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

We construct a generalized gradient approximation ~GGA! for the density nxc(r,r1u) at position r1u of the exchange-correlation hole surrounding an electron at r, or more precisely for its system and spherical average ^nxc(u)&5(4p) *dV u N *dr n(r)nxc(r,r1u). Starting from the second-order density gradient expansion, which involves the local spin densities n↑(r),n↓(r) and their gradients 1n↑(r),1n↓(r), we cut off the spurious large-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’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. @S0163-1829~96!04847-3#