Generalized gradient approximation for the exchange-correlation hole of a many-electron system

We construct a generalized gradient approximation (GGA) for the density {ital n}{sub xc}({ital r},{ital r}+{ital u}) at position {ital r}+{ital u} of the exchange-correlation hole surrounding an electron at {ital r}, or more precisely for its system and spherical average {l_angle}{ital n}{sub xc}({ital u}){r_angle}=(4{pi}){sup {minus}1}{integral}{ital d}{Omega}{sub {ital u}}{ital N}{sup {minus}1}{integral}{ital d}{sup 3}{ital r} {ital n}({ital r}){ital n}{sub xc}({ital r},{ital r}+{ital u}). Starting from the second-order density gradient expansion, which involves the local spin densities {ital n}{sub {up_arrow}}({ital r}),{ital n}{sub {down_arrow}}({ital r}) and their gradients {nabla}{ital n}{sub {up_arrow}}({ital r}),{nabla}{ital n}{sub {down_arrow}}({ital r}), we cut off the spurious large-{ital u} contributions to restore those exact conditions on the hole that the local spin density (LSD) approximation respects. Our GGA hole recovers the Perdew-Wang 1991 and Perdew-Burke-Ernzerhof GGA{close_quote}s for the exchange-correlation energy, which therefore respect the same powerful hole constraints as LSD. When applied to real systems, our hole model provides a more detailed test of these energy functionals, and also predicts the observable electron-electron structure factor. {copyright} {ital 1996 The American Physical Society.}