Density-functional-theory gradient expansion approximation for the screened-Coulomb exchange energy

1984 ◽  
Vol 29 (6) ◽  
pp. 3687-3690 ◽  
Author(s):  
Abdel-Raouf E. Mohammed ◽  
V. Sahni
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Exchange Energy ◽  
Functional Theory ◽  
Gradient Expansion

scholarly journals Ensemble Density Functional Theory Reloaded

2020 ◽  
Author(s):  
Tim Gould ◽  
Gianluca Stefanucci ◽  
Stefano Pittalis
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Low Cost ◽  
Ground States ◽  
Exchange Energy ◽  
Functional Theory ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.<br><br>

scholarly journals Ensemblization of density-functional theory: Insight from the fluctuation-dissipation theorem

2020 ◽  
Author(s):  
Tim Gould ◽  
Gianluca Stefanucci ◽  
Stefano Pittalis
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Low Cost ◽  
Ground States ◽  
Exchange Energy ◽  
Functional Theory ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

1989 ◽  
Vol 67 (3) ◽  
pp. 460-472 ◽  
Author(s):  
Vincenzo Tschinke ◽  
Tom Ziegler
Keyword(s):  
Density Functional Theory ◽  
Correlation Function ◽  
Energy Density ◽  
Density Functional ◽  
Exchange Energy ◽  
Energy Density Functional ◽  
Functional Theory ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Fermi Hole

We have compared, for atomic systems, the spherically averaged Fermi-hole correlation function [Formula: see text] in the Hartree–Fock theory with the corresponding function [Formula: see text] employed in local density functional theory. It is shown that, in contrast to [Formula: see text], the function [Formula: see text] behaves qualitatively incorrectly at positions r1 of the reference electron far from the nucleus. Furthermore, we have shown that the qualitatively incorrect behaviour of [Formula: see text] can be remedied by an approximate expansion of [Formula: see text] in powers of s, where s is the inter-electronic distance. However, such an expansion must be conducted in two regions due to the discontinuity of [Formula: see text] as a function of s at the atomic nucleus. Based on the two-region expansion of [Formula: see text] we have developed an alternative approximate density functional expansion [Formula: see text] for the spherically averaged Fermi-hole correlation function. The corresponding exchange energy density functional yields values for the exchange energies of atoms in good agreement with Hartree–Fock results. Keywords: atomic exchange energy, density functional theory, Fermi hole.

scholarly journals TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY

2008 ◽  
Vol 22 (14) ◽  
pp. 2225-2239
Author(s):  
TAMÁS GÁL
Keyword(s):  
Density Functional Theory ◽  
Ground State ◽  
Density Functional ◽  
Common Ground ◽  
Particle Density ◽  
Exchange Energy ◽  
Density Functionals ◽  
Simple Derivation ◽  
Functional Theory ◽  
Hartree Fock

Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.

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