola S.; Rainey-Smith, Stephanie R.; Rodrigues, Mark A.; Bird, Sabine M.; Brown, Belinda M.; Beilby, John; Howard, Matthew; Criddle, Arthur; Wraith, Megan; Taddei, Kevin; Martins, Georgia; Paton, Athena; Shah, Tejal; Dhaliwal, Satvinder S.; Mehta, Pankaj D.; Foster, Jonathan K.; Martins, Ian J.; Lautenschlager, Nicola T.; Mastaglia, Francis; Laws, Simon M.; Martins, Ralph N.
2015-01-01
Cognitive decline and dementia due to Alzheimer's disease (AD) have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD) and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34–87 years old (62.78 ± 9.27), were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after 3 years. Blood samples were collected for apolipoprotein E (APOE) genotyping and dual energy x-ray absorptiometry (DXA) was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status, and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms. PMID:25741279
DENSITY-FUNCTIONAL STUDY OF THE U-ZR SYSTEM
Landa, A; Soderlind, P; Turchi, P
2008-06-25
Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the {gamma} (bcc) and {delta} (C32) phases are in good agreement with experimental data. The decomposition curve for the {gamma}-based U-Zr solutions is calculated. Our calculations confirm that experimentally observed 'partial' ordering of the alloy components in the {delta}-UZr{sub 2} (AlB{sub 2}) phase, in which Zr atoms occupy the 'Al' position and the two 'B' sites are randomly shared by the U and Zr atoms, is the most energetically favorable within the C32 structure. We argue that stabilization of the {delta}-UZr{sub 2} phase relative to the {alpha}-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr. A comparison with stabilization of the {omega}-phase (also C32) in Zr under compression is made.
Remarks on time-dependent [current]-density functional theory for open quantum systems.
Yuen-Zhou, Joel; Aspuru-Guzik, Alán
2013-08-14
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Kühn, Michael; Weigend, Florian
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
NASA Astrophysics Data System (ADS)
Kühn, Michael; Weigend, Florian
2015-01-01
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation.
Kühn, Michael; Weigend, Florian
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.
Wybo, Willem A M; Boccalini, Daniele; Torben-Nielsen, Benjamin; Gewaltig, Marc-Oliver
2015-12-01
We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O(n) with the number n of inputs locations, contrary to the previously reported O(n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.
A density functional theory for colloids with two multiple bonding associating sites.
Haghmoradi, Amin; Wang, Le; Chapman, Walter G
2016-06-22
Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.
A half century of density functional theory
Zangwill, Andrew
2015-07-15
Today’s most popular method for calculating the electronic structure of atoms, molecules, liquids, solids, and plasmas began as a bold hypothesis: The electron density distribution completely characterizes the ground state of a many-electron system.
Validation of density-functional versus density-functional+U approaches for oxide ultrathin films
NASA Astrophysics Data System (ADS)
Barcaro, Giovanni; Thomas, Iorwerth Owain; Fortunelli, Alessandro
2010-03-01
A comparison between available experimental information and the predictions of density-functional and density-functional+U approaches is presented for oxide ultrathin films grown on single-crystal metal surfaces. Prototypical examples of monolayer phases of an ionic oxide (ZnO), a late transition metal oxide (NiO), and an early transition metal oxide (TiO2) are considered. The aim is to validate the theoretical approaches, focusing on the prediction of structural features and the reproduction of scanning tunneling microscopy images, rationalized in terms of the local density of states of the systems. It is found that it is possible to reasonably estimate the optimal lattice constant of ultrathin supported films and that the inclusion of the Hubbard U term appreciably improves the accuracy of theoretical predictions, especially in the case of nonpolar ultrathin phases of a transition metal oxide. Moreover, the optimal value of U for the oxide layer at the interface with the metal support is found to differ from that appropriate for the bulk oxide, as a consequence of the intermixing of oxide and support electronic states and screening effects.
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.
Michelini, Fabienne; Crépieux, Adeline; Beltako, Katawoura
2017-05-04
We discuss some thermodynamic aspects of energy conversion in electronic nanosystems able to convert light energy into electrical or/and thermal energy using the non-equilibrium Green's function formalism. In a first part, we derive the photon energy and particle currents inside a nanosystem interacting with light and in contact with two electron reservoirs at different temperatures. Energy conservation is verified, and radiation laws are discussed from electron non-equilibrium Green's functions. We further use the photon currents to formulate the rate of entropy production for steady-state nanosystems, and we recast this rate in terms of efficiency for specific photovoltaic-thermoelectric nanodevices. In a second part, a quantum dot based nanojunction is closely examined using a two-level model. We show analytically that the rate of entropy production is always positive, but we find numerically that it can reach negative values when the derived particule and energy currents are empirically modified as it is usually done for modeling realistic photovoltaic systems.
NASA Astrophysics Data System (ADS)
Riquelme-Galván, Mauricio; Robledo, Alberto
2017-02-01
We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of inhomogeneous systems and of the renormalization group (RG) method in nonlinear dynamics to provide a more accurate, formal, approach to the subject. The description of this remarkable correspondence encompasses, on the one hand, the density functional formalism, where classical and quantum mechanical analogues match the procedure for one-dimensional clusters, and, on the other, the RG fixed-point map of functional compositions that captures the essential dynamical behavior. We provide details of how the above-referred theoretical approaches interrelate and discuss the implications of the correspondence between the high-dimensional (degrees of freedom) phenomenon and low-dimensional dynamics.
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.
Quantum Electronic Stress: Density-Functional-Theory Formulation and Physical Manifestation
NASA Astrophysics Data System (ADS)
Hu, Hao; Liu, Miao; Wang, Z. F.; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng
2012-08-01
The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σQE) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σQE=ΞΔn as a quantum analog of classical Hooke’s law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.
TRL - A FORMAL TEST REPRESENTATION LANGUAGE AND TOOL FOR FUNCTIONAL TEST DESIGNS
NASA Technical Reports Server (NTRS)
Hops, J. M.
1994-01-01
A Formal Test Representation Language and Tool for Functional Test Designs (TRL) is an automatic tool and a formal language that is used to implement the Category-Partition Method and produce the specification of test cases in the testing phase of software development. The Category-Partition Method is particularly useful in defining the inputs, outputs and purpose of the test design phase and combines the benefits of choosing normal cases with error exposing properties. Traceability can be maintained quite easily by creating a test design for each objective in the test plan. The effort to transform the test cases into procedures is simplified by using an automatic tool to create the cases based on the test design. The method allows the rapid elimination of undesired test cases from consideration, and easy review of test designs by peer groups. The first step in the category-partition method is functional decomposition, in which the specification and/or requirements are decomposed into functional units that can be tested independently. A secondary purpose of this step is to identify the parameters that affect the behavior of the system for each functional unit. The second step, category analysis, carries the work done in the previous step further by determining the properties or sub-properties of the parameters that would make the system behave in different ways. The designer should analyze the requirements to determine the features or categories of each parameter and how the system may behave if the category were to vary its value. If the parameter undergoing refinement is a data-item, then categories of this data-item may be any of its attributes, such as type, size, value, units, frequency of change, or source. After all the categories for the parameters of the functional unit have been determined, the next step is to partition each category's range space into mutually exclusive values that the category can assume. In choosing partition values, all possible kinds
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…
ERIC Educational Resources Information Center
Purse, Katie; Gardner, Hilary
2013-01-01
This study aimed to consider collaborative practice in contributing to joint assessment and producing appropriate referral of children to speech and language therapy (SLT). Results of formal testing of selected comprehension skills are compared with functional/classroom performance as rated by class teachers. Thirty children aged 6.5-8.4 years,…
ERIC Educational Resources Information Center
Emick, J.; Welsh, M.
2005-01-01
Executive functions have been defined in the neuropsychological literature as those cognitive processes that underlie future-oriented, goal-directed behavior such as planning, working memory, inhibition, and self-monitoring. Piaget's final stage of cognitive development, formal operations, involves a systematic approach to problem solving that…
NASA Astrophysics Data System (ADS)
Ullrich, C. A.; Vignale, G.
2002-05-01
Time-dependent density-functional theory (TDFT) provides a way of calculating, in principle exactly, the linear response of interacting many-electron systems, and thus allows one to obtain their excitation energies. For extended systems, there exist excitations of a collective nature, such as bulk and surface plasmons in metals or intersubband plasmons in doped semiconductor quantum wells. This paper develops a quantitatively accurate first-principles description for the frequency and the linewidth of such excitations in inhomogeneous weakly disordered systems. A finite linewidth in general has intrinsic and extrinsic sources. At low temperatures and outside the region where electron-phonon interaction occurs, the only intrinsic damping mechanism is provided by electron-electron interaction. This kind of intrinsic damping can be described within TDFT, but one needs to go beyond the adiabatic approximation and include retardation effects. It has been shown [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)] that a density-functional response theory that is local in space but nonlocal in time has to be constructed in terms of the currents, rather than the density. This theory will be reviewed in the first part of this paper. For quantitatively accurate linewidths, extrinsic dissipation mechanisms, such as impurities or disorder, have to be included in the response theory. In the second part of this paper, we discuss how extrinsic dissipation can be described within the so-called memory-function formalism. This formalism will first be introduced and reviewed for homogeneous systems. We will then present a synthesis of TDFT with the memory function formalism for inhomogeneous systems, which allows one to simultaneously account for intrinsic and extrinsic damping of collective excitations. As an example where both sources of dissipation are important and where high-quality experimental data are available for comparison, we discuss intersubband
Time-dependent density functional theory quantum transport simulation in non-orthogonal basis.
Kwok, Yan Ho; Xie, Hang; Yam, Chi Yung; Zheng, Xiao; Chen, Guan Hua
2013-12-14
Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.
Schlüns, Danny; Franchini, Mirko; Götz, Andreas W; Neugebauer, Johannes; Jacob, Christoph R; Visscher, Lucas
2017-02-05
We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Kwong, N. H.; Binder, R.
2000-03-01
The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that describes coherent correlations in optically excited semiconductors. For practical reasons (including numerical evaluations), its application is limited to lowest-order nonlinearities, such as the χ(3) regime. Therefore, it is not convenient to use this formalism to examine the role played by incoherent many-body effects, such as carrier-carrier scattering and screening. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green's functions (NGF). A combination of the insights and technical advantages provided by the two (NGF and DCT) approaches will lead to a comprehensive microscopic theory for nonlinear optical phenomena in semiconductors. In this paper, we take a first step in this direction by presenting detailed one-to-one relations between the two formalisms within the χ(3) approximation. Starting from the standard perturbation theory of nonequilibrium Green's functions, we derive the essential minimal order factorization theorems, to arbitrary order, of DCT and the equations of motions for the interband polarization and the ``biexcitonic'' correlation function. This lays the foundation for future diagrammatic high-intensity generalizations of the DCT formalism.
Orthogonality of embedded wave functions for different states in frozen-density embedding theory
Zech, Alexander; Wesolowski, Tomasz A.; Aquilante, Francesco
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.
Orthogonality of embedded wave functions for different states in frozen-density embedding theory.
Zech, Alexander; Aquilante, Francesco; Wesolowski, Tomasz A
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles--embedded wave functions are only auxiliary objects used to obtain stationary densities--working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.
NASA Astrophysics Data System (ADS)
Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran
2016-09-01
In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7
Density functional calculations on hydrocarbon isodesmic reactions
NASA Astrophysics Data System (ADS)
Fortunelli, Alessandro; Selmi, Massimo
1994-06-01
Hartree—Fock, Hartree—Fock-plus-correlation and self-consistent Kohn—Sham calculations are performed on a set of hydrocarbon isodesmic reactions, i.e. reactions among hydrocarbons in which the number and type of carbon—carbon and carbon—hydrogen bonds is conserved. It is found that neither Hartree—Fock nor Kohn—Sham methods correctly predict standard enthalpies, Δ Hr(298 K), of these reactions, even though — for reactions involving molecules containing strained double bonds — the agreement between the theoretical estimates and the experimental values of Δ Hr seems to be improved by the self-consistent solution of the Kohn—Sham equations. The remaining discrepancies are attributed to intramolecular dispersion effects, that are not described by ordinary exchange—correlation functionals, and are eliminated by introducing corrections based on a simple semi-empirical model.
A perturbative density functional theory for square-well fluids.
Jin, Zhehui; Tang, Yiping; Wu, Jianzhong
2011-05-07
We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.
Testing for parity violation in nuclei using spin density matrices for nuclear density functionals
NASA Astrophysics Data System (ADS)
Barrett, B. R.; Giraud, B. G.
2015-06-01
The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a ‘hedgehog’ situation, which exists only if nuclear states contain some amount of parity violation. A toy model is given as an illustrative example.
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.
Pérez-Jiménez, Angel J; Pérez-Jordá, José M; Illas, Francesc
2004-01-01
A new method to improve the excess spin density obtained from unrestricted Hartree-Fock wave functions in terms of natural orbitals is proposed. Using this modified excess spin density to evaluate the correlation energy by means of density functionals leads to large improvements in the computed magnetic coupling constants of several materials without need to modify the exchange contribution. This is important because it reconciles the density functional theory description with the one provided by multi-determinant wave functions. Using the present approach, the leading contribution to the magnetic coupling constant arises from electron correlation effects. The performance of the new method is illustrated on various materials including high-critical-temperature superconductors parent compounds.
NASA Astrophysics Data System (ADS)
Bruno, Ezio; Mammano, Francesco; Fiorino, Antonino; Morabito, Emanuela V.
2008-04-01
The class of the generalized coherent-potential approximations (GCPAs) to the density functional theory (DFT) is introduced within the multiple scattering theory formalism with the aim of dealing with ordered or disordered metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. Most existing DFT implementations of CPA-based theories belong to the GCPA class. The analysis of the formal properties of the density functional defined by GCPA theories shows that it consists of marginally coupled local contributions. Furthermore, it is shown that the GCPA functional does not depend on the details of the charge density and that it can be exactly rewritten as a function of the appropriate charge multipole moments to be associated with each lattice site. A general procedure based on the integration of the qV laws is described that allows for the explicit construction of the same function. The coarse-grained nature of the GCPA density functional implies a great deal of computational advantages and is connected with the O(N) scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the charge-excess functional (CEF) theory [E. Bruno , Phys. Rev. Lett. 91, 166401 (2003)], which here is offered in a generalized version that includes multipolar interactions. CEF and the GCPA numerical results are compared with status of art linearized augmented plane wave (LAPW) full-potential density functional calculations for 62 bcc- and fcc-based ordered CuZn alloys, in all the range of concentrations. Two facts clearly emerge from these extensive tests. In the first place, the discrepancies between GCPA and CEF results are always within the numerical accuracy of the calculations, both for the site charges and the total energies. In the second place, the
Applications and validations of the Minnesota density functionals
NASA Astrophysics Data System (ADS)
Zhao, Yan; Truhlar, Donald G.
2011-01-01
We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.
Density-functional theory for fluid-solid and solid-solid phase transitions
NASA Astrophysics Data System (ADS)
Bharadwaj, Atul S.; Singh, Yashwant
2017-03-01
We develop a theory to describe solid-solid phase transitions. The density functional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials u (r ) =ɛ "close="1 /n )">σ /r n , where parameter n measures softness of the potential. We find that for 1 /n ≥0.154 the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.
Encouraging the Transition from Concrete to Formal Cognitive Functioning--An Experiment
ERIC Educational Resources Information Center
Lawson, Anton E.; Wollman, Warren T.
2003-01-01
According to Piaget's theory, maturation of the nervous system is sufficient for the development of formal thought. If this were the case, the job of the educational system would be small indeed. Rather, maturation determines only the totality of possibilities and impossibilities at a given stage. This study investigates whether instructional…
Internal rotations of aromatic polyamides: a density functional theory study
NASA Astrophysics Data System (ADS)
Nishikawa, Joe; Imase, Tatsuya; Koike, Masao; Fukuda, Kaoru; Tokita, Masatoshi; Watanabe, Junji; Kawauchi, Susumu
2005-05-01
Internal rotations of benzanilide ( BA) and 4-(4'-aminobenzamido)benzoic acid ( AA) were investigated by density functional theory (DFT) calculations. B3LYP/6-31G* optimization for both BA and AA structures gives non-planar trans structures as the most stable conformers with lower energy of 4.60 and 5.08 kcal/mol than cis ones, respectively. The amide bond and aniline moiety are found to be coplanar in transBA, while in trans phenyl benzoate ( PB) the ester bond and benzoyl moiety are coplanar. The relaxed potential energy surface (PES) scans were then carried out with rotations of three single bonds, i.e. amide bond and both adjacent bonds. The discontinuous point is found on the relaxed PES for the amide bond rotation. This indicates that inversion of a pyramidal amino group is involved with the amide bond rotation. Therefore, two transition states (TSs) arise for rotation around the amide bond. Two TS structures ( TS-1 and TS-2) were optimized for both BA and AA, and their activation energies were estimated as 14.34 kcal/mol ( TS-1) and 16.27 kcal/mol ( TS-2) for BA, and 12.20 kcal/mol ( TS-1) for AA, respectively. The TS-2 structure for AA failed to be optimized. The activation energy for the amide bond rotation, which is larger than that of 7.90 kcal/mol for PB, as well as the coplanarity in aromatic amide is ascribed to the partial double bond character of amide bond. This is also confirmed by the Wiberg bond index (bond order). The chain persistence length for poly(4-benzamide) was estimated by the rotation matrix formalism using the calculated structural parameters of transAA. The estimated value of 1131 Å is longer than our previously calculated value of corresponding aromatic polyester, 364 Å for poly( p-hydroxybenzoic acid) [T. Imase, S. Kawauchi, J. Watanabe, Macromol. Theory Simul. 10 (2001) 434].
CO/Pt(111) : GGA density functional study of site preference for adsorption
NASA Astrophysics Data System (ADS)
Alaei, M.; Akbarzadeh, H.; Gholizadeh, H.; de Gironcoli, S.
2008-02-01
Based on density functional formalism, we investigate the site preference for the adsorption of CO on Cu, Rh, Ag, Pt, and Au(111) surfaces. The exchange-correlation term was approximated by BLYP, a functional within the generalized gradient approximation (GGA) family that combines Becke’s exchange functional with the Lee-Yang-Parr correlation functional. Our study shows that BLYP, although not a hybrid functional, can correctly predict the adsorption site for CO. This invalidate the general belief that only hybrid functionals are able to predict the correct site preference. We analyze our results by repeating all calculations using another well-known GGA functional, Perdew-Burke-Ernzerhof, which could trace back the origin of the success of BLYP to the different behavior of the two GGA functionals at large values of the reduced density gradients, s∝(∣∇n∣)/(n3/4) . This is a region where different functionals in the GGA family may legitimately behave very differently as it is poorly constrained on physical ground. Our present observation points to the possibility of further improving the accuracy of exchange-correlation functionals in the GGA family by properly constraining the remaining flexibility in the exchange-correlation kernel in this underdetermined region so as to reproduce known results in simple but critically important systems like the one studied here.
Density Functional Calculations for the Neutron Star Matter at Subnormal Density
NASA Astrophysics Data System (ADS)
Kashiwaba, Yu; Nakatsukasa, Takashi
The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (\\bar{ρ },Yp), varying the lattice constant of the unit cell. For small Yp values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.
Towards a more accurate van der Waals density functional
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2014-03-01
The van der Waals density functional (vdW-DF) of Dion et al. [1] has attracted considerable attention, because the functional is able to describe intra- and intermolecular bondings with different natures, e.g., covalent and van der Waals bondings in a seamless fashion within the framework of density functional theory. However, the accuracy of the functional is yet to be improved for the applications to various systems. Here I propose an exchange functional for the second version of vdW-DF [2], which improves the accuracy of vdW-DF. The keys in the improved exchange are the matching to the gradient expansion approximation in the slowly varying limit and the large density gradient behavior set in Becke's exchange (B86b)[3]. Systematic study on gas phase molecules, solids, and molecular adsorption demonstrates the applicability of the proposed functional to a wide variety of materials.
Preface: Special Topic on Advances in Density Functional Theory
Yang, Weitao
2014-05-14
This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering.
Reflection-Asymmetric Nuclear Deformations within the Density Functional Theory
Olsen, E; Erler, J; Nazarewicz, W.; Stoitsov, M
2012-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection- asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver axialhfb that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even- even isotopes of radium and thorium.
Density Functional Theory with Dissipation: Transport through Single Molecules
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
Conditional Probability Density Functions Arising in Bearing Estimation
1994-05-01
and a better known performance measure: the Cramer-Rao bound . 14. SUMECT TEm IL5 NUlMN OF PAMES Probability Density Function, bearing angle estimation...results obtained using the calculated density functions and a better known performance measure: the Cramer-Rao bound . The major results obtained are as...48 15. Sampling Inteval , Propagation Delay, and Covariance Singularities ....... 52 viii List of Figures (continued
Density functional study of the electric double layer formed by a high density electrolyte.
Henderson, Douglas; Lamperski, Stanisław; Jin, Zhehui; Wu, Jianzhong
2011-11-10
We use a classical density functional theory (DFT) to study the electric double layer formed by charged hard spheres near a planar charged surface. The DFT predictions are found to be in good agreement with recent computer simulation results. We study the capacitance of the charged hard-sphere system at a range of densities and surface charges and find that the capacitance exhibits a local minimum at low ionic densities and small electrode charge. Although this charging behavior is typical for an aqueous electrolyte solution, the local minimum gradually turns into a maximum as the density of the hard spheres increases. Charged hard spheres at high density provide a reasonable first approximation for ionic liquids. In agreement with experiment, the capacitance of this model ionic liquid double layer has a maximum at small electrode charge density.
Cooling Function in Wide Range of Density and Metallicity
NASA Astrophysics Data System (ADS)
Wang, Ye; Ferland, G. J.
2013-06-01
This work focuses on how the plasma cooling function changes with density and metallicity over a wide range of temperature (104 K
Linear response of homogeneous nuclear matter with energy density functionals
NASA Astrophysics Data System (ADS)
Pastore, A.; Davesne, D.; Navarro, J.
2015-03-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
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
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
Shvets, G.; Wurtele, J.S.; Gardent, D.
1995-12-31
A matrix formalism for the optical pulse evolution in the frequency domain, is applied to the nonlinear regime of operation. The formalism was previously developed for studies of the linear evolution of the low-gain FEL oscillator with an arbitrary shape of the electron beam. By varying experimentally controllable parameters, such as cavity detunning and cavity losses, different regimes of operation of the FEL oscillator, such as a steady state saturation and limit cycle saturation, are studied numerically. It is demonstrated that the linear supermodes, numerically obtained from the matrix formalism, provide an appropriate framework for analyzing the periodic change in the output power in the limit cycle regime. The frequency of this oscillation is related to the frequencies of the lowest-order linear supermodes. The response of the output radiation to periodic variation of the electron energy is studied. It is found that the response is enhanced when the frequency of the energy variation corresponds to the difference of per-pass phase advances of the lowest linear supermodes. Finally, various nonlinear models are tested to capture the steady state saturation and limit cycle variation of the EM field in the oscillator cavity.
Optimization of an exchange-correlation density functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M.
2016-06-01
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.
Basis convergence of range-separated density-functional theory
Franck, Odile Mussard, Bastien; Luppi, Eleonora Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Basis convergence of range-separated density-functional theory.
Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
Density Functional Theory for General Hard-Core Lattice Gases
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2004-09-01
We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.
Force Density Function Relationships in 2-D Granular Media
NASA Technical Reports Server (NTRS)
Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.
2004-01-01
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
Vitale, Valerio; Dziedzic, Jacek; Dubois, Simon M-M; Fangohr, Hans; Skylaris, Chris-Kriton
2015-07-14
Density functional theory molecular dynamics (DFT-MD) provides an efficient framework for accurately computing several types of spectra. The major benefit of DFT-MD approaches lies in the ability to naturally take into account the effects of temperature and anharmonicity, without having to introduce any ad hoc or a posteriori corrections. Consequently, computational spectroscopy based on DFT-MD approaches plays a pivotal role in the understanding and assignment of experimental peaks and bands at finite temperature, particularly in the case of floppy molecules. Linear-scaling DFT methods can be used to study large and complex systems, such as peptides, DNA strands, amorphous solids, and molecules in solution. Here, we present the implementation of DFT-MD IR spectroscopy in the ONETEP linear-scaling code. In addition, two methods for partitioning the dipole moment within the ONETEP framework are presented. Dipole moment partitioning allows us to compute spectra of molecules in solution, which fully include the effects of the solvent, while at the same time removing the solvent contribution from the spectra.
Cavallo, A; Cosenza, F; De Cesare, L
2008-05-01
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.
Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Pellegrini, Camilla; Flick, Johannes; Tokatly, Ilya V.; Appel, Heiko; Rubio, Angel
2015-08-01
We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications.
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.
NASA Astrophysics Data System (ADS)
Ayalon, Michal; Watson, Anne; Lerman, Steve
2016-09-01
This study examines expressions of reasoning by some higher achieving 11 to 18 year-old English students responding to a survey consisting of function tasks developed in collaboration with their teachers. We report on 70 students, 10 from each of English years 7-13. Iterative and comparative analysis identified capabilities and difficulties of students and suggested conjectures concerning links between the affordances of the tasks, the curriculum, and students' responses. The paper focuses on five of the survey tasks and highlights connections between informal and formal expressions of reasoning about variables in learning. We introduce the notion of `schooled' expressions of reasoning, neither formal nor informal, to emphasise the role of the formatting tools introduced in school that shape future understanding and reasoning.
NASA Astrophysics Data System (ADS)
Haghmoradi, Amin; Wang, Le; Chapman, Walter G.
2017-02-01
In this manuscript we extend Wertheim’s two-density formalism beyond its first order to model a system of fluid molecules with a single association site close to a planar hard wall with association sites on its surface in a density functional theory framework. The association sites of the fluid molecules are small enough that they can form only one bond, while the wall association sites are large enough to bond with more than one fluid molecule. The effects of temperature and of bulk fluid and wall site densities on the fluid density profile, extent of association, and competition between single and double bonding of fluid segments at the wall sites versus distance from the wall are presented. The theory predictions are compared with new Monte Carlo simulation results and they are in good agreement. The theory captures the surface coverage over wide ranges of temperature and bulk density by introducing the effect of steric hindrance in fluid association at a wall site.
New link between conceptual density functional theory and electron delocalization.
Matito, Eduard; Putz, Mihai V
2011-11-17
In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.
Density functional calculations of spin-wave dispersion curves.
NASA Astrophysics Data System (ADS)
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
Density functionals that recognize covalent, metallic, and weak bonds.
Sun, Jianwei; Xiao, Bing; Fang, Yuan; Haunschild, Robin; Hao, Pan; Ruzsinszky, Adrienn; Csonka, Gábor I; Scuseria, Gustavo E; Perdew, John P
2013-09-06
Computationally efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.
Rius, Jordi
2006-09-01
The maximum-likelihood method is applied to direct methods to derive a more general probability density function of the triple-phase sums which is capable of predicting negative values. This study also proves that maximization of the origin-free modulus sum function S yields, within the limitations imposed by the assumed approximations, the maximum-likelihood estimates of the phases. It thus represents the formal theoretical justification of the S function that was initially derived from Patterson-function arguments [Rius (1993). Acta Cryst. A49, 406-409].
Integral representations of thermodynamic 1PI Green's functions in the world-line formalism
NASA Astrophysics Data System (ADS)
Sato, Haru-Tada
1999-12-01
The issue discussed is a thermodynamic version of the Bern-Kosower master amplitude formula, which contains all necessary one-loop Feynman diagrams. It is demonstrated how the master amplitude at finite values of temperature and chemical potential can be formulated within the framework of the world-line formalism. In particular we present an elegant method of how to introduce a chemical potential for a loop in the master formula. Various useful integral formulas for the master amplitude are then obtained. The nonanalytic property of the master formula is also derived in the zero temperature limit with the value of chemical potential kept finite.
Perspective: Kohn-Sham density functional theory descending a staircase
NASA Astrophysics Data System (ADS)
Yu, Haoyu S.; Li, Shaohong L.; Truhlar, Donald G.
2016-10-01
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and—like Marcel Duchamp—we hope to convey progress in a stimulating way.
Perspective: Kohn-Sham density functional theory descending a staircase.
Yu, Haoyu S; Li, Shaohong L; Truhlar, Donald G
2016-10-07
This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and-like Marcel Duchamp-we hope to convey progress in a stimulating way.
Energy density functional for nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Erler, J.; Horowitz, C. J.; Nazarewicz, W.; Rafalski, M.; Reinhard, P.-G.
2013-04-01
Background: Recent observational data on neutron star masses and radii provide stringent constraints on the equation of state of neutron rich matter [Annu. Rev. Nucl. Part. Sci.ARPSDF0163-899810.1146/annurev-nucl-102711-095018 62, 485 (2012)].Purpose: We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars.Methods: We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals—a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties—are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one.Results: The new functional TOV-min yields results for nuclear bulk properties (energy, rms radius, diffraction radius, and surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When comparing SV-min and TOV-min, isoscalar nuclear matter indicators vary slightly while isovector properties are changed considerably. We discuss neutron skins, dipole polarizability, separation energies of the heaviest elements, and proton and neutron drip lines. We confirm a correlation between the neutron skin of 208Pb and the neutron star radius.Conclusions: We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass, and that predictions can only be made within an extremely broad uncertainty band. For atomic nuclei, the new functional TOV-min performs at least as well as the standard nuclear functionals, but
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.
Kinetic-energy density functional: Atoms and shell structure
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-09-01
We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. {copyright} {ital 1996 The American Physical Society.}
Exploration of a modified density dependence in the Skyrme functional
Erler, J.; Reinhard, P.-G.; Kluepfel, P.
2010-10-15
A variant of the basic Skyrme-Hartree-Fock functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, superheavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g., for projection) and more flexibility in the regime of high densities.
On the evolution of the density probability density function in strongly self-gravitating systems
Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P{sub V} (ρ)∝ρ{sup –1.54} for the (volume-weighted) PDF and P{sub M} (ρ)∝ρ{sup –0.54} for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
On the Evolution of the Density Probability Density Function in Strongly Self-gravitating Systems
NASA Astrophysics Data System (ADS)
Girichidis, Philipp; Konstandin, Lukas; Whitworth, Anthony P.; Klessen, Ralf S.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form PV (ρ)vpropρ-1.54 for the (volume-weighted) PDF and PM (ρ)vpropρ-0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
NASA Astrophysics Data System (ADS)
Sander, Tobias; Kresse, Georg
2017-02-01
Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.
Pérès, Sabine; Felicori, Liza; Rialle, Stéphanie; Jobard, Elodie; Molina, Franck
2010-01-01
Motivation: In the available databases, biological processes are described from molecular and cellular points of view, but these descriptions are represented with text annotations that make it difficult to handle them for computation. Consequently, there is an obvious need for formal descriptions of biological processes. Results: We present a formalism that uses the BioΨ concepts to model biological processes from molecular details to networks. This computational approach, based on elementary bricks of actions, allows us to calculate on biological functions (e.g. process comparison, mapping structure–function relationships, etc.). We illustrate its application with two examples: the functional comparison of proteases and the functional description of the glycolysis network. This computational approach is compatible with detailed biological knowledge and can be applied to different kinds of systems of simulation. Availability: www.sysdiag.cnrs.fr/publications/supplementary-materials/BioPsi_Manager/ Contact: sabine.peres@sysdiag.cnrs.fr; franck.molina@sysdiag.cnrs.fr Supplementary information: Supplementary data are available at Bioinformatics online. PMID:20448138
"Sloppy" nuclear energy density functionals: Effective model reduction
NASA Astrophysics Data System (ADS)
Nikšić, Tamara; Vretenar, Dario
2016-08-01
Concepts from information geometry are used to analyze parameter sensitivity for a nuclear energy density functional, representative of a class of semiempirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are "sloppy," namely, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, sloppy functionals exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the range of parameter sensitivity. Using the manifold boundary approximation method, we illustrate how to systematically construct effective nuclear density functionals of successively lower dimension in parameter space until sloppiness is eventually eliminated and the resulting functional contains only stiff combinations of parameters.
Density functionals for the strong-interaction limit
NASA Astrophysics Data System (ADS)
Seidl, Michael; Perdew, John P.; Kurth, Stefan
2000-07-01
The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation of DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model for that limit, and its gradient expansion. The exchange-correlation (xc) energy Exc[ρ]≡∫10dαWα[ρ] follows from the xc potential energies Wα at different interaction strengths α>=0 [but at fixed density ρ(r)]. For small α~0, the integrand Wα is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large α. For that purpose, we present density functionals for the coefficients in the asymptotic expansion Wα-->W∞+W'∞α-1/2 for α-->∞ in the PC model. WPC∞ arises from strict correlation, and W'PC∞ from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W∞ and W'∞ agree with those from a self-correlation-free meta-generalized gradient approximation, both for atoms and for atomization energies of molecules. We also (i) explain the difference between the PC cell and the exchange-correlation hole, (ii) present a density-functional measure of correlation strength, (iii) describe the electron localization and spin polarization energy in a highly stretched H2 molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.
Dynamics of localized particles from density functional theory
NASA Astrophysics Data System (ADS)
Reinhardt, J.; Brader, J. M.
2012-01-01
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.
Nuclear energy density functional and the nuclear α decay
NASA Astrophysics Data System (ADS)
Lim, Yeunhwan; Oh, Yongseok
2017-03-01
The nuclear α decay of heavy nuclei is investigated based on the nuclear energy density functional, which leads to the α potential inside the parent nucleus in terms of the proton and neutron density profiles of the daughter nucleus. We use the Skyrme force model, Gogny force model, and relativistic mean-field model to get the nucleon density profiles inside heavy nuclei. Once the nucleon density profiles are determined, the parameters of the nuclear α potential are fitted to the observed α decay half-lives of heavy nuclei. This approach is then applied to predict unknown α decay half-lives of heavy nuclei. To estimate the Q values of unobserved α decays, we make use of the liquid droplet model.
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory†
Derricotte, Wallace D.; Evangelista, Francesco A.
2015-01-01
Orthogonality constrained density functional theory (OCDFT) is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree–Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine. PMID:25690350
Efficient Diffuse Basis Sets for Density Functional Theory.
Papajak, Ewa; Truhlar, Donald G
2010-03-09
Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for density functional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for density functional calculations, but the computational cost savings are a factor of about two to seven.
Semilocal density functional obeying a strongly tightened bound for exchange
Sun, Jianwei; Perdew, John P.; Ruzsinszky, Adrienn
2015-01-01
Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules. PMID:25561554
Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.
Gagliardi, Laura; Truhlar, Donald G; Li Manni, Giovanni; Carlson, Rebecca K; Hoyer, Chad E; Bao, Junwei Lucas
2017-01-17
being a function of the spin-up and spin-down densities. In work carried out so far, the multiconfigurational wave function is a multiconfiguration self-consistent-field wave function. The new formulation has the advantage that the reference wave function has the correct spatial and spin symmetry and can describe bond dissociation (of both single and multiple bonds) and electronic excitations in a formally and physically correct way. We then review the formulation of density functionals in terms of the on-top pair density. Finally we review successful applications of the theory to bond energies and bond dissociation potential energy curves of main-group and transition metal bonds, to barrier heights (including pericyclic reactions), to proton affinities, to the hydrogen bond energy of water dimer, to ground- and excited-state charge transfer, to valence and Rydberg excitations of molecules, and to singlet-triplet splittings of radicals. We find that that MC-PDFT can give accurate results not only with complete-active-space multiconfiguration wave functions but also with generalized-active-space multiconfiguration wave functions, which are practical for larger numbers of active electrons and active orbitals than are complete-active-space wave functions. The separated-pair approximation, which is a special case of generalized active space self-consistent-field theory, is especially promising. MC-PDFT, because it requires much less computer time and storage than pure WFT methods, has the potential to open larger and more complex strongly correlated systems to accurate simulation.
Density functional theory is straying from the path toward the exact functional.
Medvedev, Michael G; Bushmarinov, Ivan S; Sun, Jianwei; Perdew, John P; Lyssenko, Konstantin A
2017-01-06
The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
The isotropic Hamiltonian formalism
Vaisman, Izu
2011-02-10
A Hamiltonian formalism is a procedure that allows to associate a dynamical system to a function and that includes classical Hamiltonian mechanics as a particular case. The present, expository paper gives a survey of the Hamiltonian formalism defined by an isotropic subbundle of TM+T*M, in particular, by a Dirac structure. We discuss reduction and geometric quantization of the Hamiltonian dynamical systems provided by this formalism.
Joint density-functional theory and its application to systems in solution
NASA Astrophysics Data System (ADS)
Petrosyan, Sahak A.
The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of density functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint density functional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical density functional fail when applied directly to water. The thesis then presents a computationally efficient density-functional
Density Functional Study of Perovskite Superconductor MgCNi3
NASA Astrophysics Data System (ADS)
Kumar, Jagdish; Sharma, Devina; Kumar, Ranjan; Awana, V. P. S.; Ahluwalia, P. K.
2011-12-01
We here report the first principle density functional study of MgCNi3 which crystallize in cubic perovskite structure having critical transition temperature of 8 K. The interesting aspect of this compound is that in normal state it is non magnetic in nature despite conduction electrons in it are derived from partially filled Ni d states, which typically lead to ferromagnetism in metallic Ni and many Ni-based binary alloys. To investigate the detailed microscopic origin of the non magnetic nature we have done density functional based calculations on this compound. The lattice constant is calculated using minimum energy criteria from total energy versus lattice constant plot. By taking the calculated values of lattice constant we have done the precise calculations on the compound using Full Potential Linear Augmented Plane Wave (FP-LAPW) method implemented in ELK code. The electronic density of states is found spin degenerate that corresponds to a non-magnetic ground state. The density of states (DOS) at Fermi level, N(EF) is dominated by Ni-d states. The sharp peak observed just below Fermi level corresponds to van Hove singularity (vHs). The projected density of states (PDOS) suggests a strong hybridization of Ni-3d and C-2p states which is responsible for the observed non magnetic nature of MgCNi3.
Dynamic kinetic energy potential for orbital-free density functional theory.
Neuhauser, Daniel; Pistinner, Shlomo; Coomar, Arunima; Zhang, Xu; Lu, Gang
2011-04-14
A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) density function theory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free density functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.
Hyldgaard, P
2012-10-24
The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted 'DBT', provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the
NASA Astrophysics Data System (ADS)
Hyldgaard, P.
2012-10-01
The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted ‘DBT’, provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the
A Scalable Implementation of Van der Waals Density Functionals
NASA Astrophysics Data System (ADS)
Wu, Jun; Gygi, Francois
2010-03-01
Recently developed Van der Waals density functionals[1] offer the promise to account for weak intermolecular interactions that are not described accurately by local exchange-correlation density functionals. In spite of recent progress [2], the computational cost of such calculations remains high. We present a scalable parallel implementation of the functional proposed by Dion et al.[1]. The method is implemented in the Qbox first-principles simulation code (http://eslab.ucdavis.edu/software/qbox). Application to large molecular systems will be presented. [4pt] [1] M. Dion et al. Phys. Rev. Lett. 92, 246401 (2004).[0pt] [2] G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
Relations among several nuclear and electronic density functional reactivity indexes
NASA Astrophysics Data System (ADS)
Torrent-Sucarrat, Miquel; Luis, Josep M.; Duran, Miquel; Toro-Labbé, Alejandro; Solà, Miquel
2003-11-01
An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the "Quantum Chemical le Chatelier Principle." Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.
Dispersion corrections to density functionals for water aromatic interactions.
Zimmerli, Urs; Parrinello, Michele; Koumoutsakos, Petros
2004-02-08
We investigate recently published methods for extending density functional theory to the description of long-range dispersive interactions. In all schemes an empirical correction consisting of a C6r(-6) term is introduced that is damped at short range. The coefficient C6 is calculated either from average molecular or atomic polarizabilities. We calculate geometry-dependent interaction energy profiles for the water benzene cluster and compare the results with second-order Møller-Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.
Density differences for near-Hartree-Fock atomic wave functions
NASA Astrophysics Data System (ADS)
Schmider, Hartmut; Sagar, Robin P.; Smith, Vedene H., Jr.
1994-05-01
The widely used near-Hartree-Fock functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer functions of Bunge et al. [At. Data Nucl. Tables 53, 113 (1993)] by means of different measures of functional distance on the charge density ρ for the atoms He to Xe. The results are correlated with the energy improvement, and an empriical relation between the linear deviation in the first derivative of ρ and the total energy is reported.
Perspective: Fundamental aspects of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
NASA Astrophysics Data System (ADS)
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Multiphase aluminum equations of state via density functional theory
NASA Astrophysics Data System (ADS)
Sjostrom, Travis; Crockett, Scott; Rudin, Sven
2016-10-01
We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.
Prediction of Dislocation Cores in Aluminum from Density Functional Theory
NASA Astrophysics Data System (ADS)
Woodward, C.; Trinkle, D. R.; Hector, L. G., Jr.; Olmsted, D. L.
2008-02-01
The strain field of isolated screw and edge dislocation cores in aluminum are calculated using density-functional theory and a flexible boundary condition method. Nye tensor density contours and differential displacement fields are used to accurately bound Shockley partial separation distances. Our results of 5 7.5 Å (screw) and 7.0 9.5 Å (edge) eliminate uncertainties resulting from the wide range of previous results based on Peierls-Nabarro and atomistic methods. Favorable agreement of the predicted cores with limited experimental measurements demonstrates the need for quantum mechanical treatment of dislocation cores.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets
Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets.
Ratcliff, Laura E; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
NASA Astrophysics Data System (ADS)
Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron
2014-03-01
Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
Optimization of a van der Waals Density Functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernandez-Serra, Marivi; Soler, Jose M.
2015-03-01
In particularly delicate systems, like liquid water, ab initio exchange and correlation functionals are simply not accurate enough for many practical applications. In these cases, fitting the functional to reference data is a sensible alternative to empirical interatomic potentials. However, a global optimization requires functional forms that depend on many parameters and the usual trial and error strategy becomes cumbersome and suboptimal. We present a general and powerful optimization scheme called data projection onto parameter space (DPPS). In an arbitrarily large parameter space, DPPS expands the vector of unknown parameters in vectors of known data. Poorly sampled subspaces are determined by the physically-motivated functional shape of ab initio functionals, using Bayes' theory to combine this prior information with reference energies and electron densities of monomers, clusters, and condensed phases of water. We aknowledge support from FIS2012-37549 (MF and JMS) and DOE Early Career Award No. DE-SC0003871 (M.-V.F.-S.)
Density versus spin-density functional in DFT+U and DFT+DMFT
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew; Marianetti, Chris
2015-03-01
The construction of multi-variable effective action theories such as DFT+U and DFT+DMFT requires the choice of a local subspace of correlated orbitals and an additional variable being either the charge density or spin density. This talk examines the differences between using charge-only and spin-dependent exchange-correlation functionals with the aim of providing guidance for constructing more sophisticated beyond-density functional theories. The widely used spin-dependent approximations to the exchange-correlation functional are found to lead to a large and in some cases unphysical effective exchange coupling within the correlated subspace. Additionally, the differences between Wannier and Projector based definitions of the correlated orbitals are examined, and only small differences are found provided that the orbitals are orthonormal and strongly localized. These results are documented in the context of the rare earth nickelates. This work is supported under the Grant DOE-ER-046169 and under the FAME grant, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.
Functional responses: a question of alternative prey and predator density.
Tschanz, Britta; Bersier, Louis-Felix; Bacher, Sven
2007-05-01
Throughout the study of ecology, there has been a growing realization that indirect effects among species cause complexity in food webs. Understanding and predicting the behavior of ecosystems consequently depends on our ability to identify indirect effects and their mechanisms. The present study experimentally investigates indirect interactions arising between two prey species that share a common predator. In a natural field experiment, we introduced different densities of mealworms (Tenebrio molitor), an alternative prey, to a previously studied predator-prey system in which paper wasps (Polistes dominulus) preyed on shield beetle larvae (Cassida rubiginosa). We tested if alternative prey affects predation on the first prey (i.e., the predator-dependent functional response of paper wasps) by modifying either interference among predators or the effective number of predators foraging on shield beetles. Presence of mealworms significantly reduced the effective number of predators, whereas predator interference was not affected. In this way, the experimentally introduced alternative prey altered the wasps' functional response and thereby indirectly influenced C. rubiginosa density. In all prey-density combinations offered, paper wasps constantly preferred T. molitor. This led to an asymmetrical, indirect interaction between both prey species: an increase in mealworm density significantly relaxed predation on C. rubiginosa, whereas an increase in C. rubiginosa density intensified predation on mealworms. Such asymmetrical outcomes of a fixed food preference can significantly affect the population dynamics of the species involved. In spite of the repeated finding of a Type III functional response in this system, our experiment did not reveal switching behavior in paper wasps. The variety of mechanisms underlying direct and indirect interactions within our study system exemplifies the importance of incorporating alternative prey when investigating the impact of a
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-05
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.
Predator density and the functional responses of coral reef fish
NASA Astrophysics Data System (ADS)
Stier, A. C.; White, J. W.
2014-03-01
Predation is a key process driving coral reef fish population dynamics, with higher per capita prey mortality rates on reefs with more predators. Reef predators often forage together, and at high densities, they may either cooperate or antagonize one another, thereby causing prey mortality rates to be substantially higher or lower than one would expect if predators did not interact. However, we have a limited mechanistic understanding of how prey mortality rates change with predator densities. We re-analyzed a previously published observational dataset to investigate how the foraging response of the coney grouper ( Cephalopholis fulva) feeding on the bluehead wrasse ( Thalassoma bifasciatum) changed with shifts in predator and prey densities. Using a model-selection approach, we found that per-predator feeding rates were most consistent with a functional response that declines as predator density increases, suggesting either antagonistic interactions among predators or a shared antipredator behavioral response by the prey. Our findings suggest that variation in predator density (natural or anthropogenic) may have substantial consequences for coral reef fish population dynamics.
Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions
Liu, Shuanglong; Nurbawono, Argo; Zhang, Chun
2015-01-01
We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case. PMID:26472080
What Density Functional Theory could do for Quantum Information
NASA Astrophysics Data System (ADS)
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Exact probability-density function for phase-measurement interferometry
NASA Astrophysics Data System (ADS)
Ho, Keang-Po; Kahn, Joseph M.
1995-09-01
Conventional analyses of the accuracy of phase-measurement interferometry derive a figure of merit that is either a variance or a signal-to-noise ratio. We derive the probability-density function of the phase-measurement output, so that the measurement confidence interval can be determined. We include both laser phase noise and additive Gaussian noise, and we consider both unmodulated interferometers and those employing phase or frequency modulation. For both unmodulated and modulated interferometers the confidence interval can be obtained by numerical integration of the probability-density function. For the modulated interferometer we derive a series summation for the confidence interval. For both unmodulated and modulated interferometers we derive approximate analytical expressions for the confidence interval, which we show to be extremely accurate at high signal-to-noise ratios.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Burke, Kieron; Yang, Zeng-hui; Ullrich, Carsten A.; Trail, John R.; Needs, Richard J.
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Covariant density functional theory: The role of the pion
Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.
2009-10-15
We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the {sigma} meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
Nonequilibrium Anderson model made simple with density functional theory
NASA Astrophysics Data System (ADS)
Kurth, S.; Stefanucci, G.
2016-12-01
The single-impurity Anderson model is studied within the i-DFT framework, a recently proposed extension of density functional theory (DFT) for the description of electron transport in the steady state. i-DFT is designed to give both the steady current and density at the impurity, and it requires the knowledge of the exchange-correlation (xc) bias and on-site potential (gate). In this work we construct an approximation for both quantities which is accurate in a wide range of temperatures, gates, and biases, thus providing a simple and unifying framework to calculate the differential conductance at negligible computational cost in different regimes. Our results mark a substantial advance for DFT and may inform the construction of functionals applicable to other correlated systems.
Density-functional calculations of carbon doping in III-V compound semiconductors
NASA Astrophysics Data System (ADS)
Latham, C. D.; Jones, R.; Öberg, S.; Briddon, P. R.
2001-04-01
This article reports the results of investigations based on local-density-functional theory into the relative formation energies for single substitutional carbon atoms in nine III-V compound semiconductors. The calculations are performed using a supercell formalism derived from the AIMPRO real-space cluster method. Only a very slight trend is discernible down the periodic table. When a metal atom is replaced with carbon, it is energetically least favorable in the phosphides, very marginally lower energy in the arsenides, and ~0.5-0.7 eV lower in the antimonides. The situation is approximately reversed when a P, As, or Sb atom is substituted by a C atom: for the In compounds the energy is ~0.4-0.8 eV higher than for the Al and Ga compounds.
Variational density-functional perturbation theory for dielectrics and lattice dynamics
NASA Astrophysics Data System (ADS)
Refson, Keith; Tulip, Paul R.; Clark, Stewart J.
2006-04-01
The application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism. We derive a method to calculate the linear response of the exchange-correlation potential in the GGA at arbitrary wavevector. We introduce an efficient self-consistent solver based on all-bands conjugate-gradient minimization of the second order energy, and compare the performance of preconditioning schemes. Lattice-dynamical and electronic structure consequences of space-group symmetry are described, particularly their use in reducing the computational effort required. We discuss the implementation in the CASTEP DFT modeling code, and how DFPT calculations may be efficiently performed on parallel computers. We present results on the lattice dynamics and dielectric properties of α -quartz, the hydrogen bonded crystal NaHF2 and the liquid-crystal-forming molecule 5CB. Excellent agreement is found between theory and experiment within the GGA.
Car-Parrinello treatment for an approximate density-functional theory method
NASA Astrophysics Data System (ADS)
Rapacioli, Mathias; Barthel, Robert; Heine, Thomas; Seifert, Gotthard
2007-03-01
The authors formulate a Car-Parrinello treatment for the density-functional-based tight-binding method with and without self-consistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the Γ-point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with Born-Oppenheimer molecular dynamics calculations. Water molecules, benzene, the C60 fullerene, and liquid water have been selected as benchmark systems.
Adsorption of Ar on planar surfaces studied with a density functional theory.
Sartarelli, Salvador A; Szybisz, Leszek
2009-11-01
The adsorption of Ar on planar structureless substrates of alkali metals, alkaline-earth metal Mg, CO2 , and Au was analyzed by applying a density functional formalism which includes a recently proposed effective attractive pair potential conditioned to Ar. It is shown that this approach reproduces the experimental surface tension of the liquid-vapor interface over the entire bulk coexistence curve for temperatures T spanning from the triple point Tt up to the critical point Tc. The wetting properties were studied over the entire range temperatures Tt<-->Tc. It was found that Ar wets all the investigated surfaces. The adsorption isotherms for alkali metals exhibit first-order phase transitions. Prewetting lines were resolved even for the less attractive surfaces. In the cases of Mg, CO2 , and Au a continuous growth for T> or =Tt was obtained. A comparison with experimental data and other microscopic calculations is reported.
Computation of the spectral density of two-point functions: Complex masses, cut rules, and beyond
Dudal, David; Guimaraes, Marcelo S.
2011-02-15
We present a steepest descent calculation of the Kaellen-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators. As the presence of complex masses and the use of Euclidean space brings the theory outside of the strict validity of the Cutkosky cut rules, we discuss an alternative method based on the Widder inversion operator of the Stieltjes transformation. It turns out that the results coincide with those obtained by naively applying the cut rules. We also point out the potential usefulness of the Stieltjes (inversion) formalism when nonstandard propagators are used, in which case cut rules are not available at all.
Analytic cubic and quartic force fields using density-functional theory
NASA Astrophysics Data System (ADS)
Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J.; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth
2014-01-01
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.
Adsorption of Ar on planar surfaces studied with a density functional theory
NASA Astrophysics Data System (ADS)
Sartarelli, Salvador A.; Szybisz, Leszek
2009-11-01
The adsorption of Ar on planar structureless substrates of alkali metals, alkaline-earth metal Mg, CO2 , and Au was analyzed by applying a density functional formalism which includes a recently proposed effective attractive pair potential conditioned to Ar. It is shown that this approach reproduces the experimental surface tension of the liquid-vapor interface over the entire bulk coexistence curve for temperatures T spanning from the triple point Tt up to the critical point Tc . The wetting properties were studied over the entire range temperatures Tt↔Tc . It was found that Ar wets all the investigated surfaces. The adsorption isotherms for alkali metals exhibit first-order phase transitions. Prewetting lines were resolved even for the less attractive surfaces. In the cases of Mg, CO2 , and Au a continuous growth for T≥Tt was obtained. A comparison with experimental data and other microscopic calculations is reported.
Car-Parrinello treatment for an approximate density-functional theory method.
Rapacioli, Mathias; Barthel, Robert; Heine, Thomas; Seifert, Gotthard
2007-03-28
The authors formulate a Car-Parrinello treatment for the density-functional-based tight-binding method with and without self-consistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the Gamma-point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with Born-Oppenheimer molecular dynamics calculations. Water molecules, benzene, the C(60) fullerene, and liquid water have been selected as benchmark systems.
Association between lung function and airway wall density
NASA Astrophysics Data System (ADS)
Leader, J. Ken; Zheng, Bin; Fuhrman, Carl R.; Tedrow, John; Park, Sang C.; Tan, Jun; Pu, Jiantao; Drescher, John M.; Gur, David; Sciurba, Frank C.
2009-02-01
Computed tomography (CT) examination is often used to quantify the relation between lung function and airway remodeling in chronic obstructive pulmonary disease (COPD). In this preliminary study, we examined the association between lung function and airway wall computed attenuation ("density") in 200 COPD screening subjects. Percent predicted FVC (FVC%), percent predicted FEV1 (FEV1%), and the ratio of FEV1 to FVC as a percentage (FEV1/FVC%) were measured post-bronchodilator. The apical bronchus of the right upper lobe was manually selected from CT examinations for evaluation. Total airway area, lumen area, wall area, lumen perimeter and wall area as fraction of the total airway area were computed. Mean HU (meanHU) and maximum HU (maxHU) values were computed across pixels assigned membership in the wall and with a HU value greater than -550. The Pearson correlation coefficients (PCC) between FVC%, FEV1%, and FEV1/FVC% and meanHU were -0.221 (p = 0.002), -0.175 (p = 0.014), and -0.110 (p = 0.123), respectively. The PCCs for maxHU were only significant for FVC%. The correlations between lung function and the airway morphometry parameters were slightly stronger compared to airway wall density. MeanHU was significantly correlated with wall area (PCC = 0.720), airway area (0.498) and wall area percent (0.611). This preliminary work demonstrates that airway wall density is associated with lung function. Although the correlations in our study were weaker than a recent study, airway wall density initially appears to be an important parameter in quantitative CT analysis of COPD.
Autoionization in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Kapoor, V.
2016-06-01
We compute the exact exchange-correlation potential of the time-dependent density-functional theory (TDDFT) for the correlated process of autoionization. The potential develops barriers which regulate the autoionization rate. TDDFT employing known and practicable exchange-correlation potentials does not capture any autoionization dynamics. Approximate exchange-correlation potentials capturing such dynamics would necessarily require memory effects and are unlikely to be developed, as will be illustrated.
Density functional theory across chemistry, physics and biology.
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-03-13
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.
Density functional wavelet calculation of solid state systems
NASA Astrophysics Data System (ADS)
Daykov, I. P.; Engeness, T. D.; Arias, T. A.
2001-03-01
We present, to our knowledge, the first all-electron wavelet calculations of the electronic structure of solids within density functional theory. To make these calculations competitive with traditional approaches, we employ recent developments in algorithms for multiresolution analysis (MRA) which speed density functional calculations by three to four orders of magnitude[1,2]. MRA provides a fully systematic, integrated treatment of core and valence electrons and is ideal for exploring the limits of the accuracy of density functional theory in the calculation of EELS spectra, which involve matrix elements between the core and valence states. We shall present results for EELS spectra as well as the resolution of technical issues which arise in carrying out solid-state calculations within a wavelet-like basis. [1] ``Multiscale computation with interpolating wavelets,'' by Ross A. Lippert, T.A. Arias and Alan Edelman, Journal of Computational Physics, 140:2, 278--310 (1 March 1998). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805283 . [2] ``Multiresolution analysis of electronic structure: semicardinal and wavelet bases,'' T.A. Arias, Reviews of Modern Physics 71:1, 267--311 (January 1999). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805262 .
Chemical reactivity in the framework of pair density functional theories.
Otero, Nicolás; Mandado, Marcos
2012-05-15
Chemical reactivity descriptors are derived within the framework of the pair density functional theory. These indices provide valuable information about bonding rearrangements and activating mechanisms upon electrophilic or nucleophilic reactions. Indices derived and tested in this work represent nonlocal counterparts of the local reactivity indices derived in the context of conceptual density functional theory (CDFT) and frequently used in reactivity studies; the Fukui function, the local softness and the dual descriptor. In this work, we show how these nonlocal indices provide a quantum chemical basis to explain the success of qualitative resonance models in chemical reactivity predictions. Also, local information is implicitly contained as CDFT indices are obtained by simple integration. As illustrative examples, we have considered in this work the Markovnikov's rule, the reactivity of enolate anion, the nucleophilic conjugate addition to α,β-unsaturated compounds and the electrophilic aromatic substitution of benzene derivatives. The densities used in this work were obtained with Hartree-Fock, Kohn-Sham DFT, and singles and doubles configuration interaction (CISD) approaches.
Surface regulated arsenenes as Dirac materials: From density functional calculations
NASA Astrophysics Data System (ADS)
Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu
2017-02-01
Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.
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.
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
On the calculation of Δ for electronic excitations in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Myneni, Hemanadhan; Casida, Mark E.
2017-04-01
Excited states are often treated within the context of time-dependent (TD) density-functional theory (DFT), making it important to be able to assign the excited spin-state symmetry. While there is universal agreement on how Δ , the difference between for ground and excited states, should be calculated in a wave-function-like formalism such as the Tamm-Dancoff approximation (TDA), confusion persists as to how to determine the spin-state symmetry of excited states in TD-DFT. We try to clarify the origins of this confusion by examining various possibilities for the parameters (σ1 ,σ2) in the formula
Density functional theory and chromium: Insights from the dimers
Würdemann, Rolf; Kristoffersen, Henrik H.; Moseler, Michael; Walter, Michael
2015-03-28
The binding in small Cr clusters is re-investigated, where the correct description of the dimer in three charge states is used as criterion to assign the most suitable density functional theory approximation. The difficulty in chromium arises from the subtle interplay between energy gain from hybridization and energetic cost due to exchange between s and d based molecular orbitals. Variations in published bond lengths and binding energies are shown to arise from insufficient numerical representation of electron density and Kohn-Sham wave-functions. The best functional performance is found for gradient corrected (GGA) functionals and meta-GGAs, where we find severe differences between functionals from the same family due to the importance of exchange. Only the “best fit” from Bayesian error estimation is able to predict the correct energetics for all three charge states unambiguously. With this knowledge, we predict small bond-lengths to be exclusively present in Cr{sub 2} and Cr{sub 2}{sup −}. Already for the dimer cation, solely long bond-lengths appear, similar to what is found in the trimer and in chromium bulk.
Franco-Pérez, Marco; Ayers, Paul W; Gázquez, José L; Vela, Alberto
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Franco-Pérez, Marco E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Ayers, Paul W. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Gázquez, José L. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Vela, Alberto E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Current density partitioning in time-dependent current density functional theory
Mosquera, Martín A.; Wasserman, Adam
2014-05-14
We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.
2007 Time_Dependent Density-Functional Therory (July 15-20, 2007 Colby College, Maine)
Ullrich Carsten Nancy Ryan Gray
2008-09-19
Time-dependent density-functional theory (TDDFT) provides an efficient, elegant, and formally exact way of describing the dynamics of interacting many-body quantum systems, circumventing the need for solving the full time-dependent Schroedinger equation. In the 20 years since it was first rigorously established in 1984, the field of TDDFT has made rapid and significant advances both formally as well as in terms of successful applications in chemistry, physics and materials science. Today, TDDFT has become the method of choice for calculating excitation energies of complex molecules, and is becoming increasingly popular for describing optical and spectroscopic properties of a variety of materials such as bulk solids, clusters and nanostructures. Other growing areas of applications of TDDFT are nonlinear dynamics of strongly excited electronic systems and molecular electronics. The purpose and scope of this Gordon Research Conference is to provide a platform for discussing the current state of the art of the rapidly progressing, highly interdisciplinary field of TDDFT, to identify and debate open questions, and to point out new promising research directions. The conference will bring together experts with a diverse background in chemistry, physics, and materials science.
Generation of time histories with a specified auto spectral density and probability density function
Smallwood, D.O.
1996-08-01
It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.
Downlink Probability Density Functions for EOS-McMurdo Sound
NASA Technical Reports Server (NTRS)
Christopher, P.; Jackson, A. H.
1996-01-01
The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Density-dependence of functional spiking networks in vitro
Ham, Michael I; Gintautuas, Vadas; Rodriguez, Marko A; Bettencourt, Luis M A; Bennett, Ryan; Santa Maria, Cara L
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Baczewski, Andrew David; Shulenburger, Luke; Desjarlais, Michael Paul; Magyar, Rudolph J.
2014-02-01
In recent years, DFT-MD has been shown to be a useful computational tool for exploring the properties of WDM. These calculations achieve excellent agreement with shock compression experiments, which probe the thermodynamic parameters of the Hugoniot state. New X-ray Thomson Scattering diagnostics promise to deliver independent measurements of electronic density and temperature, as well as structural information in shocked systems. However, they require the development of new levels of theory for computing the associated observables within a DFT framework. The experimentally observable x-ray scattering cross section is related to the electronic density-density response function, which is obtainable using TDDFT - a formally exact extension of conventional DFT that describes electron dynamics and excited states. In order to develop a capability for modeling XRTS data and, more generally, to establish a predictive capability for rst principles simulations of matter in extreme conditions, real-time TDDFT with Ehrenfest dynamics has been implemented in an existing PAW code for DFT-MD calculations. The purpose of this report is to record implementation details and benchmarks as the project advances from software development to delivering novel scienti c results. Results range from tests that establish the accuracy, e ciency, and scalability of our implementation, to calculations that are veri ed against accepted results in the literature. Aside from the primary XRTS goal, we identify other more general areas where this new capability will be useful, including stopping power calculations and electron-ion equilibration.
Density functional calculation of transition metal adatom adsorption on graphene.
Mao, Yuliang; Yuan, Jianmei; Zhong, Jianxin
2008-03-19
The functionalization of graphene (a single graphite layer) by the addition of transition metal atoms of Mn, Fe and Co to its surface has been investigated computationally using density functional theory. In the calculation, the graphene surface supercell was constructed from a single layer of graphite (0001) surface separated by vertical vacuum layers 2 nm thick. We found that the center of the hexagonal ring formed by carbon from graphene is the most stable site for Mn, Fe, Co to stay after optimization. The calculated spin-polarized band structures of the graphene encapsulating the Mn adatom indicate that the conduction bands are modified and move down due to the coupling between the Mn atom and graphene. For Fe adsorbed on the graphene surface, it is semi-half-metallic, and the spin polarization P is found to be 100%. The system of Co adatom on graphene exhibits metallic electronic structure due to the density of states (DOS) peak at the band center with both majority and minority spins. Local density of states analyses indicate a larger promotion of 4s electrons into the 3d state in Fe and Co, resulting in lower local moments compared to an Mn adatom on the graphite surface.
Time-dependent density-functional description of nuclear dynamics
NASA Astrophysics Data System (ADS)
Nakatsukasa, Takashi; Matsuyanagi, Kenichi; Matsuo, Masayuki; Yabana, Kazuhiro
2016-10-01
The basic concepts and recent developments in the time-dependent density-functional theory (TDDFT) for describing nuclear dynamics at low energy are presented. The symmetry breaking is inherent in nuclear energy density functionals, which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in the description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, the quantum fluctuations associated with slow collective motions are explicitly treated assuming that time evolution of densities is determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.
Massively parallel density functional calculations for thousands of atoms: KKRnano
NASA Astrophysics Data System (ADS)
Thiess, A.; Zeller, R.; Bolten, M.; Dederichs, P. H.; Blügel, S.
2012-06-01
Applications of existing precise electronic-structure methods based on density functional theory are typically limited to the treatment of about 1000 inequivalent atoms, which leaves unresolved many open questions in material science, e.g., on complex defects, interfaces, dislocations, and nanostructures. KKRnano is a new massively parallel linear scaling all-electron density functional algorithm in the framework of the Korringa-Kohn-Rostoker (KKR) Green's-function method. We conceptualized, developed, and optimized KKRnano for large-scale applications of many thousands of atoms without compromising on the precision of a full-potential all-electron method, i.e., it is a method without any shape approximation of the charge density or potential. A key element of the new method is the iterative solution of the sparse linear Dyson equation, which we parallelized atom by atom, across energy points in the complex plane and for each spin degree of freedom using the message passing interface standard, followed by a lower-level OpenMP parallelization. This hybrid four-level parallelization allows for an efficient use of up to 100000 processors on the latest generation of supercomputers. The iterative solution of the Dyson equation is significantly accelerated, employing preconditioning techniques making use of coarse-graining principles expressed in a block-circulant preconditioner. In this paper, we will describe the important elements of this new algorithm, focusing on the parallelization and preconditioning and showing scaling results for NiPd alloys up to 8192 atoms and 65536 processors. At the end, we present an order-N algorithm for large-scale simulations of metallic systems, making use of the nearsighted principle of the KKR Green's-function approach by introducing a truncation of the electron scattering to a local cluster of atoms, the size of which is determined by the requested accuracy. By exploiting this algorithm, we show linear scaling calculations of more
2011-09-01
for Lithospheric Structure Beneath Asia and North Africa, 27th Seismic Research Review: Ground-Based Nuclear Explosion Monitoring Technologies, LA...Tomography for Lithospheric Structure Beneath the Middle East and North Africa, in Proceedings of the 26th Seismic Research , Review - Trends in Nuclear...dispersion and teleseismic receiver functions: Implications for lithospheric structure of the Arabian Peninsula. J. Geophys. Res., 111(B11311): 10.1029
Verrilli, David; Marin, F P; Rangel, Rafael
2014-01-01
We study the I-V characteristic of mesoscopic systems or quantum dot (QD) attached to a pair of superconducting leads. Interaction effects in the QD are considered through the charging energy of the QD; that is, the treatment of current transport under a voltage bias is performed within a coupled Poisson nonequilibrium Green function (PNEGF) formalism. We derive the expression for the current in full generality but consider only the regime where transport occurs only via a single particle current. We show for this case and for various charging energies values U 0 and associated capacitances of the QD the effect on the I-V characteristic. Also the influence of the coupling constants on the I-V characteristic is investigated. Our approach puts forward a novel interpretation of experiments in the strong Coulomb regime.
Marin, F. P.
2014-01-01
We study the I-V characteristic of mesoscopic systems or quantum dot (QD) attached to a pair of superconducting leads. Interaction effects in the QD are considered through the charging energy of the QD; that is, the treatment of current transport under a voltage bias is performed within a coupled Poisson nonequilibrium Green function (PNEGF) formalism. We derive the expression for the current in full generality but consider only the regime where transport occurs only via a single particle current. We show for this case and for various charging energies values U 0 and associated capacitances of the QD the effect on the I-V characteristic. Also the influence of the coupling constants on the I-V characteristic is investigated. Our approach puts forward a novel interpretation of experiments in the strong Coulomb regime. PMID:24977220
Verreck, Devin Groeseneken, Guido; Verhulst, Anne S.; Mocuta, Anda; Collaert, Nadine; Thean, Aaron; Van de Put, Maarten; Magnus, Wim; Sorée, Bart
2015-10-07
Efficient quantum mechanical simulation of tunnel field-effect transistors (TFETs) is indispensable to allow for an optimal configuration identification. We therefore present a full-zone 15-band quantum mechanical solver based on the envelope function formalism and employing a spectral method to reduce computational complexity and handle spurious solutions. We demonstrate the versatility of the solver by simulating a 40 nm wide In{sub 0.53}Ga{sub 0.47}As lineTFET and comparing it to p-n-i-n configurations with various pocket and body thicknesses. We find that the lineTFET performance is not degraded compared to semi-classical simulations. Furthermore, we show that a suitably optimized p-n-i-n TFET can obtain similar performance to the lineTFET.
Nonlocal van der Waals density functional made simple and efficient
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Gorni, Tommaso; de Gironcoli, Stefano
2013-01-01
We present a simple revision of the VV10 nonlocal density functional by Vydrov and Van Voorhis [J. Chem. Phys.JCPSA60021-960610.1063/1.3521275 133, 244103 (2010)] for dispersion interactions. Unlike the original functional our modification allows nonlocal correlation energy and its derivatives to be efficiently evaluated in a plane wave framework along the lines pioneered by Román-Pérez and Soler [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.096102 103, 096102 (2009)]. Our revised functional maintains the outstanding precision of the original VV10 in noncovalently bound complexes and performs well in representative covalent, ionic, and metallic solids.
Applications of large-scale density functional theory in biology
NASA Astrophysics Data System (ADS)
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
NASA Astrophysics Data System (ADS)
Deur, Killian; Mazouin, Laurent; Fromager, Emmanuel
2017-01-01
Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple excitations, for example, can be easily taken into account in an ensemble), eDFT is not standard, which is essentially due to the lack of reliable approximate exchange-correlation (x c ) functionals for ensembles. Following Smith et al. [Phys. Rev. B 93, 245131 (2016), 10.1103/PhysRevB.93.245131], we propose in this work to construct an exact eDFT for the nontrivial asymmetric Hubbard dimer, thus providing more insight into the weight dependence of the ensemble x c energy in various correlation regimes. For that purpose, an exact analytical expression for the weight-dependent ensemble exchange energy has been derived. The complementary exact ensemble correlation energy has been computed by means of Legendre-Fenchel transforms. Interesting features like discontinuities in the ensemble x c potential in the strongly correlated limit have been rationalized by means of a generalized adiabatic connection formalism. Finally, functional-driven errors induced by ground-state density-functional approximations have been studied. In the strictly symmetric case or in the weakly correlated regime, combining ensemble exact exchange with ground-state correlation functionals gives better ensemble energies than when calculated with the ground-state exchange-correlation functional. However, when approaching the asymmetric equiensemble in the strongly correlated regime, the former approximation leads to highly curved ensemble energies with negative slope which is unphysical. Using both ground-state exchange and correlation functionals gives much better results in that case. In fact, exact ensemble energies are almost recovered in some density domains. The analysis of density-driven errors is left for future work.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
De Laender, Frederik; Taub, Frieda B; Janssen, Colin R
2011-12-01
Understanding whether and to what extent ecosystem functions respond to chemicals is a major challenge in environmental toxicology. The available data gathered by ecosystem-level experiments (micro- and mesocosms) often describe the responses of taxa densities to stress. However, whether these responses are proportional to the responses of associated ecosystem functions to stress is unclear. By combining a carbon budget modeling technique with data from a standardized microcosm experiment with a known community composition, we quantified three ecosystem functions (net primary production [NPP], net mesozooplankton production [NZP], and net bacterial production [NBP]) at three Cu concentrations, with a control. Changes of these ecosystem functions with increasing chemical concentrations were not always proportional to the Cu effects on the densities of the contributing functional groups. For example, Cu treatments decreased mesozooplankton density by 100-fold and increased phytoplankton density 10- to 100-fold while increasing NZP and leaving NPP unaltered. However, in contrast, Cu affected microzooplankton and the associated function (NBP) in a comparable way. We illustrate that differences in the response of phytoplankton/mesozooplankton densities and the associated ecosystem functions to stress occur because functional rates (e.g., photosynthesis rates/ingestion rates) vary among Cu treatments and in time. These variations could be explained by food web ecology but not by direct Cu effects, indicating that ecology may be a useful basis for understanding environmental effects of stressors.
Characterizing the Spatial Density Functions of Neural Arbors
NASA Astrophysics Data System (ADS)
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
Zhang, Xing; Herbert, John M
2015-02-14
We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinant. Numerical results, including comparison to full configuration interaction calculations, suggest that the two approaches perform equally well for many molecular systems, provided that the underlying DFT method affords accurate potential energy surfaces. The response contributions are found to be important for certain systems with high symmetry, but can be calculated with only a moderate increase in computational cost beyond what is required for the pseudo-wavefunction approach. In the case of spin-flip TDDFT, we provide a formal proof that the derivative couplings obtained using response theory are identical to those obtained from the pseudo-wavefunction formulation, which validates our previous implementation based on the latter formalism.
Zhang, Xing; Herbert, John M.
2015-02-14
We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinant. Numerical results, including comparison to full configuration interaction calculations, suggest that the two approaches perform equally well for many molecular systems, provided that the underlying DFT method affords accurate potential energy surfaces. The response contributions are found to be important for certain systems with high symmetry, but can be calculated with only a moderate increase in computational cost beyond what is required for the pseudo-wavefunction approach. In the case of spin-flip TDDFT, we provide a formal proof that the derivative couplings obtained using response theory are identical to those obtained from the pseudo-wavefunction formulation, which validates our previous implementation based on the latter formalism.
Adsorption of Ne on alkali surfaces studied with a density functional theory.
Sartarelli, Salvador A; Szybisz, Leszek; Urrutia, Ignacio
2009-01-01
A density functional formalism is applied to investigate the wetting behavior of Ne adsorbed on planar substrates. The study is performed over the complete range of temperatures spanned from the triple point T_{t} up to the critical one T_{c} . For this purpose, an effective attractive pair potential was built on the basis of a separation procedure. This approach yields a good description of properties of the liquid-vapor interface at coexistence in the whole range of temperatures T_{t} < or = T < or = T_{c} . The adsorption of Ne on alkali metals and the alkaline-earth metal Mg is analyzed. This sequence of substrates exhibit increasing attractive strength leading to a variety of wetting situations throughout the interval T_{t}<-->T_{c} . A comparison with experimental data and other microscopic calculations is done. The predictions of a simple model are discussed. For NeRb we were able to resolve prewetting lines. Results obtained from a density functional are reported for NeK and NeMg . In the case of the latter system the interesting behavior occurs close to T_{t} . According to our results, Ne wets surfaces of Na and Li, and this statement is in agreement with the whole picture of the analyzed substrates.
Adsorption of Ne on alkali surfaces studied with a density functional theory
NASA Astrophysics Data System (ADS)
Sartarelli, Salvador A.; Szybisz, Leszek; Urrutia, Ignacio
2009-01-01
A density functional formalism is applied to investigate the wetting behavior of Ne adsorbed on planar substrates. The study is performed over the complete range of temperatures spanned from the triple point Tt up to the critical one Tc . For this purpose, an effective attractive pair potential was built on the basis of a separation procedure. This approach yields a good description of properties of the liquid-vapor interface at coexistence in the whole range of temperatures Tt⩽T⩽Tc . The adsorption of Ne on alkali metals and the alkaline-earth metal Mg is analyzed. This sequence of substrates exhibit increasing attractive strength leading to a variety of wetting situations throughout the interval Tt↔Tc . A comparison with experimental data and other microscopic calculations is done. The predictions of a simple model are discussed. For Ne/Rb we were able to resolve prewetting lines. Results obtained from a density functional are reported for Ne/K and Ne/Mg . In the case of the latter system the interesting behavior occurs close to Tt . According to our results, Ne wets surfaces of Na and Li, and this statement is in agreement with the whole picture of the analyzed substrates.
A formal approach to detect functionally irrelevant barriers in MPI programs.
Sharma, S.; Vakkalanka, S.; Gopalakrishnan, G.; Kirby, R. M.; Thakur, R.; Gropp, W.
2008-01-01
We examine the unsolved problem of automatically and efficiently detecting functionally irrelevant barriers in MPI programs. A functionally irrelevant barrier is a set of MPI-Barrier calls, one per MPI process, such that their removal does not alter the overall MPI communication structure of the program. Static analysis methods are incapable of solving this problem, as MPI programs can compute many quantities at runtime, including send targets, receive sources, tags, and communicators, and also can have data-dependent control flows. We offer an algorithm called Fib to solve this problem based on dynamic (runtime) analysis. Fib applies to MPI programs that employ 24 widely used two-sided MPI operations. We show that it is sufficient to detect barrier calls whose removal causes a wildcard receive statement placed before or after a barrier to now begin matching a send statement with which it did not match before. Fib determines whether a barrier becomes relevant in any interleaving of the MPI processes of a given MPI program. Since the number of interleavings can grow exponentially with the number of processes, Fib employs a sound method to drastically reduce this number, by computing only the relevant interleavings. We show that many MPI programs do not have data dependent control flows, thus making the results of Fib applicable to all the input data the program can accept.
Graphene oxide and adsorption of chloroform: A density functional study
NASA Astrophysics Data System (ADS)
Kuisma, Elena; Hansson, C. Fredrik; Lindberg, Th. Benjamin; Gillberg, Christoffer A.; Idh, Sebastian; Schröder, Elsebeth
2016-05-01
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, and are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances are important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory, and the recently developed consistent-exchange functional for the van der Waals density-functional method is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likely oxidize, and thus adsorption onto graphene oxide, rather than clean graphene, is a more relevant process to study.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Electron response in van der Waals density functionals
NASA Astrophysics Data System (ADS)
Hyldgaard, Per
2013-03-01
There is significant interest in density functional theory (DFT) of dispersive or van der Waals (vdW) interactions and in DFT studies of sparse systems where vdW forces contribute to the cohesion and behavior. The Rutgers-Chalmers van der Waals density functional (vdW-DF) method [PRL 92, 246401 (2004); PRB 76, 125112 (2007)] is a nonempirical approach to calculate vdW bonding and for DFT characterizations of sparse matter. The vdW-DF framework is defined by a single exchange-correlation density functional that rests on a plasmon-type description for both semilocal components and for a parameter-free evaluation of nonlocal correlation. My talk summarizes a set of vdW-DF studies that seeks to map and analyze details in the vdW-DF electron-response nature. The purpose is in part to extract consequences that can facilitate an experiment-theory comparison that goes beyond binding geometries and energies. The aim is also to seek implications that can help develop the vdW-DF framework. I present an analysis of the relative importance of morphology, screening (image-plane formation), and collective effects in the vdW-DF description of molecular systems. In addition, I compare vdW-DF results with Cu(111) experiments that tests the electron-response behavior in terms of adsorption-induced band shifts, the form of the overall light-molecule physisorption potential, and the corrugation in the kinetic-energy repulsion of molecules at surfaces. Overall, the vdW-DF studies suggest the importance of benchmarking vdW methods across different length scales and by exploring the variation that arise when related structures have a different balance between exchange repulsion and vdW attraction.
Quantification of Uncertainties in Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
Schunck, N.; McDonnell, J. D.; Higdon, D.; Sarich, J.; Wild, S.
2015-01-01
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Density Functional Study of the structural properties in Tamoxifen
NASA Astrophysics Data System (ADS)
de Coss-Martinez, Romeo; Tapia, Jorge A.; Quijano-Quiñones, Ramiro F.; Canto, Gabriel I.
2013-03-01
Using the density functional theory, we have studied the structural properties of Tamoxifen. The calculations were performed with two methodological approaches, which were implemented in SIESTA and Spartan codes. For SIESTA, we considerate a linear combination of atomic orbitals method, using pseudopotentials and the van der Waals approximation for the exchange-correlation potential. Here we analyzed and compared the atomic structure between our results and other theoretical study. We found differences in the bond lengths between the results, that could be attributed to code approaches in each one. This work was supported under Grant FOMIX 2011-09 N: 170297 of Ph.D. A. Tapia.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-03-01
Sodium azide is intriguing because it could potentially be used as a precursor to a high-nitrogen energetic material. Furthermore, recent absorption and Raman spectroscopic results have shown that novel nitrogen structures may indeed be attainable from sodium azide. First-principles density functional theory calculations were performed to characterize possible novel crystalline structures of sodium azide including their atomic structure, vibrational properties, Raman spectra, and equation of state up to 90 GPa. Calculated Raman peaks and intensities show good agreement with experiment.
Density Functional Theory Investigation of Sodium Azide at High Pressure
NASA Astrophysics Data System (ADS)
Steele, Brad; Landerville, Aaron; Oleynik, Ivan
2013-06-01
Sodium azide is being investigated as a potential precursor to a high-nitrogen content energetic material. Changes in the experimentally measured raman spectra under compression and high temperature indicate that a structural change may have taken place. Accurate mode assignments of new peaks arising in the raman spectra have been inconclusive. In this work, the first order raman spectra of sodium azide's alpha and beta phases are calculated using Density Function Pertubation Theory (DFPT) under compression and expansion. Normal mode assignments are made and compared to experiment. In addition, the equation of state of both phases is obtained up to 90 GPa.
Classical density functional study of wetting transitions on nanopatterned surfaces
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Parry, A. O.; Rascón, C.; Kalliadasis, S.
2017-03-01
Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.
Relativistic Energy Density Functionals: Exotic modes of excitation
Vretenar, D.; Paar, N.; Marketin, T.
2008-11-11
The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of {beta}-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.
Determining Ionospheric Irregularity Spectral Density Function from Japan GEONET
NASA Astrophysics Data System (ADS)
Lay, E. H.; Light, M. E.; Parker, P. A.; Carrano, C. S.; Haaser, R. A.
2015-12-01
Japan's GEONET GPS network is the densest GPS monitoring network in the world, with 1200+ receivers over the area of Japan. Measuring and calibrating the integrated total electron content (TEC) from each station has been done in many cases to provide detailed maps of ionospheric disturbances over Japan. We use TEC measurements from Japan's GEONET array to determine an empirically derived description of the 2-dimensional scale sizes of spatial irregularities above Japan. The contributions from various scale sizes will be included in a statistical description for the irregularity spectral density (ISD) function. We will compare the statistics of the spatial irregularities between calm and moderately scintillated conditions.
Augmented Lagrangian method for constrained nuclear density functional theory
NASA Astrophysics Data System (ADS)
Staszczak, A.; Stoitsov, M.; Baran, A.; Nazarewicz, W.
2010-10-01
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multi-dimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves the accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Atomic volumes and polarizabilities in density-functional theory.
Kannemann, Felix O; Becke, Axel D
2012-01-21
Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.
Nuclear clustering in the energy density functional approach
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Thorvaldsen, Andreas J; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-07
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
NASA Astrophysics Data System (ADS)
Thorvaldsen, Andreas J.; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-01
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Lithium adsorption on graphite from density functional theory calculations.
Valencia, Felipe; Romero, Aldo H; Ancilotto, Francesco; Silvestrelli, Pier Luigi
2006-08-03
The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.
Ab initio molecular dynamics using hybrid density functionals.
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; VandeVondele, Joost
2008-06-07
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.
Ab initio molecular dynamics using hybrid density functionals
NASA Astrophysics Data System (ADS)
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; Vandevondele, Joost
2008-06-01
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Schunck, N; McDonnell, J D; Higdon, D; Sarich, J; Wild, S M
2015-03-17
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.
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.
BUILDING A UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL (UNEDF)
Nazarewicz, Witold
2012-07-01
The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties. Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data. Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Molecular acidity: A quantitative conceptual density functional theory description.
Liu, Shubin; Schauer, Cynthia K; Pedersen, Lee G
2009-10-28
Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.
Nuclear charge radii: density functional theory meets Bayesian neural networks
NASA Astrophysics Data System (ADS)
Utama, R.; Chen, Wei-Chia; Piekarewicz, J.
2016-11-01
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.
Direct Neutron Capture Calculations with Covariant Density Functional Theory Inputs
NASA Astrophysics Data System (ADS)
Zhang, Shi-Sheng; Peng, Jin-Peng; Smith, Michael S.; Arbanas, Goran; Kozub, Ray L.
2014-09-01
Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Supported by the U.S. Dept. of Energy, Office of Nuclear Physics.
Fluids Density Functional Theory of Diblock Copolymers for Electrolyte Applications
NASA Astrophysics Data System (ADS)
Brown, Jonathan R.; Hall, Lisa M.
We use classical, fluids density functional theory (fDFT) to study microphase separation in block copolymer systems. We are motivated by systems used as battery electrolytes or in other transport applications, in which the two blocks of the system have different mechanical, dielectric, and transport properties that allow one phase to act as a charge/penetrant carrier and the other to make the film mechanically strong. We find density profiles of penetrants, showing to what degree they segregate into the A phase and their concentration near the interface, depending on the penetrant-A and penetrant-B interaction strengths as well as the A-B segregation strength. We also study the effect of tapering, or adding a gradient region (taper) between the pure A and B blocks of an AB diblock copolymer; the taper changes in composition along its length from pure A to pure B (or from B to A for an inverse taper). The effect of both penetrants and tapering on microphase domain spacing as a function of segregation strength will be discussed. Adjusting taper length allows one to tune the phase behavior of the system for easier processing or access to specific desired microphase structures. Based upon work supported by NSF Grant 1454343 and DOE Grant SC0014209.
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.
2007-06-01
Atomistic simulations employing Density Functional Theory (DFT) have recently emerged as a powerful way of increasing our understanding of materials and processes in high energy density physics. Knowledge of the properties of water (equation of state, electrical conductivity, diffusion, low-energy opacity) is essential for correctly describing the physics of giant planets as well as shock waves in water. Although a qualitative picture of water electrical conductivity has emerged, the necessary quantitative information is scarce over a wide range of temperature and density. Since experiments can only access certain areas of phase space, and often require modeling as a part of the analysis, Quantum Molecular Dynamics simulations play a vital role. Using finite-temperature density functional theory (FT-DFT), we have investigated the structure and electronic conductivity of water across three phase transitions (molecular liquid/ ionic liquid/ superionic/ electronic liquid). The ionic contribution to the conduction is calculated from proton diffusion and the electronic contribution is calculated using the Kubo-Greenwood formula. The calculations are performed with VASP, a plane-wave pseudo-potential code. There is a rapid transition to ionic conduction at 2000 K and 2 g/cm^3, whereas electronic conduction dominates at temperatures at and above 6000 K&[tilde;1]. Contrary to earlier results using the Car-Parrinello method&[tilde;2], we predict that the fluid bordering the superionic phase is conducting above 4000 K and 100 GPa. Our comprehensive use of FT-DFT explains the new findings. The calculated conductivity is compared to experimental data. I gratefully acknowledge Mike Desjarlais, my collaborator in this effort. The LDRD office at Sandia supported this work. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL
Structural Stability and Functional Remodeling of High-Density Lipoproteins
Gursky, Olga
2015-01-01
Lipoproteins are protein-lipid nanoparticles that transport lipids in circulation and are central in atherosclerosis and other disorders of lipid metabolism. Apolipoproteins form flexible structural scaffolds and important functional ligands on the particle surface and direct lipoprotein metabolism. Lipoproteins undergo multiple rounds of metabolic remodeling that is crucial to lipid transport. Important aspects of this remodeling, including apolipoprotein dissociation and particle fusion, are mimicked in thermal or chemical denaturation and are modulated by free energy barriers. Here we review our biophysical studies that revealed kinetic mechanism of lipoprotein stabilization and unraveled its structural basis. The main focus is on high-density lipoprotein (HDL). An inverse correlation between stability and functions of various HDLs in cholesterol transport suggests functional role of structural disorder. A mechanism for conformational adaptation of the major HDL proteins, apoA-I and apoA-II, to the increasing lipid load is proposed. Together, these studies help understand why HDL form discrete subclasses separated by kinetic barriers, which have distinct composition, conformation and functional properties. Understanding these properties may help improve HDL quality and develop novel therapies for cardiovascular disease. PMID:25749369
Abnormal Functional Connectivity Density in Post-traumatic Stress Disorder.
Zhang, Youxue; Xie, Bing; Chen, Heng; Li, Meiling; Liu, Feng; Chen, Huafu
2016-05-01
Post-traumatic stress disorder (PTSD) is a psychiatric disorder that occurs in individuals who have experienced life-threatening mental traumas. Previous neuroimaging studies have indicated that the pathology of PTSD may be associated with the abnormal functional integration among brain regions. In the current study, we used functional connectivity density (FCD) mapping, a novel voxel-wise data-driven approach based on graph theory, to explore aberrant FC through the resting-state functional magnetic resonance imaging of the PTSD. We calculated both short- and long-range FCD in PTSD patients and healthy controls (HCs). Compared with HCs, PTSD patients showed significantly increased long-range FCD in the left dorsolateral prefrontal cortex (DLPFC), but no abnormal short-range FCD was found in PTSD. Furthermore, seed-based FC analysis of the left DLPFC showed increased connectivity in the left superior parietal lobe and visual cortex of PTSD patients. The results suggested that PTSD patients experienced a disruption of intrinsic long-range functional connections in the fronto-parietal network and visual cortex, which are associated with attention control and visual information processing.
Daubechies wavelets for linear scaling density functional theory.
Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Towards simple orbital-dependent density functionals for molecular dissociation
NASA Astrophysics Data System (ADS)
Zhang, Igor Ying; Richter, Patrick; Scheffler, Matthias
2015-03-01
Density functional theory (DFT) is one of the leading first-principles electronic-structure theories. However, molecular dissociation remains a challenge, because it requires a well-balanced description of the drastically different electronic structure at different bond lengths. One typical and well-documented case is the dissociation of both H2+ and H2, for which all popular DFT functionals fail. We start from the Bethe-Goldstone equation to propose a simple orbital-dependent correlation functional which generalizes the linear adiabatic connection approach. The resulting scheme is based on second-order perturbation theory (PT2), but includes the self-consistent coupling of electron-hole pairs, which ensures the correct H2 dissociation limit and gives a finite correlation energy for systems with a (near)-degenerate energy gap. This coupling PT2-like (CPT2) approximation delivers a significant improvement over all existing functionals for both H2 and H2+ dissociation. We will demonstrate the reason for this improvement analytically for H2 in a minimal basis.
NASA Astrophysics Data System (ADS)
García-Aldea, David; Alvarellos, J. E.
2009-03-01
We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac'on-Alvarellos-Tarazona, Garc'ia-Gonz'alez et al., Wang-Govind-Carter and Garc'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same ansatz can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined).
Asaadi, Sina; Ashrafi, Farzad; Omidbeigi, Mahmoud; Nasiri, Zahra; Pakdaman, Hossein; Amini-Harandi, Ali
2016-01-01
Background: Cognitive impairment in patients with Parkinson’s disease (PD) mainly involves executive function (EF). The frontal assessment battery (FAB) is an efficient tool for the assessment of EFs. The aims of this study were to determine the validity and reliability of the psychometric properties of the Persian version of FAB and assess its correlation with formal measures of EFs to provide normative data for the Persian version of FAB in patients with PD. Methods: The study recruited 149 healthy participants and 49 patients with idiopathic PD. In PD patients, FAB results were compared to their performance on EF tests. Reliability analysis involved test-retest reliability and internal consistency, whereas validity analysis involved convergent validity approach. FAB scores compared in normal controls and in PD patients matched for age, education, and Mini-Mental State Examination (MMSE) score. Results: In PD patients, FAB scores were significantly decreased compared to normal controls, and correlated with Stroop test and Wisconsin Card Sorting Test (WCST). In healthy subjects, FAB scores varied according to the age, education, and MMSE. In the FAB subtest analysis, the performances of PD patients were worse than the healthy participants on similarities, fluency tasks, and Luria’s motor series. Conclusion: Persian version of FAB could be used as a reliable scale for the assessment of frontal lobe functions in Iranian patients with PD. Furthermore, normative data provided for the Persian version of this test improve the accuracy and confidence in the clinical application of the FAB. PMID:27141272
Benchmarking Density Functionals for Chemical Bonds of Gold.
Kepp, Kasper P
2017-03-09
Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark data set probes all types of bonding to gold from very electronegative halides that force Au(+) electronic structure, via covalently bonded systems, hard and soft Lewis acids and bases that either work against or complement the softness of gold, the Au2 molecule probing gold's bond with itself, and weak bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au-X bonds, ∼ 11-12 kJ/mol except for Au-H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP correlation produce weaker bonds to gold. Most functionals provide similar trend accuracy, though somewhat lower for M06 and M06L, but very different numerical accuracy. Notably, PBE and TPSS functionals with dispersion display the smallest numerical errors and very small mean signed errors (0-6 kJ/mol), i.e. no bias toward over- or under-binding. Errors are evenly distributed versus atomic number, suggesting that relativistic effects are treated fairly; the mean absolute error is almost halved from B3LYP (45 kJ/mol) to TPSS and PBE (23 kJ/mol, including difficult cases); 23 kJ/mol is quite respectable considering the diverse bonds to gold and the complication of relativistic effects. Thus, studies that use DFT with effective core potentials for gold chemistry, with no alternative due
Cluster density functional theory for lattice models based on the theory of Möbius functions
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2005-08-01
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Akashi, Ryosuke; Arita, Ryotaro
2013-08-02
We extend the density-functional theory for superconductors (SCDFT) to take account of the dynamical structure of the screened Coulomb interaction. We construct an exchange-correlation kernel in the SCDFT gap equation on the basis of the random-phase approximation, where electronic collective excitations such as plasmons are properly treated. Through an application to fcc lithium under high pressures, we demonstrate that our new kernel gives higher transition temperatures (T(c)) when the plasmon and phonon cooperatively mediate pairing and it improves the agreement between the calculated and experimentally observed T(c). The present formalism opens the door to nonempirical studies on unconventional electron mechanisms of superconductivity based on density-functional theory.
Perspective: Fifty years of density-functional theory in chemical physics.
Becke, Axel D
2014-05-14
Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.
Perspective: Fifty years of density-functional theory in chemical physics
Becke, Axel D.
2014-05-14
Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.
Density functional theory based generalized effective fragment potential method
Nguyen, Kiet A. E-mail: ruth.pachter@wpafb.af.mil; Pachter, Ruth E-mail: ruth.pachter@wpafb.af.mil; Day, Paul N.
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.
Specification of optical components using the power spectral density function
Lawson, J.K.; Wolfe, C.R.; Manes, K.R.; Trenholme, J.B.; Aikens, D.M.; English, R.E. Jr.
1995-06-20
This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as ``residuals.`` A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.
Density Functional Theory Study on Interaction between Catechin and Thymine
NASA Astrophysics Data System (ADS)
Cai, Wan-fei; Zheng, Yan; Li, Lai-cai; Tian, An-min
2012-12-01
The interacting patterns and mechanism of the catechin and thymine have been investigated with the density functional theory Becke's three-parameter nonlocal exchange functional and the Lee, Yang, and Parr nonlocal correlation functional (B3LYP) method by 6-31+G* basis set. Thirteen stable structures for the catechin-thymine complexes have been found which form two hydrogen bonds at least. The vibrational frequencies are also studied at the same level to analyze these complexes. The results indicated that catechin interacted with thymine by three different hydrogen bonds as N—H···O, C—H···O, O—H···O and the complexes are mainly stabilized by the hydrogen bonding interactions. Theories of atoms in molecules and natural bond orbital have been adopted to investigate the hydrogen bonds involved in all systems. The interaction energies of all complexes have been corrected for basis set superposition error, which are from -18.15 kJ/mol to -32.99 kJ/mol. The results showed that the hydrogen bonding contribute to the interaction energies dominantly. The corresponding bonds stretching motions in all complexes are red-shifted relative to that of the monomer, which is in agreement with experimental results.
Insights into phase transitions and entanglement from density functional theory
NASA Astrophysics Data System (ADS)
Wei, Bo-Bo
2016-11-01
Density functional theory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.
Particle-vibration coupling within covariant density functional theory
Litvinova, E.; Ring, P.; Tselyaev, V.
2007-06-15
Covariant density functional theory, which has so far been applied only within the framework of static and time-dependent mean-field theory, is extended to include particle-vibration coupling (PVC) in a consistent way. Starting from a conventional energy functional, we calculate the low-lying collective vibrations in the relativistic random phase approximation (RRPA) and construct an energy-dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole (p-h) channel is solved in the time blocking approximation (TBA). No additional parameters are used, and double counting is avoided by a proper subtraction method. The same energy functional, i.e., the same set of coupling constants, generates the Dirac-Hartree single-particle spectrum, the static part of the residual p-h interaction, and the particle-phonon coupling vertices. Therefore, a fully consistent description of nuclear excited states is developed. This method is applied for an investigation of damping phenomena in the spherical nuclei with closed shells {sup 208}Pb and {sup 132}Sn. Since the phonon coupling terms enrich the RRPA spectrum with a multitude of p-hxphonon components, a noticeable fragmentation of the giant resonances is found, which is in full agreement with experimental data and with results of the semiphenomenological nonrelativistic approach.
Building A Universal Nuclear Energy Density Functional (UNEDF)
Joe Carlson; Dick Furnstahl; Mihai Horoi; Rusty Lusk; Witek Nazarewicz; Esmond Ng; Ian Thompson; James Vary
2012-09-30
During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.
Density functional theory for comprehensive orbital energy calculations.
Nakata, Ayako; Tsuneda, Takao
2013-08-14
This study reveals the reason core 1s orbital energies and the highest occupied molecular orbital (HOMO) energies of hydrogen and rare gas atoms are underestimated by long-range corrected (LC) density functional theory (DFT), which quantitatively reproduces the HOMO energies of other systems and the lowest unoccupied molecular orbital (LUMO) energies. Applying the pseudospectral regional (PR) self-interaction correction (SIC) drastically improved the underestimated orbital energies in LC-DFT calculations, while maintaining or improving the accuracies in the calculated valence HOMO and LUMO energies. This indicates that the self-interaction error in exchange functionals causes the underestimations of core 1s orbital energies and the HOMO energies of hydrogen and rare gas atoms in LC-DFT calculations. To clarify the reason for the improvement, the fractional occupation dependences of total electronic energies and orbital energies were examined. The calculated results clearly showed that the LC-PR functional gives almost linear dependences of total electronic energies for a slight decrease in the occupation number of core 1s orbitals, although this linear dependence disappears for significant decrease due to the shrinking of exchange self-interaction regions. It was also clarified that the PRSIC hardly affects the occupation number dependences of the total electronic energies and orbital energies for the fractional occupations of HOMOs and LUMOs. As a result, it was concluded that core orbital energies are obtained accurately by combining LC-DFT with PRSIC.
Yu, Kuang; Libisch, Florian
2015-09-14
We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.
Density functional theory and phytochemical study of 8-hydroxyisodiospyrin
NASA Astrophysics Data System (ADS)
Ullah, Zakir; Ata-ur-Rahman; Fazl-i-Sattar; Rauf, Abdur; Yaseen, Muhammad; Hassan, Waseem; Tariq, Muhammad; Ayub, Khurshid; Tahir, Asif Ali; Ullah, Habib
2015-09-01
Comprehensive theoretical and experimental studies of a natural product, 8-hydroxyisodiospyrin (HDO) have been carried out. Based on the correlation of experimental and theoretical data, an appropriate computational model was developed for obtaining the electronic, spectroscopic, and thermodynamic parameters of HDO. First of all, the exact structure of HDO is confirmed from the nice correlation of theory and experiment, prior to determination of its electroactive nature. Hybrid density functional theory (DFT) is employed for all theoretical simulations. The experimental and predicted IR and UV-vis spectra [B3LYP/6-31+G(d,p) level of theory] have excellent correlation. Inter-molecular non-covalent interaction of HDO with different gases such as NH3, CO2, CO, H2O is investigated through geometrical counterpoise (gCP) i.e., B3LYP-gCP-D3/6-31G∗ method. Furthermore, the inter-molecular interaction is also supported by geometrical parameters, electronic properties, thermodynamic parameters and charge analysis. All these characterizations have corroborated each other and confirmed the electroactive nature (non-covalent interaction ability) of HDO for the studied gases. Electronic properties such as Ionization Potential (IP), Electron Affinities (EA), electrostatic potential (ESP), density of states (DOS), HOMO, LUMO, and band gap of HDO have been estimated for the first time theoretically.
Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides
NASA Astrophysics Data System (ADS)
Millis, Andrew
2015-03-01
The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Vibrational spectroscopy and density functional theory study of 4-mercaptophenol
NASA Astrophysics Data System (ADS)
Li, Ran; Ji, Wei; Chen, Lei; Lv, Haiming; Cheng, Jianbo; Zhao, Bing
2014-03-01
In this paper, 4-mercaptophenol (4-MPH) was designed as a model molecule for theoretical and experimental studies of the molecule structure. Density functional theory (DFT) calculations have been performed to predict the IR and Raman spectra for the molecule. In addition, Fourier transform infrared (FTIR) and Raman spectra of the compound have been obtained experimentally. All FTIR and Raman bands of the compound obtained experimentally were assigned based on the modeling results obtained at the B3LYP/6-311 + G** level. Our calculated vibrational frequencies are in good agreement with the experimental vales. The molecular electrostatic potential surface calculation was performed and the result suggested that the 4-MPH has two hydrogen bond donors and three hydrogen bond acceptors. HOMO-LUMO gap was also obtained theoretically at B3LYP/6-311 + G** level.
Density functional theory and simulations of colloidal triangular prisms.
Marechal, Matthieu; Dussi, Simone; Dijkstra, Marjolein
2017-03-28
Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlocomputer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld's version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms.
Machine-learned approximations to Density Functional Theory Hamiltonians
NASA Astrophysics Data System (ADS)
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Native defects in Tl6SI4: Density functional calculations
NASA Astrophysics Data System (ADS)
Shi, Hongliang; Du, Mao-Hua
2015-05-01
Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges and large static dielectric constant, which provides effective screening of charged defects and impurities.
Direct recursive identification of the Preisach hysteresis density function
NASA Astrophysics Data System (ADS)
Ruderman, Michael
2013-12-01
In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.
The photochemistry of transition metal complexes using density functional theory.
Garino, Claudio; Salassa, Luca
2013-07-28
The use of density functional theory (DFT) and time-dependent DFT (TD-DFT) to study the photochemistry of metal complexes is becoming increasingly important among chemists. Computational methods provide unique information on the electronic nature of excited states and their atomic structure, integrating spectroscopy observations on transient species and excited-state dynamics. In this contribution, we present an overview on photochemically active transition metal complexes investigated by DFT. In particular, we discuss a representative range of systems studied up to now, which include CO- and NO-releasing inorganic and organometallic complexes, haem and haem-like complexes dissociating small diatomic molecules, photoactive anti-cancer Pt and Ru complexes, Ru polypyridyls and diphosphino Pt derivatives.
Machine-learned approximations to Density Functional Theory Hamiltonians.
Hegde, Ganesh; Bowen, R Chris
2017-02-15
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Self-consistent polarization density functional theory: Application to Argon
Maerzke, Katie A.; Murdachaew, Garold; Mundy, Christopher J.; Schenter, Gregory K.; Siepmann, J. I.
2009-03-12
We present a comprehensive set of results for argon, a case study in weak interactions, using the selfconsistent polarization density functional theory (SCP-DFT). With minimal parameterization, SCPDFT is found is give excellent results for the dimer interaction energy, the second virial coefficient, the liquid structure, and the lattice constant and cohesion energy of the face-centered cubic (fcc) crystal compared to both accurate theoretical and experimental benchmarks. Thus, SCP-DFT holds promise as a fast, efficient, and accurate method for performing ab initio dynamics that include additional polarization and dispersion interactions for large, complex systems involving solvation and bond breaking. This work was supported by the U.S. Department of Energy's (DOE) Office of Basic Energy Sciences, Chemical Sciences program. The Pacific Northwest National Laboratory is operated by Battelle for DOE.
Nitrotyrosine adsorption on defective graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Majidi, R.; Karami, A. R.
2015-06-01
We have applied density functional theory to study adsorption of nitrotyrosine on perfect and defective graphene sheets. The graphene sheets with Stone-Wales (SW) defect, pentagon-nonagon (5-9) single vacancy, and pentagon-octagon-pentagon (5-8-5) double vacancy were considered. The calculations of adsorption energy showed that nitrotyrosine presents a more strong interaction with defective graphene rather than with perfect graphene sheet. The order of interaction strength is: SW>5-9>5-8-5>perfect graphene. It is found that the electronic properties of perfect and defective graphene are sensitive to the presence of nitrotyrosine. Hence, graphene sheets can be considered as a good sensor for detection of nitrotyrosine molecule which is observed in connection with several human disorders, such as Parkinson's and Alzheimer's disease.
Native defects in Tl6SI4: Density functional calculations
Shi, Hongliang; Du, Mao -Hua
2015-05-05
In this study, Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges andmore » large static dielectric constant, which provides effective screening of charged defects and impurities.« less
Descriptions of carbon isotopes within the energy density functional theory
Ismail, Atef; Cheong, Lee Yen; Yahya, Noorhana; Tammam, M.
2014-10-24
Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.
Density functional theory studies of HCOOH decomposition on Pd(111)
NASA Astrophysics Data System (ADS)
Scaranto, Jessica; Mavrikakis, Manos
2016-08-01
The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, density functional theory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Density functional theory study of hexagonal carbon phases.
Wang, Zhibin; Gao, Faming; Li, Na; Qu, Nianrui; Gou, Huiyang; Hao, Xianfeng
2009-06-10
It is reported frequently that the new carbon phases may be harder than diamond (Wang et al 2004 Proc. Natl Acad. Sci. 101 13699 and Mao et al 2003 Science 302 425). However, the mechanism is still unclear. In this paper we systematically investigate the structural, electronic, and mechanical properties of the diamond polytypes using first-principles density functional calculations. The results show that the bulk modulus and shear modulus for the hexagonal form of diamond approach those of diamond, suggesting they might be hard and low compressibility materials. According to the semiempirical method for hardness based on the Mulliken overlap population, the hardnesses for hexagonal forms have been evaluated and compared to diamond. The results indicate that these phases are superhard. More importantly, the bonds in some specific directions of the hexagonal phases are harder than those in diamond, which may lead to the noticeable indentation marks on the diamond anvils observed in experiments.
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
Origin of anomeric effect: A density functional steric analysis
Huang, Ying; Zhong, Ai-Guo; Yang, Qinsong; Liu, Shubin
2011-01-01
The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial–equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange–correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial–equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostaticinteractions, synchronously working together. Another explanation in terms of exchange–correlation and electrostaticinteractions has also been obtained in this work.
Jordan, Daniel K; Mazziotti, David A
2005-02-22
Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.
Minimizing density functional failures for non-covalent interactions beyond van der Waals complexes.
Corminboeuf, Clemence
2014-11-18
CONSPECTUS: Kohn-Sham density functional theory offers a powerful and robust formalism for investigating the electronic structure of many-body systems while providing a practical balance of accuracy and computational cost unmatched by other methods. Despite this success, the commonly used semilocal approximations have difficulties in properly describing attractive dispersion interactions that decay with R(-6) at large intermolecular distances. Even in the short to medium range, most semilocal density functionals fail to give an accurate description of weak interactions. The omnipresence of dispersion interactions, which are neglected in the most popular electronic structure framework, has stimulated intense developments during the past decade. In this Account, we summarize our effort to develop and implement dispersion corrections that dramatically reduce the failures of both inter- and intramolecular interaction energies. The proposed schemes range from improved variants of empirical atom pairwise dispersion correction (e.g., dD10) to robust formulations dependent upon the electron density. Emphasis has been placed on introducing more physics into a modified Tang and Toennies damping function and deriving accurate dispersion coefficients. Our most sophisticated and established density-dependent correction, dDsC, is based on a simple generalized gradient approximation (GGA)-like reformulation of the exchange hole dipole moment introduced by Becke and Johnson. Akin to its empirical precursor, dDsC dramatically improves the interaction energy of a variety of standard density functionals simultaneously for typical intermolecular complexes and shorter-range interactions occurring within molecules. The broad applicability and robustness of the dDsC scheme is demonstrated on various representative reaction energies, geometries, and molecular dynamic simulations. The suitability of the a posteriori correction is also established through comparisons with the more
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
A density functional for core-valence correlation energy
NASA Astrophysics Data System (ADS)
Ranasinghe, Duminda S.; Frisch, Michael J.; Petersson, George A.
2015-12-01
A density functional, ɛCV-DFT(ρc, ρv), describing the core-valence correlation energy has been constructed as a linear combination of ɛLY Pcorr(ρc), ɛV WN5corr(ρc, ρv), ɛPBEcorr(ρc, ρv), ɛSlaterex(ρc, ρv), ɛHCTHex(ρc, ρv), ɛHFex(ρc, ρv), and F CV -DFT (" separators=" N i , Z i ) , a function of the nuclear charges. This functional, with 6 adjustable parameters, reproduces (±0.27 kcal/mol rms error) a benchmark set of 194 chemical energy changes including 9 electron affinities, 18 ionization potentials, and 167 total atomization energies covering the first- and second-rows of the periodic table. This is almost twice the rms error (±0.16 kcal/mol) obtained with CCSD(T)/MTsmall calculations, but less than half the rms error (±0.65 kcal/mol) obtained with MP2/GTlargeXP calculations, and somewhat smaller than the rms error (±0.39 kcal/mol) obtained with CCSD/MTsmall calculations. The largest positive and negative errors from ɛCV-DFT(ρc, ρv) were 0.88 and -0.75 kcal/mol with the set of 194 core-valence energy changes ranging from +3.76 kcal/mol for the total atomization energy of propyne to -9.05 kcal/mol for the double ionization of Mg. Evaluation of the ɛCV-DFT(ρc, ρv) functional requires less time than a single SCF iteration, and the accuracy is adequate for any model chemistry based on the CCSD(T) level of theory.
Augmented Lagrangian formulation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Suryanarayana, Phanish; Phanish, Deepa
2014-10-01
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas-Fermi-von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Self-interaction corrections in density functional theory
Tsuneda, Takao; Hirao, Kimihiko
2014-05-14
Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications. The self-interaction corrections get rid of the self-interaction error, which is the sum of the Coulomb and exchange self-interactions that remains because of the use of an approximate exchange functional. The most frequently used self-interaction correction is the Perdew-Zunger correction. However, this correction leads to instabilities in the electronic state calculations of molecules. To avoid these instabilities, several self-interaction corrections have been developed on the basis of the characteristic behaviors of self-interacting electrons, which have no two-electron interactions. These include the von Weizsäcker kinetic energy and long-range (far-from-nucleus) asymptotic correction. Applications of self-interaction corrections have shown that the self-interaction error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons. This finding is supported by the fact that the distribution of self-interacting electrons indicates that they are near atomic nuclei rather than in chemical bonds.
Density functional computations for inner-shell excitation spectroscopy
NASA Astrophysics Data System (ADS)
Hu, Ching-Han; Chong, Delano P.
1996-11-01
The 1 s → π ∗ inner-shell excitation spectra of seven molecules have been studied using density functional theory along with the unrestricted generalized transition state (uGTS) approach. The exchange-correlation potential is based on a combined functional of Becke's exchange (B88) and Perdew's correlation (P86). A scaling procedure based on Clementi and Raimondi's rules for atomic screening is applied to the cc-pVTZ basis set of atoms where a partial core-hole is created in the uGTS calculations. The average absolute deviation between our predicted 1 s → π ∗ excitations eneergies and experimental values is only 0.16 eV. Singlet-triplet splittings of C 1 s → π ∗ transitions of CO, C 2H 2, C 2H 4, and C 6H 6 also agree with experimental observations. The average absolute deviation of our predicted core-electron binding energies and term values is 0.23 and 0.29 eV, respectively.
Density functional steric analysis of linear and branched alkanes.
Ess, Daniel H; Liu, Shubin; De Proft, Frank
2010-12-16
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E(s)[ρ]), an electrostatic energy term (E(e)[ρ]), and a fermionic quantum energy term (E(q)[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.
Density Functional Steric Analysis of Linear and Branched Alkanes
Ess, Daniel H.; Liu, Shubin; De Proft, Frank
2010-11-18
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E_{e}[[ρ]), an electrostatic energy term (E_{e}[ρ]), and a fermionic quantum energy term (E_{q}[[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.
Hardness of FeB4: density functional theory investigation.
Zhang, Miao; Lu, Mingchun; Du, Yonghui; Gao, Lili; Lu, Cheng; Liu, Hanyu
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).
Metallophilic interactions from dispersion-corrected density-functional theory
Otero-de-la-Roza, Alberto Mallory, Joel D.; Johnson, Erin R.
2014-05-14
In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH{sub 3}){sub 4}]{sup +} cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal.
Extracting electron transfer coupling elements from constrained density functional theory
NASA Astrophysics Data System (ADS)
Wu, Qin; Van Voorhis, Troy
2006-10-01
Constrained density functional theory (DFT) is a useful tool for studying electron transfer (ET) reactions. It can straightforwardly construct the charge-localized diabatic states and give a direct measure of the inner-sphere reorganization energy. In this work, a method is presented for calculating the electronic coupling matrix element (Hab) based on constrained DFT. This method completely avoids the use of ground-state DFT energies because they are known to irrationally predict fractional electron transfer in many cases. Instead it makes use of the constrained DFT energies and the Kohn-Sham wave functions for the diabatic states in a careful way. Test calculations on the Zn2+ and the benzene-Cl atom systems show that the new prescription yields reasonable agreement with the standard generalized Mulliken-Hush method. We then proceed to produce the diabatic and adiabatic potential energy curves along the reaction pathway for intervalence ET in the tetrathiafulvalene-diquinone (Q-TTF-Q) anion. While the unconstrained DFT curve has no reaction barrier and gives Hab≈17kcal /mol, which qualitatively disagrees with experimental results, the Hab calculated from constrained DFT is about 3kcal /mol and the generated ground state has a barrier height of 1.70kcal/mol, successfully predicting (Q-TTF-Q)- to be a class II mixed-valence compound.
Acrolein impairs the cholesterol transport functions of high density lipoproteins.
Chadwick, Alexandra C; Holme, Rebecca L; Chen, Yiliang; Thomas, Michael J; Sorci-Thomas, Mary G; Silverstein, Roy L; Pritchard, Kirkwood A; Sahoo, Daisy
2015-01-01
High density lipoproteins (HDL) are considered athero-protective, primarily due to their role in reverse cholesterol transport, where they transport cholesterol from peripheral tissues to the liver for excretion. The current study was designed to determine the impact of HDL modification by acrolein, a highly reactive aldehyde found in high abundance in cigarette smoke, on the cholesterol transport functions of HDL. HDL was chemically-modified with acrolein and immunoblot and mass spectrometry analyses confirmed apolipoprotein crosslinking, as well as acrolein adducts on apolipoproteins A-I and A-II. The ability of acrolein-modified HDL (acro-HDL) to serve as an acceptor of free cholesterol (FC) from COS-7 cells transiently expressing SR-BI was significantly decreased. Further, in contrast to native HDL, acro-HDL promotes higher neutral lipid accumulation in murine macrophages as judged by Oil Red O staining. The ability of acro-HDL to mediate efficient selective uptake of HDL-cholesteryl esters (CE) into SR-BI-expressing cells was reduced compared to native HDL. Together, the findings from our studies suggest that acrolein modification of HDL produces a dysfunctional particle that may ultimately promote atherogenesis by impairing functions that are critical in the reverse cholesterol transport pathway.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Computational characterization of sodium selenite using density functional theory.
Barraza-Jiménez, Diana; Flores-Hidalgo, Manuel Alberto; Galvan, Donald H; Sánchez, Esteban; Glossman-Mitnik, Daniel
2011-04-01
In this theoretical study we used density functional theory to calculate the molecular and crystalline structures of sodium selenite. Our structural results were compared with experimental data. From the molecular structure we determined the ionization potential, electronic affinity, and global reactivity parameters like electronegativity, hardness, softness and global electrophilic index. A significant difference in the IP and EA values was observed, and this difference was dependent on the calculation method used (employing either vertical or adiabatic energies). Thus, values obtained for the electrophilic index (2.186 eV from vertical energies and 2.188 eV from adiabatic energies) were not significantly different. Selectivity was calculated using the Fukui functions. Since the Mulliken charge study predicted a negative value, it is recommended that AIM should be used in selectivity characterization. It was evident from the selectivity index that sodium atoms are the most sensitive sites to nucleophilic attack. The results obtained in this work provide data that will aid the characterization of compounds used in crop biofortification.
Antisites in III-V semiconductors: Density functional theory calculations
Chroneos, A.; Tahini, H. A.; Schwingenschlögl, U.; Grimes, R. W.
2014-07-14
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
NASA Astrophysics Data System (ADS)
Basurto, Luis; Zope, Rajendra R.; Baruah, Tunna
2016-05-01
We report an electronic structure study of a multichromophoric molecular complex containing two of each borondipyrromethane dye, Zn-tetraphenyl-porphyrin, bisphenyl anthracene and a fullerene. The snowflake shaped molecule behaves like an antenna capturing photon at different frequencies and transferring the photon energy to the porphyrin where electron transfer occurs from the porphyrin to the fullerene. The study is performed within density functional formalism using large polarized Guassian basis sets (12,478 basis functions in total). The energies of the HOMO and LUMO states in the complex, as adjudged by the ionization potential and the electron affinity values, show significant differences with respect to their values in participating subunits in isolation. These differences are also larger than the variations of the ionization potential and electron affinity values observed in non-bonded C60-ZnTPP complexes in co-facial arrangement or end-on orientations. An understanding of the origin of these differences is obtained by a systematic study of the effect of structural strain, the presence of ligands, the effect of orbital delocalization on the ionization energy and the electron affinity. Finally, a few lowest charge transfer energies involving electronic transitions from the porphyrin component to the fullerene subunit of the complex are predicted.
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory.
Derricotte, Wallace D; Evangelista, Francesco A
2015-06-14
Orthogonality constrained density functional theory (OCDFT) [F. A. Evangelista, P. Shushkov and J. C. Tully, J. Phys. Chem. A, 2013, 117, 7378] is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree-Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.
Rethinking Formalisms in Formal Education
ERIC Educational Resources Information Center
Nathan, Mitchell J.
2012-01-01
I explore a belief about learning and teaching that is commonly held in education and society at large that nonetheless is deeply flawed. The belief asserts that mastery of "formalisms"--specialized representations such as symbolic equations and diagrams with no inherent meaning except that which is established by convention--is prerequisite to…
Mossahebi, Sina; Zhu, Simeng; Chen, Howard; Shmuylovich, Leonid; Ghosh, Erina; Kovács, Sándor J
2014-09-01
Quantitative cardiac function assessment remains a challenge for physiologists and clinicians. Although historically invasive methods have comprised the only means available, the development of noninvasive imaging modalities (echocardiography, MRI, CT) having high temporal and spatial resolution provide a new window for quantitative diastolic function assessment. Echocardiography is the agreed upon standard for diastolic function assessment, but indexes in current clinical use merely utilize selected features of chamber dimension (M-mode) or blood/tissue motion (Doppler) waveforms without incorporating the physiologic causal determinants of the motion itself. The recognition that all left ventricles (LV) initiate filling by serving as mechanical suction pumps allows global diastolic function to be assessed based on laws of motion that apply to all chambers. What differentiates one heart from another are the parameters of the equation of motion that governs filling. Accordingly, development of the Parametrized Diastolic Filling (PDF) formalism has shown that the entire range of clinically observed early transmitral flow (Doppler E-wave) patterns are extremely well fit by the laws of damped oscillatory motion. This permits analysis of individual E-waves in accordance with a causal mechanism (recoil-initiated suction) that yields three (numerically) unique lumped parameters whose physiologic analogues are chamber stiffness (k), viscoelasticity/relaxation (c), and load (xo). The recording of transmitral flow (Doppler E-waves) is standard practice in clinical cardiology and, therefore, the echocardiographic recording method is only briefly reviewed. Our focus is on determination of the PDF parameters from routinely recorded E-wave data. As the highlighted results indicate, once the PDF parameters have been obtained from a suitable number of load varying E-waves, the investigator is free to use the parameters or construct indexes from the parameters (such as stored
Marco-Contelles, José; de Opazo, Elsa
2002-05-31
The free radical cyclization (FR) and the ring-closing metathesis (RCM) reaction have been analyzed in order to develop new and original synthetic protocols for the synthesis of enantiomerically pure, highly functionalized, medium-sized carbocycles from carbohydrates. As a result, we report here for the first time examples of the 7-exo FR cyclization of acyclic radical precursors derived from sugars. This process appears to be extremely sensitive to the conformational mobility of the radical species in the transition state. The use of two isopropylidene groups blocking four of the total present hydroxyl groups and a good radical acceptor (as an alpha,beta-unsaturated ester) are mandatory conditions for a successful ring closure protocol. The RCM reaction by using Grubbs' catalyst on selected carbohydrate-derived precursors has afforded variable yields of the expected unsaturated cycloheptane or cycloctane derivatives. The synthesis of the cycloheptitols has been carried out in good yields, regardless of the absolute configuration at the different stereocenters and the nature of the O-functional groups bound in allylic positions to one of the double bonds implicated in the metathesis reaction. Conversely, in the cyclooctane synthesis, we have observed that the success of the reaction depends not only on the absolute configuration at the different stereocenters close to the double bonds but also on the nature of the O-protecting groups on these stereocenters. Finally, the RCM strategy has been used in an attempt to prepare natural (+)-calystegine B(2) from D-glucose. The synthesis of compound 92 from D-glucose constitutes a formal total synthesis of (+)-calystegine B(2), showing the importance of the steric hindrance in allylic positions for a successful RCM reaction.
NASA Astrophysics Data System (ADS)
Lipparini, Enrico; Pederiva, Francesco
2016-08-01
The time dependent local isospin density approximation (TDLIDA) has been extended to the study of the transverse isospin response function in nuclear matter with an arbitrary neutron-proton asymmetry parameter ξ . The energy density functional has been chosen in order to fit existing accurate quantum Monte Carlo calculations with a density dependent potential. The evolution of the response with ξ in the Δ Tz=±1 channels is quite different. While the strength of the Δ Tz=+1 channel disappears rather quickly by increasing the asymmetry, the Δ Tz=-1 channel develops a stronger and stronger collective mode that in the regime typical of neutron star matter at β equilibrium almost completely exhausts the excitation spectrum of the system. The neutrino mean free paths obtained from the TDLIDA responses are strongly dependent on ξ and on the presence of collective modes, leading to a sizable difference with respect to the prediction of the Fermi gas model.
NASA Astrophysics Data System (ADS)
Lovett, Ronald
1988-06-01
All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the density functional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these equations which are satisified by the correct kernels, which guarantee a unique solution to the integral equations, and which provide a natural constraint on approximations which can be used in density functional theory. It is also shown that this sensitive behavior is a general property of density functional problems and that the methodology for constructing the constraints is equally general. A variety of applications of density functional theory are reviewed to illustrate practical consequences of this sensitivity.
Velocity analysis with local event slopes related probability density function
NASA Astrophysics Data System (ADS)
Zhang, Peng; Lu, Wenkai; Zhang, Yingqiang
2015-12-01
Macro velocity model plays a key role in seismic imaging and inversion. The performance of traditional velocity analysis methods is degraded by multiples and amplitude-versus-offset (AVO) anomalies. Local event slopes, containing the subsurface velocity information, have been widely used to accomplish common time-domain seismic processing, imaging and velocity estimation. In this paper, we propose a method for velocity analysis with probability density function (PDF) related to local event slopes. We first estimate local event slopes with phase information in the Fourier domain. An adaptive filter is applied to improve the performance of slopes estimator in the low signal-to-noise ratio (SNR) situation. Second, the PDF is approximated with the histogram function, which is related to attributes derived from local event slopes. As a graphical representation of the data distribution, the histogram function can be computed efficiently. By locating the ray path of the first arrival on the semblance image with straight-ray segments assumption, automatic velocity picking is carried out to establish velocity model. Unlike local event slopes based velocity estimation strategies such as averaging filters and image warping, the proposed method does not make the assumption that the errors of mapped velocity values are symmetrically distributed or that the variation of amplitude along the offset is slight. Extension of the method to prestack time-domain migration velocity estimation is also given. With synthetic and field examples, we demonstrate that our method can achieve high resolution, even in the presence of multiples, strong amplitude variations and polarity reversals.
Understanding density functional theory (DFT) and completing it in practice
Bagayoko, Diola
2014-12-15
We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice.
NASA Technical Reports Server (NTRS)
Denning, Peter J.
1991-01-01
The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.
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
Spin propensities of octahedral complexes from density functional theory.
Mortensen, Sara R; Kepp, Kasper P
2015-04-30
The fundamental balance between high- and low-spin states of transition metal systems depends on both the metal ion and the ligands surrounding it, as often visualized by the spectrochemical series. Most density functionals do not reproduce this balance, and real spin state propensities depend on orbital pairing and vibrational entropies absent in the spectrochemical series. Thus, we systematically computed the tendency toward high or low spin of "text-book" octahedral metal complexes versus ligand and metal type, using eight density functionals. Dispersion effects were generally <5 kJ/mol, favoring low-spin states. Zero-point energies favored high-spin states up to 33 kJ/mol for strong ligands, but down to a few kilojoules per mole for weak ligands. Vibrational entropy also favored high-spin states up to 40 kJ/mol, most for strong ligands. Jahn-Teller distortion in Co(II) low-spin states, particularly stable d(6) low-spin states, and entropy corrections were consistent with experiment. Entropy and zero-point energy corrections were markedly lower for Co(II) and Mn(III), viz., the differential ligand field stabilization energy, and can only be ignored for weak ligands. The data enable simple assessment of spin state propensities versus ligand and metal type and reveal, e.g., that CN(-) is consistently weaker than CO for M(II) but stronger than CO for M(III) and SCN(-) and NCS(-) change order in M(II) versus M(III) complexes. Contrary to expectation based on the spectrochemical series, Cl(-) and Br(-) are very close in spin state propensity because the pairing penalty for low spin is smaller in Br(-). Thus, for the M(II) complexes, we find a consensus order of Br(-) ∼ Cl(-) < H2O < SCN(-) < NCS(-) ∼ NH3 < CN(-) < CO, whereas for the M(III) complexes, an approximate order is Br(-) ∼ Cl(-) < H2O ∼ NCS(-) ∼ SCN(-)< NH3 < CO < CN(-).
Subsystem functional and the missing ingredient of confinement physics in density functionals.
Armiento, Rickard Roberto; Mattsson, Ann Elisabet; Hao, Feng
2010-08-01
The subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The 'confinement physics,' an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential {yields} density and the density {yields} exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed.
Dai, Yafei; Li, Zhenyu; Yang, Jinlong
2015-08-06
The atomically precise edge chlorination of nanographenes has recently been reported as a crucial technology of functionalization through which the planar structure and optical properties of nanographenes can be significantly changed. To check the effects of molecular size, geometrical symmetry and edge functionalization of nanographenes on their optical properties, a series of nanographenes is studied in the framework of density functional theory with the B3LYP functional. Our results indicate that edge functionalization remarkably changes the nonlinear optical properties and increases the anisotropy of nanographenes compared to the effects of the molecular size and system geometric symmetry. Furthermore, the nonlinear optical properties of nanographenes can be tuned by precise edge functionalization, which opens a new avenue for using nanographenes as nonlinear optical materials.
Global and local curvature in density functional theory
NASA Astrophysics Data System (ADS)
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Calaminici, Patrizia; Janetzko, Florian; Köster, Andreas M; Mejia-Olvera, Roberto; Zuniga-Gutierrez, Bernardo
2007-01-28
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
Density-functional study of plutonium monoxide monohydride
NASA Astrophysics Data System (ADS)
Qiu, Ruizhi; Lu, Haiyan; Ao, Bingyun; Tang, Tao; Chen, Piheng
2017-03-01
The structural, electronic, mechanical, optical, thermodynamic properties of plutonium monoxide monohydride (PuOH) are studied by density-functional calculations within the framework of LDA/GGA and LDA/GGA+U. From the total energy calculation, the lowest-energy crystal structure of PuOH is predicted to have space group F 4 bar 3 m (No. 216). Within the LDA+U framework, the calculated lattice parameter of F 4 bar 3 m -PuOH is in good agreement with the experimental value and the corresponding ground state is predicted to be an antiferromagnetic charge-transfer insulator. Furthermore, we investigate the bonding character of PuOH by analyzing the electron structure and find that there are a stronger Pu-O bond and a weaker Pu-H bond. The mechanical properties including the elastic constants, elastic moduli and Debye's temperature, and the optical properties including the reflectivity and absorption coefficient are also calculated. We then compute the phonon spectrum which verified the dynamical stability of F 4 bar 3 m -PuOH. Some thermodynamic quantities such as the specific heat are evaluated. Finally we calculate the formation energy of PuOH, and the reaction energies for the oxidation of PuOH and PuOH-coated Pu, which are in reasonable agreement with the experimental values.
Dynamical Density Functional Theory and Hydrodynamic Interactions in Confined Systems
NASA Astrophysics Data System (ADS)
Goddard, Benjamin; Nold, Andreas; Kalliadasis, Serafim
2016-11-01
Colloidal systems consist of nano- to micrometer-sized particles suspended in a bath of many more, much smaller and much lighter particles. Motion of the colloidal particles through the bath, e.g. when driven by external forces such as gravity, induces flows in the bath. These flows in turn impart forces on the colloid particles. These bath-mediated forces, known as Hydrodynamic Interactions (HIs) strongly influence the dynamics of the colloid particles. This is particularly true in confined systems, in which the presence of walls substantially modifies the HIs compared to unbounded geometries. For many-particle systems, the many of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. We employ elements from the statistical mechanics of classical fluids, namely Dynamical Density Functional Theory (DDFT), the computational complexity of which is independent of the number of particles to include both inter-particle and particle-wall HI and demonstrate the physical importance of using the correct description of HIs in confined systems. In addition, DDFT allows us to isolate and investigate different components of HIs. Supported by EPSRC Grant EP/L025159.
Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics.
Copan, Andreas V; Sokolov, Alexander Yu; Schaefer, Henry F
2014-06-10
We present an extensive benchmark study of density cumulant functional theory (DCFT) for thermochemistry and kinetics of closed- and open-shell molecules. The performance of DCFT methods (DC-06, DC-12, ODC-06, and ODC-12) is compared to that of coupled-electron pair methods (CEPA0 and OCEPA0) and coupled-cluster theory (CCSD and CCSD(T)) for the description of noncovalent interactions (A24 database), barrier heights of hydrogen-transfer reactions (HTBH38), radical stabilization energies (RSE30), adiabatic ionization energies (AIE), and covalent bond stretching in diatomic molecules. Our results indicate that out of four DCFT methods the ODC-12 method is the most reliable and accurate DCFT formulation to date. Compared to CCSD, ODC-12 shows superior results for all benchmark tests employed in our study. With respect to coupled-pair theories, ODC-12 outperforms CEPA0 and shows similar accuracy to the orbital-optimized CEPA0 variant (OCEPA0) for systems at equilibrium geometries. For covalent bond stretching, ODC-12 is found to be more reliable than OCEPA0. For the RSE30 and AIE data sets, ODC-12 shows competitive performance with CCSD(T). In addition to benchmark results, we report new reference values for the RSE30 data set computed using coupled cluster theory with up to perturbative quadruple excitations.
Van der Waals interactions in density functional theory
NASA Astrophysics Data System (ADS)
Langreth, David C.
2009-03-01
The van der Waals density functional which we introduced half a decade agoootnotetextM. Dion et al. Phys. Rev. Lett. 92, 246401 (2004). and its self-consistent generalizationootnotetextT. Thonhauser et al., Phys. Rev. B 76, 125112 (2007). will be briefly reviewed. There are many collaborators in the application review that will follow, not only those who worked in the physics department at Rutgers% ootnotetextMaxime Dion, Aaron Puzder, T. Thonhauser, Valentino R. Cooper, Shen Li, Eamonn Murray, Lingzhu Kong, and Kyuho Lee. and at Chalmers,% ootnotetextHenrik Rydberg, Svetla Chakarova-K"ack, Jesper Kleis, Elsebeth Schr"oder, Per Hyldgaard, and Bengt I. Lundqvist. but also at Denmarks Technical University,% ootnotetextAndrei Kelkkanen, Poul G. Moses, Jesper Kleis, and Bengt I. Lundqvist. the chemistry department at Rutgers,% ootnotetextKonhoa Li, Jing Li, Yves Chabal, and Wilma K. Olson. and most recently at the University of Texas at Dallas.% ootnotetextNour Nijem and Yves Chabal. I will expand on our recent review article,ootnotetextD. C. Langreth et al., J. Phys. Cond. Mat. (in press). which hopefully will be published before the present talk, and include applications by other groups not listed below. If possible, I will also review results from a more recent collaboration to study nucleosomal DNA and beyond.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Hoft, Jan; Weber, J. K.; Raut, E.; Larson, Vincent E.; Wang, Minghuai; Rasch, Philip J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection.These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; ...
2014-06-11
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Density functional theory investigation of sodium azide at high pressure
NASA Astrophysics Data System (ADS)
Steele, B. A.; Landerville, A. C.; Oleynik, I. I.
2014-05-01
High pressure experiments utilizing Raman spectroscopy indicate that the a phase of sodium azide undergoes a polymeric phase transition at high pressure. In this work, the structural and vibrational properties, including the first order Raman and infrared spectra, of the a phase of sodium azide are calculated using first-principles density functional theory up to 92 GPa. The equation of state of α NaN3 is obtained within the quasi-harmonic approximation at various temperatures. Each Raman-active mode blue shifts under compression whereas the doubly degenerate IR-active azide bending mode red-shifts under compression. However, at 70 GPa, the intensity of the Bu IR-active bending mode decreases substantially, and a new distorted azide bending lattice mode appears in the IR spectrum. In contrast to the bending mode, this new mode blue-shifts under compression. No new modes appear in the Raman spectra at high pressure, indicating that the changes in the Raman spectrum seen in experiment at high pressure are signs of new high nitrogen content structures, but not due to sodium azide.
Density functional theory study of phase IV of solid hydrogen
NASA Astrophysics Data System (ADS)
Pickard, Chris J.; Martinez-Canales, Miguel; Needs, Richard J.
2012-06-01
We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using density functional theory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250-295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater.1476-112210.1038/nmat3175 10, 927 (2011) and R. T. Howie , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.125501 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.
Density functional and neutron diffraction studies of lithium polymer electrolytes.
Baboul, A. G.
1998-06-26
The structure of PEO doped with lithium perchlorate has been determined using neutron diffraction on protonated and deuterated samples. The experiments were done in the liquid state. Preliminary analysis indicates the Li-O distance is about 2.0 {angstrom}. The geometries of a series of gas phase lithium salts [LiCF{sub 3}SO{sub 3}, Li(CF{sub 3}SO{sub 2}){sub 2}N, Li(CF{sub 3}SO{sub 2}){sub 2}CH, LiClO{sub 4}, LiPF{sub 6}, LiAsF{sub 6}] used in polymer electrolytes have been optimized at B3LYP/6-31G(d) density functional level of theory. All local minima have been identified. For the triflate, imide, methanide, and perchlorate anions, the lithium cation is coordinated to two oxygens and have binding energies of ca 141 kcal/mol at the B3LYP/6-311+G(3df,2p)/B3LYP/6-31G* level of theory. For the hexafluoroarsenate and hexafluorophosphate the lithium cation is coordinated to three oxygens and have binding energies of ca. 136 kcal/mol.
Excess electrons in ice: a density functional theory study.
Bhattacharya, Somesh Kr; Inam, Fakharul; Scandolo, Sandro
2014-02-21
We present a density functional theory study of the localization of excess electrons in the bulk and on the surface of crystalline and amorphous water ice. We analyze the initial stages of electron solvation in crystalline and amorphous ice. In the case of crystalline ice we find that excess electrons favor surface states over bulk states, even when the latter are localized at defect sites. In contrast, in amorphous ice excess electrons find it equally favorable to localize in bulk and in surface states which we attribute to the preexisting precursor states in the disordered structure. In all cases excess electrons are found to occupy the vacuum regions of the molecular network. The electron localization in the bulk of amorphous ice is assisted by its distorted hydrogen bonding network as opposed to the crystalline phase. Although qualitative, our results provide a simple interpretation of the large differences observed in the dynamics and localization of excess electrons in crystalline and amorphous ice films on metals.
Probability Density Function Analysis of Turbulent Condensation Using GPU Hardware
NASA Astrophysics Data System (ADS)
Keedy, Ryan; Riley, James; Aliseda, Alberto
2014-11-01
Growth of liquid droplets by condensation is an important phenomenon in many environmental and industrial applications. In a homogenous, supersaturated environment, condensation will tend to narrow the diameter distribution of a poly-disperse collection of droplets. However, free shear turbulence can broaden the diameter distribution due to intermittency in the mixing and by subjecting droplets to non-Gaussian supersaturation statistics. In order to understand the condensation behavior of water droplets in a turbulent flow, it is necessary to understand the dispersion of the droplets and transported scalars. We describe a hybrid approach for predicting droplet growth and dispersion in a turbulent mixing layer and compare our computational predictions to experimental data. The approach utilizes a finite-volume code to calculate the fluid velocity field and a particle-mesh Monte Carlo method to track the locations and thermodynamics of the large number of stochastic particles throughout the domain required to resolve the Probability Density Function of the water vapor and droplets. The particle tracking algorithm is designed to take advantage of the computational power of a large number of GPU cores, with significant speed-up when compared against a baseline CPU configuration.
Density Functional Theory for Phase-Ordering Transitions
Wu, Jianzhong
2016-03-30
Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic density functional theory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.
Density functional theory study of oxygen migration in molten carbonate
NASA Astrophysics Data System (ADS)
Lei, Xueling; Haines, Kahla; Huang, Kevin; Qin, Changyong
2016-02-01
The process of oxygen migration in alkali molten carbonate salts has been examined using density functional theory method. All geometries were optimized at the B3LYP/6-31G(d) level, while single point energy corrections were performed using MP4 and CCSD(T). At TS, a O-O-O linkage is formed and O-O bond forming and breaking is concerted. A cooperative "cogwheel" mechanism as described in the equation of CO42- + CO32- → CO32- ⋯O ⋯ CO32- → CO32- + CO42- is involved. The energy barrier is calculated to be 103.0, 136.3 and 127.9 kJ/mol through an intra-carbonate pathway in lithium, sodium and potassium carbonate, respectively. The reliability and accuracy of B3LYP/6-31G(d) were confirmed by CCSD(T). The calculated low values of activation energy indicate that the oxygen transfer in molten carbonate salts is fairly easy. In addition, it is found that lithium carbonate is not only a favorable molten carbonate salt for better cathode kinetics, but also it is widely used for reducing the melting point of Li/Na and Li/K eutectic MC mixtures. The current results imply that the process of oxygen reduction in MC modified cathodes is facilitated by the presence of MC, resulting in an enhancement of cell performance at low operating temperatures.
Density functional studies of model cerium oxide nanoparticles.
Loschen, Christoph; Migani, Annapaola; Bromley, Stefan T; Illas, Francesc; Neyman, Konstantin M
2008-10-01
Density functional plane-wave calculations have been performed to investigate a series of ceria nanoparticles (CeO2-x)(n), n
Embedding germanium in graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Xu, Zhuo; Li, Yangping; Tan, Tingting; Liu, Zhengtang
2017-03-01
Based on the density functional theory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 μB is observed in single Ge-chain incorporated 4 × 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices.
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
Xie, Yuanwei; Yu, Chenxia; Li, Tuanjie; Tu, Shujiang; Yao, Changsheng
2015-03-27
An in situ NHC-catalyzed activation strategy to β-functionalize saturated carboxylic acid was developed. This asymmetric formal [3+2] annulation could deliver spirocyclic oxindolo-γ-butyrolactones from saturated carboxylic acid and isatin in good yields with high to excellent enantioselectivities. The easy availability of the starting materials, direct installation of functional units at unreactive carbon atom and the convergent assembly make this protocol attractive in the field of organic synthesis.
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional
NASA Astrophysics Data System (ADS)
Chacón, Enrique; Tarazona, Pedro
2016-06-01
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Symmetry Energy as a Function of Density and Mass
Danielewicz, Pawel; Lee, Jenny
2007-10-26
Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the symmetry energy at subnormal densities produces mass dependence of nuclear symmetry coefficient and, thus, can be constrained by that latter dependence. We deduce values of the mass dependent symmetry coefficients, by using excitation energies to isobaric analog states. The coefficient systematic, for intermediate and high masses, is well described in terms of the symmetry coefficient values of a{sub a}{sup V} = (31.5-33.5) MeV for the volume coefficient and a{sub a}{sup S} = (9-12) MeV for the surface coefficient. These two further correspond to the parameter values describing density dependence of symmetry energy, of L{approx}95 MeV and K{sub sym}{approx}25 MeV.
Density functional study of condensation in capped capillaries
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Savva, N.; Kalliadasis, S.
2015-07-01
We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤slant {{T}\\text{cw}} ) or continuous (at T\\gt {{T}\\text{cw}} ), where {{T}\\text{cw}} is the capillary wetting temperature. At T \\gt {{T}\\text{cw}} , the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.
Antioxidant Properties of Kynurenines: Density Functional Theory Calculations
2016-01-01
Kynurenines, the main products of tryptophan catabolism, possess both prooxidant and anioxidant effects. Having multiple neuroactive properties, kynurenines are implicated in the development of neurological and cognitive disorders, such as Alzheimer's, Parkinson's, and Huntington's diseases. Autoxidation of 3-hydroxykynurenine (3HOK) and its derivatives, 3-hydroxyanthranilic acid (3HAA) and xanthommatin (XAN), leads to the hyperproduction of reactive oxygen species (ROS) which damage cell structures. At the same time, 3HOK and 3HAA have been shown to be powerful ROS scavengers. Their ability to quench free radicals is believed to result from the presence of the aromatic hydroxyl group which is able to easily abstract an electron and H-atom. In this study, the redox properties for kynurenines and several natural and synthetic antioxidants have been calculated at different levels of density functional theory in the gas phase and water solution. Hydroxyl bond dissociation enthalpy (BDE) and ionization potential (IP) for 3HOK and 3HAA appear to be lower than for xanthurenic acid (XAA), several phenolic antioxidants, and ascorbic acid. BDE and IP for the compounds with aromatic hydroxyl group are lower than for their precursors without hydroxyl group. The reaction rate for H donation to *O-atom of phenoxyl radical (Ph-O*) and methyl peroxy radical (Met-OO*) decreases in the following rankings: 3HOK ~ 3HAA > XAAOXO > XAAENOL. The enthalpy absolute value for Met-OO* addition to the aromatic ring of the antioxidant radical increases in the following rankings: 3HAA* < 3HOK* < XAAOXO* < XAAENOL*. Thus, the high free radical scavenging activity of 3HAA and 3HOK can be explained by the easiness of H-atom abstraction and transfer to O-atom of the free radical, rather than by Met-OO* addition to the kynurenine radical. PMID:27861556
Laser Spectroscopy and Density Functional Study on Niobium Dimer Cation
NASA Astrophysics Data System (ADS)
Aydin, Metin; Lombardi, John R.
2009-06-01
Resonant multiphoton fragmentation spectra of niobium dimer cation (Nb2+) have been obtained by utilizing laser vaporization of a Nb metal target. Ions are mass-selected with a time-of-flight mass spectrometer followed by a mass gate, then fragmented with a pulsed dye laser, and the resulting fragment ions are detected with a second time-of-flight reflectron mass spectrometer and multichannel plate. Photon resonances are detected by monitoring ion current as a function of fragmentation laser wavelength. A rich, but complex spectrum of the cation is obtained. The bands display a characteristic multiplet structure that may be interpreted as due to transitions from the ground state X^{4}{Σ}^{-}({Ω}g) to several excited states, X^{4}{Π}({Ω}u) and X^{4}{Σ}(^{-}{Ω}u). The ground state X^{4}{Σ}^{-}({Ω}g) is derived from the electron configuration ({π}{_u})^{4} (1{σ}{_g})^{2}(2{σ}{_g})^{1} ({δ}{_g})^{2}. The two spin-orbit components are split by 145 cm^{-1} due to a strong second-order isoconfigurational spin-orbit interaction with the low-lying ^{2}{Σ}^{+}({Ω}g) state. The vibrational frequencies of the ground sate and the excited state of Nb2+ are identified as well as molecular spin-orbit constants (A{_S}{_O}) in the excited state. The electronic structure of niobium dimer cation was investigated using density functional theory. For the electronic ground state, the predicted spectroscopic properties were in good agreement with experiment. Calculations on excited states reveal congested manifolds of quartet and doublet electronic states in the range 0-30,000 cm^{-1}, reflecting the multitude of possible electronic promotions among the 4d- and 5s-based molecular orbitals. Comparisons are drawn between Nb^{+}{_2} and the prevalent isoelectronic molecules V^{+}{_2}/NbV^{+}/Nb{_2}/V{_2}/NbV. M. Aydin and John R. Lombardi J. Phys. Chem. A. xx XXXX 2009.
Price, A. Martinez, A.
2015-04-28
Using quantum transport simulations, the impact of electron-phonon scattering on the transfer characteristic of a gate-all-around nanowire (GaAs) field effect transistor (NWFET) has been thoroughly investigated. The Non-Equilibrium Green's Function formalism in the effective mass approximation using a decoupled mode decomposition has been deployed. NWFETs of different dimensions have been considered, and scattering mechanisms including acoustic, optical and polar optical phonons have been included. The effective masses were extracted from tight binding simulations. High and low drain bias have been considered. We found substantial source to drain tunnelling current and significant impact of phonon scattering on the performance of the NWFET. At low drain bias, for a 2.2 × 2.2 nm{sup 2} cross-section transistor, scattering caused a 72%, 77%, and 81% decrease in the on-current for a 6 nm, 10 nm, and 20 nm channel length, respectively. This reduction in the current due to scattering is influenced by the increase in the tunnelling current. We include the percentage tunnelling for each valley at low and high drain bias. It was also found that the strong quantisation caused the relative position of the valleys to vary with the cross-section. This had a large effect on the overall tunnelling current. The phonon-limited mobility was also calculated, finding a mobility of 950 cm{sup 2}/V s at an inversion charge density of 10{sup 12 }cm{sup −2} for a 4.2 × 4.2 nm{sup 2} cross-section device.
Stoitsov, M.; Kortelainen, M.; Schunck, N.; Bogner, S. K.; Gebremariam, B.; Duguet, T.
2010-11-15
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
Advanced Density Functional Theory Methods for Materials Science
NASA Astrophysics Data System (ADS)
Demers, Steven
In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description. Zinc Phosphide (Zn3P2) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn3P2 and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems. Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via 'classical' molecular
NASA Astrophysics Data System (ADS)
Zhang, Ping; Wang, Bao-Tian; Zhao, Xian-Geng
2010-10-01
Plutonium dioxide is of high technological importance in nuclear fuel cycle and is particularly crucial in long-term storage of Pu-based radioactive waste. Using first-principles density-functional theory, in this paper we systematically study the structural, electronic, mechanical, thermodynamic properties, and pressure-induced structural transition of PuO2 . To properly describe the strong correlation in Pu5f electrons, the local-density approximation (LDA)+U and the generalized gradient approximation+U theoretical formalisms have been employed. We optimize U parameter in calculating the total energy, lattice parameters, and bulk modulus at nonmagnetic, ferromagnetic, and antiferromagnetic configurations for both ground-state fluorite structure and high-pressure cotunnite structure. Best agreement with experiments is obtained by tuning the effective Hubbard parameter U at around 4 eV within LDA+U approach. After carefully testing the validity of the ground-state calculation, we further investigate the bonding nature, elastic constants, various moduli, Debye temperature, hardness, ideal tensile strength, and phonon dispersion for fluorite PuO2 . Some thermodynamic properties, e.g., Gibbs free energy, volume thermal expansion, and specific heat are also calculated. As for cotunnite phase, besides elastic constants, various moduli, and Debye temperature at 0 GPa, we have further presented our calculated electronic, structural, and magnetic properties for PuO2 under pressure up to 280 GPa. A metallic transition at around 133 GPa and an isostructural transition in pressure range of 75-133 GPa are predicted. Additionally, as an illustration on the valency trend and subsequent effect on the mechanical properties, the calculated results for other actinide metal dioxides ( ThO2 , UO2 , and NpO2 ) are also presented.
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
ERIC Educational Resources Information Center
Herrera, D.; Valencia, A. M.; Pennini, F.; Curilef, S.
2008-01-01
In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 "Phys. Rev." B 1 4584) and recent (Kowalski and Rembielinski 2005 "J. Phys. A: Math. Gen." 38 8247) formulations of coherent states for this problem. We introduce a general…
Zhang, Igor Ying; Xu, Xin; Jung, Yousung
2011-01-01
We develop and validate the XYGJ-OS functional, based on the adiabatic connection formalism and Görling-Levy perturbation theory to second order and using the opposite-spin (OS) ansatz combined with locality of electron correlation. XYGJ-OS with local implementation scales as N3 with an overall accuracy of 1.28 kcal/mol for thermochemistry, bond dissociation energies, reaction barrier heights, and nonbonded interactions, comparable to that of 1.06 kcal/mol for the accurate coupled-cluster based G3 method (scales as N7) and much better than many popular density functional theory methods: B3LYP (4.98), PBE0 (4.36), and PBE (12.10). PMID:22114187
Zhang, Igor Ying; Xu, Xin; Jung, Yousung; Goddard, William A
2011-12-13
We develop and validate the XYGJ-OS functional, based on the adiabatic connection formalism and Görling-Levy perturbation theory to second order and using the opposite-spin (OS) ansatz combined with locality of electron correlation. XYGJ-OS with local implementation scales as N(3) with an overall accuracy of 1.28 kcal/mol for thermochemistry, bond dissociation energies, reaction barrier heights, and nonbonded interactions, comparable to that of 1.06 kcal/mol for the accurate coupled-cluster based G3 method (scales as N(7)) and much better than many popular density functional theory methods: B3LYP (4.98), PBE0 (4.36), and PBE (12.10).
Exohedral functionalization of the icosahedral cluster Si 20H 20: a density functional theory study
NASA Astrophysics Data System (ADS)
Pichierri, Fabio; Kumar, Vijay; Kawazoe, Yoshiyuki
2004-01-01
We report results of density functional theory calculations on three derivatives of the recently predicted hydrogenated silicon fullerene cluster Si 20H 20 using the B3PW91 hybrid exchange-correlation functional with the 6-311+G(d) basis set. The cluster has been exohedrally functionalized by replacing one of its H atoms with -CH 2OH, -COOH, and -CONH 2. The resulting functionalized clusters have nearly the same HOMO-LUMO gaps as that of the perhydrogenated silicon fullerene leading to the possibility of developing new silicon fullerene-based molecules for medico-biological applications. The deprotonated Si 20H 19(COO -) cluster displays a very large permanent dipole moment along with a strongly localized HOMO on its carboxyl group.
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.
Stoitsov, M. V.; Kortelainen, Erno M; Bogner, S. K.; Duguet, T.; Furnstahl, R. J.; Gebremariam, B.; Schunck, N.
2010-01-01
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically-based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction in {chi}^{2} compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Nonparametric Estimation of Distribution and Density Functions with Applications.
1982-05-01
have been used: kurtosis, Hogg’s Q statistic, and percentile ratios. Applications of the discriminants in parametric estimation problem can be found...particularly in the sense of parametric estimation (Ref 108). Reiss proposes minimum distance estimators of unimodal densities. He proves consistency and...in distribution and density estimation, and goodness of fit testing. 129 The next chapter will venture into the realm of parametric estimation using
2010-01-01
The optoelectronic and excitonic properties in a series of linear acenes (naphthalene up to heptacene) are investigated using range-separated methods within time-dependent density functional theory (TDDFT). In these rather simple systems, it is well-known that TDDFT methods using conventional hybrid functionals surprisingly fail in describing the low-lying La and Lb valence states, resulting in large, growing errors for the La state and an incorrect energetic ordering as a function of molecular size. In this work, we demonstrate that the range-separated formalism largely eliminates both of these errors and also provides a consistent description of excitonic properties in these systems. We further demonstrate that reoptimizing the percentage of Hartree−Fock exchange in conventional hybrids to match wave function-based benchmark calculations still yields serious errors, and a full 100% Hartree−Fock range separation is essential for simultaneously describing both of the La and Lb transitions. From an analysis of electron−hole transition density matrices, we finally show that conventional hybrid functionals over-delocalize excitons and underestimate quasiparticle energy gaps in the acene systems. The results of our present study emphasize the importance of both a range-separated and asymptotically correct contribution of exchange in TDDFT for investigating optoelectronic and excitonic properties, even for these simple valence excitations. PMID:21170284
NASA Astrophysics Data System (ADS)
Duguet, T.; Bender, M.; Ebran, J.-P.; Lesinski, T.; Somà, V.
2015-12-01
This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the off-diagonal energy and norm kernels that lie at the heart of the nuclear EDF method. The many-body formalism of interest relies on the concepts of symmetry breaking and restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come.
Tellgren, E I; Teale, A M; Furness, J W; Lange, K K; Ekström, U; Helgaker, T
2014-01-21
We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Density functional theory study of the oligomerization of carboxylic acids.
Di Tommaso, Devis; Watson, Ken L
2014-11-20
We present a density functional theory [M06-2X/6-31+G(d,p)] study of the structures and free energies of formation of oligomers of four carboxylic acids (formic acid, acetic acid, tetrolic acid, and benzoic acid) in water, chloroform, and carbon tetrachloride. Solvation effects were treated using the SMD continuum solvation model. The low-lying energy structures of molecular complexes were located by adopting an efficient search procedure to probe the potential energy surfaces of the oligomers of carboxylic acids (CA)n (n = 2-6). The free energies of the isomers of (CA)n in solution were determined as the sum of the electronic energy, vibrational-rotational-translational gas-phase contribution, and solvation free energy. The assessment of the computational protocol adopted in this study with respect to the dimerization of acetic acid, (AA)2, and formic acid, (FA)2, located new isomers of (AA)2 and (FA)2 and gave dimerization constants in good agreement with the experimental values. The calculation of the self-association of acetic acid, tetrolic acid, and benzoic acid shows the following: (i) Classic carboxylic dimers are the most stable isomer of (CA)2 in both the gas phase and solution. (ii) Trimers of carboxylic acid are stable in apolar aprotic solvents. (iii) Molecular clusters consisting of two interacting classic carboxylic dimers (CA)4,(D+D) are the most stable type of tetramers, but their formation from the self-association of classic carboxylic dimers is highly unfavorable. (iv) For acetic acid and tetrolic acid the reactions (CA)2 + 2CA → (CA)4,(D+D) and (CA)3 + CA → (CA)4,(D+D) are exoergonic, but these aggregation pathways go through unstable clusters that could hinder the formation of tetrameric species. (v) For tetrolic acid the prenucleation species that are more likely to form in solution are dimeric and trimeric structures that have encoded structural motifs resembling the α and β solid forms of tetrolic acid. (vi) Stable tetramers of
Density Functional Theory Calculations of Mass Transport in UO2
Andersson, Anders D.; Dorado, Boris; Uberuaga, Blas P.; Stanek, Christopher R.
2012-06-26
In this talk we present results of density functional theory (DFT) calculations of U, O and fission gas diffusion in UO{sub 2}. These processes all impact nuclear fuel performance. For example, the formation and retention of fission gas bubbles induce fuel swelling, which leads to mechanical interaction with the clad thereby increasing the probability for clad breach. Alternatively, fission gas can be released from the fuel to the plenum, which increases the pressure on the clad walls and decreases the gap thermal conductivity. The evolution of fuel microstructure features is strongly coupled to diffusion of U vacancies. Since both U and fission gas transport rates vary strongly with the O stoichiometry, it is also important to understand O diffusion. In order to better understand bulk Xe behavior in UO{sub 2{+-}x} we first calculate the relevant activation energies using DFT techniques. By analyzing a combination of Xe solution thermodynamics, migration barriers and the interaction of dissolved Xe atoms with U, we demonstrate that Xe diffusion predominantly occurs via a vacancy-mediated mechanism. Since Xe transport is closely related to diffusion of U vacancies, we have also studied the activation energy for this process. In order to explain the low value of 2.4 eV found for U migration from independent damage experiments (not thermal equilibrium) the presence of vacancy clusters must be included in the analysis. Next we investigate species transport on the (111) UO{sub 2} surface, which is motivated by the formation of small voids partially filled with fission gas atoms (bubbles) in UO{sub 2} under irradiation. Surface diffusion could be the rate-limiting step for diffusion of such bubbles, which is an alternative mechanism for mass transport in these materials. As expected, the activation energy for surface diffusion is significantly lower than for bulk transport. These results are further discussed in terms of engineering-scale fission gas release models
Lymphatic vessel density and function in experimental bladder cancer
Saban, Marcia R; Towner, Rheal; Smith, Nataliya; Abbott, Andrew; Neeman, Michal; Davis, Carole A; Simpson, Cindy; Maier, Julie; Mémet, Sylvie; Wu, Xue-Ru; Saban, Ricardo
2007-01-01
Background The lymphatics form a second circulatory system that drains the extracellular fluid and proteins from the tumor microenvironment, and provides an exclusive environment in which immune cells interact and respond to foreign antigen. Both cancer and inflammation are known to induce lymphangiogenesis. However, little is known about bladder lymphatic vessels and their involvement in cancer formation and progression. Methods A double transgenic mouse model was generated by crossing a bladder cancer-induced transgenic, in which SV40 large T antigen was under the control of uroplakin II promoter, with another transgenic mouse harboring a lacZ reporter gene under the control of an NF-κB-responsive promoter (κB-lacZ) exhibiting constitutive activity of β-galactosidase in lymphatic endothelial cells. In this new mouse model (SV40-lacZ), we examined the lymphatic vessel density (LVD) and function (LVF) during bladder cancer progression. LVD was performed in bladder whole mounts and cross-sections by fluorescent immunohistochemistry (IHC) using LYVE-1 antibody. LVF was assessed by real-time in vivo imaging techniques using a contrast agent (biotin-BSA-Gd-DTPA-Cy5.5; Gd-Cy5.5) suitable for both magnetic resonance imaging (MRI) and near infrared fluorescence (NIRF). In addition, IHC of Cy5.5 was used for time-course analysis of co-localization of Gd-Cy5.5 with LYVE-1-positive lymphatics and CD31-positive blood vessels. Results SV40-lacZ mice develop bladder cancer and permitted visualization of lymphatics. A significant increase in LVD was found concomitantly with bladder cancer progression. Double labeling of the bladder cross-sections with LYVE-1 and Ki-67 antibodies indicated cancer-induced lymphangiogenesis. MRI detected mouse bladder cancer, as early as 4 months, and permitted to follow tumor sizes during cancer progression. Using Gd-Cy5.5 as a contrast agent for MRI-guided lymphangiography, we determined a possible reduction of lymphatic flow within the
Understanding trichloroethylene chemisorption to iron surfaces using density functional theory.
Zhang, Nianliu; Luo, Jing; Blowers, Paul; Farrell, James
2008-03-15
This research investigated the thermodynamic favorability and resulting structures for chemical adsorption of trichloroethylene (TCE) to metallic iron using periodic density functional theory (DFT). Three initial TCE positions having the plane defined by HCC atoms parallel to the iron surface resulted in formation of three different chemisorption complexes between carbon atoms in TCE and the iron surface. The Cl-bridge initial configuration with the HCC plane of TCE perpendicular to the iron surface did not result in C-Fe bond formation. The most energetically favorable complex formed at the C-bridge site where the initial configuration had the C=C bond in TCE at a bridge site between adjacent iron atoms. In the C-bridge complex, one C atom formed two a bonds to different Fe atoms, while the second C atom formed a sigma bond with a second Fe atom. Surface complexation atthe C-bridge site resulted in scission of all three C-Cl bonds and also resulted in a shortening of the C==C bond to a distance intermediate between a double and a triple bond. Initial configurations with the C==C bond adsorbed at top or hollow sites on the iron surface resulted in formation of C-Fe a bonds between a single C and two adjacent Fe atoms, and the scission of only two C==Cl bonds. Bond angles and bond lengths indicated that there were no changes in bond order of the C==C bond for top and hollow adsorption. Chemisorption at the C-bridge site had an activation energy of 49 kJ/mol and an early transition state where all three C-CI bonds were activated. The early transition state and the loss of all three Cl atoms upon chemisorption are consistent with most experimental observations that TCE undergoes complete dechlorination in one interaction with the iron surface. The absence of chemisorption and scission of only two C--Cl bonds at the Cl-bridge site is consistent with experimental observations that trace amounts of chloroacetylene may also be produced from reactions of TCE with iron.
Zinc surface complexes on birnessite: A density functional theory study
Kwon, Kideok D.; Refson, Keith; Sposito, Garrison
2009-01-05
Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized Density Functional Theory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.
Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura
2015-08-11
The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.
Density Dependent Functional Forms Drive Compensation in Populations Exposed to Stressors
The interaction between density dependence (DD) and environmental stressors can result in a compensatory or synergistic response in population growth, and population models that use density-independent demographic rates or generic DD functions may be introducing bias into managem...
Error estimates for density-functional theory predictions of surface energy and work function
NASA Astrophysics Data System (ADS)
De Waele, Sam; Lejaeghere, Kurt; Sluydts, Michael; Cottenier, Stefaan
2016-12-01
Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
NASA Astrophysics Data System (ADS)
Ye, Zhencheng; Cai, Jun; Liu, Honglai; Hu, Ying
2005-11-01
Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.
Density functional theory study on oligosilane-functionalized C60 fullerene
NASA Astrophysics Data System (ADS)
Yoshizawa, Saori; Abe, Shigeaki; Mutoh, Mami; Kusaka, Teruo; Nakamura, Mariko; Yoshida, Yasuhiro; Iida, Junichiro; Kawabata, Hiroshi; Tachikawa, Hiroto
2017-01-01
Oligosilane-functionalized C60 fullerenes [namely, C60-(SiH2) n -H, n = 1-4] have been investigated by the density functional theory (DFT) method to elucidate the structures and electronic states of oligosilane-radical added fullerene. The DFT calculation showed that oligosilane radicals bind to the carbon atom of C60 in the on-top site, and a strong Si-C heterojunction is formed. The binding energies of oligosilane radicals to C60 were calculated to be 24.6-28.2 kcal/mol at the CAM-B3LYP/6-311G(d,p) level. The electronic states of oligosilane-functionalized fullerenes C60-(SiH2) n -H are discussed on the basis of theoretical results.
Sundararajan, Mahesh; Sinha, Vivek; Bandyopadhyay, Tusar; Ghosh, Swapan K
2012-05-03
The feasibility of using cucurbituril host molecule as a probable actinyl cation binders candidate is investigated through density functional theory based calculations. Various possible binding sites of the cucurbit[5]uril host molecule to uranyl are analyzed and based on the binding energy evaluations, μ(5)-binding is predicted to be favored. For this coordination, the structure, vibrational spectra, and binding energies are evaluated for the binding of three actinyls in hexa-valent and penta-valent oxidation states with functionalized cucurbiturils. Functionalizing cucurbituril with methyl and cyclohexyl groups increases the binding affinities of actinyls, whereas fluorination decreases the binding affinities as compared to the native host molecule. Surprisingly hydroxylation of the host molecule does not distinguish the oxidation state of the three actinyls.
NASA Astrophysics Data System (ADS)
Robledo, L. M.
2010-06-01
I discuss the inadequacy of the 'projected density' prescription to be used in density-dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that, at least for the restoration of spatial symmetries like rotations, translations or parity, the above prescription yields catastrophic results for the energy that drive the intrinsic wave-function to configurations with infinite deformation, thereby preventing its use both in projection after and before variation.
Font-Ribera, Andreu; Miralda-Escudé, Jordi E-mail: miralda@icc.ub.edu
2012-07-01
We present a study of the effect of High Column Density (HCD) systems on the Lyα forest correlation function on large scales. We study the effect both numerically, by inserting HCD systems on mock spectra for a specific model, and analytically, in the context of two-point correlations and linear theory. We show that the presence of HCDs substantially contributes to the noise of the correlation function measurement, and systematically alters the measured redshift-space correlation function of the Lyα forest, increasing the value of the density bias factor and decreasing the redshift distortion parameter β{sub α} of the Lyα forest. We provide simple formulae for corrections on these derived parameters, as a function of the mean effective optical depth and bias factor of the host halos of the HCDs, and discuss the conditions under which these expressions should be valid. In practice, precise corrections to the measured parameters of the Lyα forest correlation for the HCD effects are more complex than the simple analytical approximations we present, owing to non-linear effects of the damped wings of the HCD systems and the presence of three-point terms. However, we conclude that an accurate correction for these HCD effects can be obtained numerically and calibrated with observations of the HCD-Lyα cross-correlation. We also discuss an analogous formalism to treat and correct for the contaminating effect of metal lines overlapping the Lyα forest spectra.
NASA Astrophysics Data System (ADS)
Hino, S.; Kumano, S.
1999-05-01
We discuss a general formalism for the structure functions which can be investigated in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. To be specific, the formalism can be applied to the proton-deuteron Drell-Yan processes. Because of the spin-1 nature, there are new structure functions which cannot be studied in the proton-proton reactions. Imposing Hermiticity, parity conservation, and time-reversal invariance, we find that 108 structure functions exist in the Drell-Yan processes. However, the number reduces to 22 after integrating the cross section over the virtual-photon transverse momentum Q-->T or after taking the limit QT-->0. There are 11 new structure functions in addition to the 11 in the Drell-Yan processes of spin-1/2 hadrons. The additional structure functions are associated with the tensor structure of the spin-1 hadron, and they could be measured by quadrupole spin asymmetries. For example, the structure functions exist for ``intermediate'' polarization although their contributions vanish in the longitudinal and transverse polarization reactions. We show a number of spin asymmetries for extracting the polarized structure functions. The proton-deuteron reaction may be realized in the RHIC-SPIN project and other future ones, and it could be a new direction of next generation high-energy spin physics.
Reimers, Jeffrey R; Solomon, Gemma C; Gagliardi, Alessio; Bilić, Ante; Hush, Noel S; Frauenheim, Thomas; Di Carlo, Aldo; Pecchia, Alessandro
2007-07-05
A review is presented of the nonequilibrium Green's function (NEGF) method "gDFTB" for evaluating elastic and inelastic conduction through single molecules employing the density functional tight-binding (DFTB) electronic structure method. This focuses on the possible advantages that DFTB implementations of NEGF have over conventional methods based on density functional theory, including not only the ability to treat large irregular metal-molecule junctions with high nonequilibrium thermal distributions but perhaps also the ability to treat dispersive forces, bond breakage, and open-shell systems and to avoid large band lineup errors. New results are presented indicating that DFTB provides a useful depiction of simple gold-thiol interactions. Symmetry is implemented in DFTB, and the advantages it brings in terms of large savings of computational resources with significant increase in numerical stability are described. The power of DFTB is then harnessed to allow the use of gDFTB as a real-time tool to discover the nature of the forces that control inelastic charge transport through molecules and the role of molecular symmetry in determining both elastic and inelastic transport. Future directions for the development of the method are discussed.
Surface energy and work function of fcc and bcc crystals: Density functional study
NASA Astrophysics Data System (ADS)
Wang, Jian; Wang, Shao-Qing
2014-12-01
The surface energies and work functions for six close-packed surfaces of 19 common fcc and bcc metals in the periodic table have been systematically calculated by means of the density functional theory (DFT) method. The accuracy of the results is established in comparison with the experimental and other theoretical values. The variations of work functions with the surface crystallographic orientation display a good regularity. For alkali metals, the work functions follow the sequence Φ(110) > Φ(133) > Φ(311) > Φ(120) > Φ(100) > Φ(111). But for the same crystal structure of bcc transition metals (Nb, Mo, Ta, W), the order is Φ(110) > Φ(133) > Φ(120) > Φ(111) > Φ(311) > Φ(100). The work functions for 3d, 4d and 5d transition fcc metals also display an obvious regularity and ordered as Φ(111) > Φ(100) > Φ(211) > Φ(123) > Φ(310) > Φ(110). Particular attention is paid to the surface energies anisotropy with the same crystal structure metals and the variations present a good regularity, too. Especially, a roughly inverse proportional relationship between the surface energy and work function is found.
Nazarian, Ara; Araiza Arroyo, Francisco J; Rosso, Claudio; Aran, Shima; Snyder, Brian D
2011-09-02
Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure-function properties of the skeleton. Tensile properties of cancellous and cortical bone have been reported previously; however, no relationships describing these properties for rat bone as a function of volumetric bone mineral density (ρ(MIN)), apparent density or bone volume fraction (BV/TV) have been reported in the literature. We have shown that at macro level, compression and torsion properties of rat cortical and cancellous bone can be well described as a function of BV/TV, apparent density or ρ(MIN) using non-destructive micro-computed tomographic imaging and mechanical testing to failure. Therefore, the aim of this study is to derive a relationship expressing the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of normal and pathologic bones. We used bones from normal, ovariectomized and osteomalacic animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial tension to failure. We obtained univariate relationships describing 74-77% of the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity to provide a non-invasive method to assess the tensile behavior of bones affected by pathology and/or treatment options.
Derivation of dynamical density functional theory using the projection operator technique.
Español, Pep; Löwen, Hartmut
2009-12-28
Density functional theory is a particular case of a general theory of conjugate variables that serves as the basis of the projection operator technique. By using this technique we derive a general dynamical version of density functional theory which involves a generalized diffusion tensor. The diffusion tensor is given by a Green-Kubo expression. For Brownian dynamics of dilute colloidal suspensions, the standard dynamical density functional theory is recovered.
Stretched hydrogen molecule from a constrained-search density-functional perspective
Valone, Steven M; Levy, Mel
2009-01-01
Constrained-search density functional theory gives valuable insights into the fundamentals of density functional theory. It provides exact results and bounds on the ground- and excited-state density functionals. An important advantage of the theory is that it gives guidance in the construction of functionals. Here they engage constrained search theory to explore issues associated with the functional behavior of 'stretched bonds' in molecular hydrogen. A constrained search is performed with familiar valence bond wavefunctions ordinarily used to describe molecular hydrogen. The effective, one-electron hamiltonian is computed and compared to the corresponding uncorrelated, Hartree-Fock effective hamiltonian. Analysis of the functional suggests the need to construct different functionals for the same density and to allow a competition among these functions. As a result the correlation energy functional is composed explicitly of energy gaps from the different functionals.
Ruggenthaler, Michael; Penz, Markus; van Leeuwen, Robert
2015-05-27
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.
Stability Analysis and Stabilization of Nonlinear Systems via Locally Defined Density Functions
NASA Astrophysics Data System (ADS)
Masubuchi, Izumi
This paper considers local stability analysis of nonlinear systems with deriving a positively invariant set based on the Rantzer's stability theory by using density functions. We define a notion of locally defined density functions around an equilibrium that give monotonously increasing positive measures near the equilibrium of a nonlinear system. Under certain assumptions, it is shown that some level set of a locally defined density function is a positively invariant set where almost all of the system trajectories converge to the equilibrium. We also mention an SOS (sum-of-squares) formulation for synthesis of a nonlinear gain via locally defined density functions.
Particle number and probability density functional theory and A-representability.
Pan, Xiao-Yin; Sahni, Viraht
2010-04-28
In Hohenberg-Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density rho(r): E = E[rho] with the internal energy component F(HK)[rho] being universal. Knowledge of the functional F(HK)[rho] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E = E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N; N = 1, ..., infinity, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Psi(p) that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent.
Accurate van der Waals coefficients from density functional theory
Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn
2012-01-01
The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765
NASA Astrophysics Data System (ADS)
Somà, V.; Duguet, T.; Barbieri, C.
2011-12-01
An ab initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly magic and semimagic nuclei employing state-of-the-art microscopic nuclear interactions and explicitly treating pairing correlations through the breaking of U(1) symmetry associated with particle number conservation. The present paper introduces the formalism necessary to undertake applications at (self-consistent) second order using two-nucleon interactions in a detailed and self-contained fashion. First applications of such a scheme will be reported soon in a forthcoming publication. Future works will extend the present scheme to include three-nucleon interactions and implement more advanced truncation schemes.
Filtered Density Function for Subgrid Scale Modeling of Turbulent Combustion
2009-02-25
Turbulent Jet Flow, in Knight, D . and Sakell, L ., editors, Recent Advances in DNS and LES, Fluid Mechanics and its Applications, Vol. 54, pp. 155-166...Simulations: Application to a Turbulent Piloted Methane/Air Diffusion Flame (Sandia D ), Combust. Flame, 145( l -2):88-104 (2006). [29] Jones, W. P., Navarro...density form of SFDF, was developed by Jaberi et al. [14,15] and Garrick et al. [16]. The marginal velocity FDF (VFDF) was developed by Gicquel et
NASA Astrophysics Data System (ADS)
Glossman, M. Daniel; Castro, Eduardo A.
1989-05-01
By using an approximate analytical trial density and the consideration of an energy density functional which includes a modified gradient correction, the relationship between the zeroth-order and the first gradient correction is tested and the results compared with those obtained through the use of Hartree-Fock-Roothaan-Clementi densities.
Element orbitals for Kohn-Sham density functional theory
Lin, Lin; Ying, Lexing
2012-05-08
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems.
NASA Astrophysics Data System (ADS)
Solovyeva, Alisa; Pavanello, Michele; Neugebauer, Johannes
2012-05-01
Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a π-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.
NASA Astrophysics Data System (ADS)
König, Carolin; Schlüter, Nicolas; Neugebauer, Johannes
2013-01-01
In subsystem time-dependent density functional theory (TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007), 10.1063/1.2713754] localized excitations are used to calculate delocalized excitations in large chromophore aggregates. We have extended this formalism to allow for the Tamm-Dancoff approximation (TDA). The resulting response equations have a form similar to a perturbative configuration interaction singles (CIS) approach. Thus, the inter-subsystem matrix elements in subsystem TDA can, in contrast to the full subsystem-TDDFT case, directly be interpreted as exciton coupling matrix elements. Here, we present the underlying theory of subsystem TDDFT within the TDA as well as first applications. Since for some classes of pigments, such as linear polyenes and carotenoids, TDA has been reported to perform better than full TDDFT, we also report applications of this formalism to exciton couplings in dimers of such pigments and in mixed bacteriochlorophyll-carotenoid systems. The improved description of the exciton couplings can be traced back to a more balanced description of the involved local excitations.
NASA Astrophysics Data System (ADS)
Oettel, M.; Görig, S.; Härtel, A.; Löwen, H.; Radu, M.; Schilling, T.
2010-11-01
We perform a comparative study of the free energies and the density distributions in hard-sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique [T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 (2009)10.1063/1.3274951] we obtain crystal free energies to a high precision. The free energies from fundamental measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that fundamental measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional [H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 (2006)10.1088/0953-8984/18/37/002] exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.
Density Functional Theory (dft) Simulations of Shocked Liquid Xenon
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.; Magyar, Rudolph J.
2009-12-01
Xenon is not only a technologically important element used in laser technologies and jet propulsion, but it is also one of the most accessible materials in which to study the metal-insulator transition with increasing pressure. Because of its closed shell electronic configuration, xenon is often assumed to be chemically inert, interacting almost entirely through the van der Waals interaction, and at liquid density, is typically modeled well using Leonard-Jones potentials. However, such modeling has a limited range of validity as xenon is known to form compounds under normal conditions and likely exhibits considerably more chemistry at higher densities when hybridization of occupied orbitals becomes significant. We present DFT-MD simulations of shocked liquid xenon with the goal of developing an improved equation of state. The calculated Hugoniot to 2 MPa compares well with available experimental shock data. Sandia is a mul-tiprogram 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.
NASA Astrophysics Data System (ADS)
Lykissa, Iliana; Li, Shu-Yi; Ramzan, Muhammad; Chakraborty, Sudip; Ahuja, Rajeev; Granqvist, Claes G.; Niklasson, Gunnar A.
2014-05-01
Thin films of V2O5 were prepared by sputter deposition onto transparent and electrically conducting substrates and were found to be X-ray amorphous. Their electrochemical density of states was determined by chronopotentiometry and displayed a pronounced low-energy peak followed by an almost featureless contribution at higher energies. These results were compared with density functional theory calculations for amorphous V2O5. Significant similarities were found between measured data and computations; specifically, the experimental low-energy peak corresponds to a split-off part of the conduction band apparent in the computations. Furthermore, the calculations approximately reproduce the experimental band gap observed in optical measurements.
From dilute matter to the equilibrium point in the energy-density-functional theory
NASA Astrophysics Data System (ADS)
Yang, C. J.; Grasso, M.; Lacroix, D.
2016-09-01
Due to the large value of the scattering length in nuclear systems, standard density-functional theories based on effective interactions usually fail to reproduce the nuclear Fermi-liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in effective field theories for systems with large scattering lengths, a new energy-density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.
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.
Afanasjev, A. V.
2015-10-15
The assessment of the global performance of the state-of-the-art covariant energy density functionals and related theoretical uncertainties in the description of ground state observables has recently been performed. Based on these results, the correlations between global description of binding energies and nuclear matter properties of covariant energy density functionals have been studied in this contribution.
Helbig, N.; Fuks, J. I.; Verstraete, M. J.; Marques, M. A. L.; Tokatly, I. V.; Rubio, A.
2011-03-15
We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations obtained by exploiting the mapping of an N-electron system in d dimensions onto a single electron in Nxd dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.
Evaluation of Density Functionals and Basis Sets for Carbohydrates
Technology Transfer Automated Retrieval System (TEKTRAN)
Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of alpha and beta-D-allopyranose, 15 of ...
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.
Peverati, Roberto; Truhlar, Donald G
2014-03-13
Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading--as a long-range goal--to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed-building on earlier work of our group-a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.