Exchange-correlation potentials in density-functional and spin-density-functional theory

Abstract

Exact expressions for the exchange-correlation potential Wxc(r) in density- and spin-density-functional theories are derived under a very general situation where Wxc(r) is expressed in terms of two- and three-particle correlation functions. Within the random-phase approximation it is shown that there exist nonlocal contributions to Wxc(r) which cannot be reproduced in any local-density type of approximations (LDA). In the nonmagnetic case, nonlocal contributions are found to be present only in Vxc(q=0), which leads to the famous band-gap problem. In the magnetic case it is found that nonlocality is present in all components of Wxc(r) in general, indicating that the LDA is in general an inadequate approximation for exchange-correlation potentials in magnetic systems. An alternative approximation for Wxc(r) is proposed which also includes nonlocality in an approximate way.