Non-local energy density functionals: models plus some exact general results

Holas and March (Phys. Rev. A51, 2040, 1995) gave a formally exact expression for the force - δVxc(r-tilde)/δr-tilde associated with the exchange-correlation potential Vxc(r-tilde) of density functional theory. This forged a precise link between first- and second-order density matrices and Vxc(r-tilde). Here models are presented in which these low-order matrices can be related to the ground-state electron density. This allows non-local energy density functionals to be constructed within the framework of such models. Finally, results emerging from these models have led to the derivation of some exact 'nuclear cusp' relations for exchange and correlation energy densities in molecules, clusters and condensed phases. (author)