Title:Density functional theory for molecules of fractional charge and molecular size consistency

Abstract:This article concerns the development of density functional theory for electron densities integrated to fractional charges and for molecular fragments separated distantly. We start from a model external potential where a molecule with fractional charge (referred to as fractional molecule) can be defined as part of a single non-fractional molecule. A universal functional of densities of fractional charge, F_{FC}, can be derived from this model. The derived functional has the same form as the one from the grand-canonical-ensemble treatment. The Kohn-Sham noninteracting assumption is extendable to densities of fractional charge and the density of a fractional molecule is noninteracting v-representable under a nondegeneracy condition. The noninteracting kinetic energy and the exact exchange energy functionals of such a density are well defined and have the same forms as those for nonfractional systems. A correlation functional is defined that pertains to the fractionally occupied highest occupied molecular orbital only. The exact exchange energy is discontinuous as the number of electrons passing through an odd integer but its sum with the new correlation energy is continuous. For a system made of distantly separated densities rho_x and rho_y, the corresponding universal functional can be accurately approximated as a sum of local parts F_{FC}(rho_x)+F_{FC}(rho_y), and the size consistency of a molecular system can be satisfied using F_{FC} with a modified outer loop in the two-step constrained search formalism and an appropriate constraint due to the localized external potential. The proposed exchange-correlation functional yields the correct result for a well-designed example in literature.