Local behavior of the kinetic energy in density functional theory

Abstract

The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsacker term t, = (V p)'/S p as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.

Energy Density Functional Theory of Many-Electron Systems

“…~Iarch and Bader (1980), Gazquez and Ludeiia (1981), ~Iarch and Pucci (1981a), J\Iarch (1982b) and Beznosjuk and Kryachko (1984) in completely independent ways (for a review, see also Ghosh and Deb, 1982;Parr, 1983Parr, , 1984Chattaraj and Deb, 1984;Kryachko, 1984band Ludeiia, 1984a). (2A-22) we see that the real kinetic energy density depends on the 1matrix in the following form is a diYergence term whose contribution to the total kinetic energy vanishes upon integration (Bader and Preston, 1969;Tal and Bader, 1978; see also Zorita et al, 1985). (2A-22) we see that the real kinetic energy density depends on the 1matrix in the following form is a diYergence term whose contribution to the total kinetic energy vanishes upon integration (Bader and Preston, 1969;Tal and Bader, 1978; see also Zorita et al, 1985).…”

Density functional calculation of the electronegativity and other related properties of atoms and ions of the principal groups of the periodic table

“…This functional for the kinetic energy density of the valence electrons of a free atom or ion has been proposed and justified by several authors [26][27][28]. With the approximations of (20)- (22) the calculation of the ground state energy and ground state electron density is easily performed.…”

“…Assuming atom Y more electronegative than atom X, we first write the heat of formation of a diatomic X Y molecule as (28) where (2 is the number of electrons transferred from X to Y and R is the internuclear separation. The first two terms in (28) include the change in the energy of the atoms when their configuration is changed, the third term is the Madelung energy of the molecule and the fourth term is the covalent contribution to the XY bond. Minimization with respect to Q leads to…”