Exchange-correlation potential in terms of the idempotent Dirac density matrix of DFT

Abstract

A formal proof has recently been proposed [I.A. Howard, N.H. March, Chem. Phys. Lett. 402 (2005) 1.] to show that the exchange-correlation potential V xc( r) of density functional theory (DFT) is, in principle, determined by the idempotent Dirac density matrix γ( r, r′) generated by the one-body potential V( r) = V ext( r) + V Hartree( r) + V xc( r). Here we turn this ‘existence’ theorem into a concrete result by expressing the Laplacian ∇ 2 V xc( r) solely in terms of γ( r, r′), which, although idempotent and therefore not many-electron in character, has the exact ground state density ρ( r) on its diagonal γ( r, r). As a specific illustration, we calculate ρ( r) by diffusion QMC and hence γ( r, r′) for the Be atom ground-state. V xc( r) is thereby obtained with satisfactory accuracy.