Why the Generalized Gradient Approximation Works and How to Go Beyond It

Ž . The local spin density LSD approximation, while of only moderate accuracy, has proven extremely reliable over three decades of use. We argue that any gradient-corrected functional should preserve the correct features of LSD, even if the system under study Ž . contains no regions of small density gradient. The Perdew]Wang 1991 PW91 functional Ž . respects this condition, while, e.g., the Lee]Yang]Parr LYP correlation functional violates it. We extend this idea to the next generation of density functionals, those which Ž . incorporate exact exchange via the optimized effective potential OEP , with a model in which the correlation hole is constructed from the exact exchange hole. The resulting exchange-correlation hole is deeper and less diffuse than the exact exchange hole. We denote such a functional as ‘‘locally correlated Hartree]Fock’’ and list a variety of conditions such a functional should satisfy. We demonstrate the promise of this approach with a crude simple model. Q 1997 John Wiley & Sons, Inc. Introduction and Summary of Conclusions Ž . or many years, the local spin density LSD F w x approximation 1 has been the mainstay of electronic structure calculations in solid-state * To whom correspondence should be addressed. Permanent address after July 1, 1996: Department of Chemistry, Rutgers University, Camden, NJ 08102. w x physics 2]4 . This approximation may be written LSD 3 unif w x Ž . Ž . Ž . E n , n s d r n r e n r , n r , H xc ­ x xc ­ x