First-order gradient correction for the exchange-energy density functional for atoms

1992 ◽  
Vol 84 (3) ◽  
pp. 237-243 ◽  
Author(s):  
Zhongxiang Zhou ◽  
P. K. Chattaraj ◽  
Robert G. Parr ◽  
Chengteh Lee
Keyword(s):  
Energy Density ◽  
Density Functional ◽  
Exchange Energy ◽  
Energy Density Functional ◽  
First Order ◽  
Gradient Correction

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.

The Exchange-Energy Density Functional Based on the Modified Becke-Roussel Model

2010 ◽  
Vol 6 (3) ◽  
pp. 647-661 ◽  
Author(s):  
Hideaki Takahashi ◽  
Ryohei Kishi ◽  
Masayoshi Nakano
Keyword(s):  
Energy Density ◽  
Density Functional ◽  
Exchange Energy ◽  
Energy Density Functional
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