Nonlocal Wigner-like correlation-energy density functional through coordinate scaling

Abstract

A nonlocal Wigner-like correlation-energy functional for electronic systems is presented. The functional is constructed to satisfy certain uniform, as well as nonuniform, coordinate-scaling requirements and is the simplest nonlocal form to do this. Our numerical results appear to compare

Correlation energy density from ab initio first- and second-order density matrices: A benchmark for approximate functionals

“…⑀ c ͑r͒ as well as its kinetic t c ͑r͒ and potential w c ͑r͒ components are obtained for the He atom and H 2 molecule ͑in the latter case for both equilibrium internuclear distance and near-dissociation limit͒. The corresponding functions e c ͑r͒ are compared with the gradient-dependent models e c mod (r) of Perdew and Wang ͑PW͒, 5, 6 Lee, Yang, and Parr ͑LYP͒, 7 Wilson and Levy, 8 and also with some local models. 9,10 To fur-ther examine the observed trends, the form of e c mod (r) is investigated for the Be 2 and F 2 molecules and E c values are calculated and discussed for a number of atomic and molecular systems.…”

“…8 Its parameters were fitted to reproduce the E c value for He and the scaling relations for the E c functional 35 for the eight above-mentioned atomic systems.…”

Exchange-correlation energy functional and virial theorem in the extended constrained-search theory

“…We know that such an approach had already been used in the development of the density-gradient expansion for the exchangecorrelation energy functional. [27][28][29] At the end of this section, we shall give a comment on the meaning of the above sum rule. Even though the approximate functional is satisfied with some of sum rules, it would not necessarily give the quantitatively better results than the functional which is not satisfied with sum rules.…”

Ionization potentials of atoms calculated with a nonlocal exchange and a local correlation functional

“…These results, and those obtained in [26] using GGA exchange functionals combined with various recent correlation functionals, are compared in Tables VII-IX with the accurate results for the total and correlation energies given in 1271 (where Davidson and co-workers derived nonrelativistic correlation energies of atomic ions, by combining experimental data and ab initio calculations). In addition to our results, the entries in these tables correspond to Perdew's exchange-correlation functional (GGA91) [ 161, to Becke's exchange functional plus the Lee-Yang-Parr correlation energy (BLYP) (which is a development of the Colle-Salvetti Correlation functional [36]), and to Becke's exchange plus the correlation functional of Wilson and Levy (BWL) [37]. As a general observation, we note that, after inclusion of correlation, the error in the total energy is roughly the sum of A E , ( A E , = E, D" -E F t ) and AE, of Tables IV-VI.…”