The gradient-expansion approximation (GEA) and the generalized gradient approximation (GGA) to nonlocal exchange energy in concert with the nonlocal correlation energy functional of Perdew [Phys. Rev. B 33, 8822 (1986)] are analyzed when implemented in a fully self-consistent way in conjunction with the Vosko-Wilk-Nusair parametrization for the local exchange-correlation energy. It is shown that the lowest-order gradient expansion, even with corrected asymptotic behavior in the large-density-gradient limit, is still unsatisfactory in the chemically important region of electron densities where the basic assumption of the GEA (‖∇n‖/2${\mathit{k}}_{\mathit{F}}$n<1) breaks down. In contrast, the GGA expansion behaves better. A shift by a constant additive term of an effective one-body Kohn-Sham potential in concert with the GGA nonlocal functional provides, within the framework of density-functional theory, a way of interpreting excitation energies. The nonlocal functionals significantly improve binding energies. The resulting nonlocal exchange-correlation potential is state independent; thus the present method is convenient from the computational point of view. Applications are presented for a number of atoms and small molecules, including ${\mathrm{O}}_2$, ${\mathrm{Mg}}_2$, ${\mathrm{CH}}_2$, and for a transition-metal cluster, ${\mathrm{Ni}}_4$.

• Received 6 June 1990

DOI:https://doi.org/10.1103/PhysRevB.43.1399