Chapter 30 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 quan-tum chemical methods such as second-order Møller-Plesset pertur-bation 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 lo-cal spin-density approximation and the Perdew-Wang 1991 GGA work. The real-space decomposition shows that the near universal-ity 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 ap proximated 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 sys tems with static correlation. Density functionals in quantum chemistry The main goal of quantum chemistry is the reliable prediction of molecular proper ties [1]. The development of generalized gradient approximations ( G G A ' s) [2-10] has made density functional theory [11-13] a serious competitor to conventional quantum chemistry methods for ground-state properties. The latter methods include Configuration Interaction techniques, Coupled-Cluster methods, and th