Density functionals from LDA to GGA

Abstract

For ab initio calculations in quantum chemistry, materials science, biochemistry, and nanoelectronics, the Kohn–Sham density functional theory is a widely used method to solve the ground-state many-electron problem. Density functional theory requires approximations for the exchange–correlation (xc) energy as a functional of the density. The simplest approximations are the local density approximation (LDA) and the local spin density (LSD) approximation, which employ the xc energy of the (respectively, spin-unpolarized and spin-polarized) uniform electron gas as an input. Generalized gradient approximations (GGA's) go beyond the LDA and LSD descriptions by including density gradients, and improve calculated results significantly. Some GGA success stories are summarized.