Nonlocal Energy Density Functionals: Models Plus Some Exact General Results

Holas and March (Phys Rev 1995 A51, 2040) gave a formally exact expression for the force – ∂V_xc(r)/∂r associated with the exchange-correlation potential V_xc(r) of density functional theory. This forged a precise link between first- and second-order density matrices and V_xc(r). Here models are presented in which these low-order matrices can be related to the ground-state electron density. This allows nonlocal 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.