M. Ernzerhof et Jp. Perdew, GENERALIZED GRADIENT APPROXIMATION TO THE ANGLE-AVERAGED AND SYSTEM-AVERAGED EXCHANGE HOLE, The Journal of chemical physics, 109(9), 1998, pp. 3313-3320
A simple analytic model is proposed for the angle- and system-averaged
exchange hole of a many-electron system. The model hole depends on th
e local density and density gradient. It recovers a nonoscillatory loc
al-spin density (LSD) approximation to the exchange hole for a vanishi
ng density gradient. The model hole reproduces the exchange energy den
sity of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approxim
ation (GGA) for;exchange, and facilitates a detailed understanding of
the PBE GGA. The hole model is applied to atoms and molecules, and a c
omparison is made to exact and LSD angle- and system-averaged exchange
holes. We fmd that the GGA hole model significantly improves upon the
LSD model. Furthermore, the GGA hole model accurately describes the c
hange in the exchange hole upon the formation of single bonds, but is
less accurate for the formation of multiple bonds, where it misses the
appearance pf a long-range tail. (C) 1998 American Institute of Physi
cs.