Long-range van der Waals interactions in density functional theory

The early difficulties in accounting for long-range van der Waals interactions in the framework of density functional theory (DFT) have been overcome to a certain extent in recent works by several groups, and those interactions can be computed numerically. In this paper a derivation of the analytical form of the attractive van der Waals interaction between two neutral atoms with polarizabilities alpha(1) and alpha(2) at large distance R, namely E-int = -C-6 alpha(1)alpha(2)/R-6 is performed within the context of DFT. Use is made of the properties of the Coulomb correlation hole, and it is shown that nonlocal Coulomb correlations are responsible for long-range dispersion interactions.