Local and Gradient-Corrected Density Functionals

The generalized gradient approximation (GGA) corrects many of the shortcomings of the local spin-density (LSD) approximation. The accuracy of GGA for ground-state properties of molecules is comparable to or better than the accuracy of conventional quantum chemical methods such as second-order Møller-Plesset perturbation theory. By studying various decompositions of the exchange-correlation energy Exc, we show that the real-space decomposition of Exc facilitates the most detailed understanding of how the local spin-density approximation and the Perdew-Wang 1991 GGA work. The real-space decomposition shows that the near universality of the on-top value for the exchange-correlation hole connects the homogeneous electron gas to inhomogeneous systems such as atoms and molecules. The coupling-constant decomposition shows that the exchange-correlation energy at full coupling strength Exc,λ=1 is approximated more accurately by local and semi-local functionals than is the coupling-constant average Exc. We use this insight both to critique popular hybrid functionals and to extract accurate energies from exact electron densities by using functionals for the exchange-correlation energy at full coupling strength. Finally, we show how a reinterpreted spin density functional theory can be applied to systems with static correlation.