QUANTUM-MECHANICAL INTERPRETATION OF THE LOCAL MANY-BODY POTENTIAL OF DENSITY-FUNCTIONAL THEORY

The local many-body potential of density-functional theory is thus far understood in its mathematical context as the functional derivative of the exchange-correlation energy functional of the density. In recent work we have attempted to provide a physical interpretation for this potential. We interpret it as the work required to move an electron against the electric field of its Fermi-Coulomb hole charge distribution. Implicit in this interpretation is that the potential is path-independent. For symmetric systems this is rigorously the case. For systems where this may not be the case, the potential may be derived from an effective charge distribution given by the divergence of the field, thus ensuring its path independence. Also implicit as a consequence of the total Coulomb hole charge being zero is that the asymptotic structure of the potential is entirely due to the Fermi hole charge distribution, and thus known precisely. The potential lies explicitly within the rubric of density-functional theory in that within the exchange-only approximation it satisfies the exchange energy virial theorem sum rule and all scaling properties that the exact exchange potential must satisfy. The potential does not satisfy the virial theorem sum rule for the correlation energy, and consequently a term proportional to the difference between the interacting and noninteracting system kinetic energies must be added for the sum rule to be satisfied exactly. The formalism differs from density-functional theory in that it is not derived from the variational principle for the energy, thus obviating the requirement of determining functional derivatives, as well as allowing for the study of excited states. The interpretation also leads to insights into the exact Slater exchange potential, and other approximation schemes such as the X-alpha-method, and local density and gradient expansion approximations. The results of application to few-electron atomic and many-electron metallic surface inhomogeneous electronic systems are remarkably accurate when compared with other theoretical calculations and experiment.