Current Density Functional Theory

Abstract

The nonlocality of the exchange-correlation (xc) potential, i.e., the fact that the xc potential at a certain position depends on the global distribution of the particle density in space, is the curse of density functional theory. It is mainly because of this fact that, even after years of intensive studies, the exact form of the xc potential as a functional of the density remains unknown. Nevertheless, it is true that many accurate and useful results can be obtained from the use of an approximation – the local density approximation (LDA) – which ignores the problem altogether. Apparently, the nonlocal dependence of the Kohn-Sham orbitals on the density is sufficient in many cases to give the right quantum chemistry. Furthermore, a number of successful strategies have been designed to go beyond the LDA when needed: in one such approach (the generalized gradient approximation – GGA) one goes beyond the LDA by including the dependence of the xc potential on the gradient of the local density; in another one expresses the xc potential as a functional of the Kohn-Sham orbitals, and, finally, in the “meta-GGA” approach one fights the problem by including additional local variables, such as the kinetic energy density.