PHYSICAL INTERPRETATION OF DENSITY-FUNCTIONAL THEORY AND OF ITS REPRESENTATION OF THE HARTREE-FOCK AND HARTREE THEORIES

In this paper we provide a rigorous physical interpretation of the Koh n-Sham (KS) density-functional theory electron-interaction energy func tional E(ee)(KS)[rho] and its functional derivative upsilon(ee)(KS)(r) = delta E(ee)(KS)[rho]/delta rho(r) based on the original ideas of Ha rbola and Sahni, and of their extension by Holas and March, The functi onal, and hence the derivative, incorporate electron correlations due to the Pauli exclusion principle and Coulomb repulsion as well as thos e of the correlation contribution to the kinetic energy. The interpret ation is in terms of a field F(r), which is the sum of two fields whos e sourer distributions are expectations of Hermitian operators. The fi rst of these fields epsilon(ee)(r) accounts for Pauli and Coulomb corr elations. its sourer is the pair-correlation density and it is determi ned by Coulomb's law. The second Z(tc) (r) accounts for the correlatio n-kinetic contribution, and its source is the difference between the k inetic-energy-density tensor for the noninteracting and interacting sy stems. The corresponding field is the derivative of this tenser. The f unctional derivative upsilon(ee)(KS)(r)(r) is the work done to move an electron in the field F(r). Since the field F(r) is conservative, thi s work done is path independent. The quantum-mechanical electron-inter action energy E(ee)[rho] and correlation-kinetic energy T-c[rho] compo nents of E(ee)(KS)[rho] can also be expressed in virial form in terms of the respective fields epsilon(ee)(r) and Z(tc)(r), which give rise to them. A similar rigorous physical interpretation of the Kohn-Sham t heory representation of the Hartree-Fock and Hartree approximations is also given. If in these representations. the correlation kinetic ener gy is neglected the equations reduce to the corresponding approximatio ns of the work formalism of electronic structure. Finally, it is argue d on physical grounds that the interpretation provided for the ground state is equally valid for excited states.