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 y(r, r') generated by the one-body potential V(r) = V-max(r) + V-Hartree(r) + V-xc(r). Here we turn this 'existence' theorem into a concrete result by expressing the Laplacian del V-2(xc)(r) solely in terms of y(r, r'), which, although idempotent and therefore not many-electron in character, has the exact ground state density p(r) on its diagonal y(r, r). As a specific illustration, we calculate p(r) by diffusion QMC and hence y(r, r') for the Be atom ground-state. V-xc(r) is thereby obtained with satisfactory accuracy. (c) 2006 Elsevier B.V. All rights reserved.