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

Abstract

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.