Why the generalized gradient approximation works and how to go beyond it

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 contains no regions of small density gradient. The Perdew-Wang 1991 (PW91) functional 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 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. © 1997 John Wiley & Sons, Inc.