Properties of the exact universal functional in multicomponent densityfunctional theory

摘要

Multicomponent density functional theory has been developed to treat systems with more than onetype of quantum particle, such as electrons and nuclei, in an external potential. The existence of theexact universal multicomponent density functional in terms of the one-particle densities for eachtype of quantum particle has been proven. In the present paper, a number of important mathematicalproperties of the exact universal multicomponent density functional are derived. The expressionrelating the electron-proton pair density to the one-particle densities leads to an inequality for thepotential energy component of the electron-proton correlation functional under well-definedconditions. General inequalities for the kinetic energy correlation functionals and the totalelectron-proton correlation functional are also derived. The coordinate scaling analysis leads tomathematical inequalities describing the effect of scaled densities on the kinetic, potential, and totalenergy functionals. The adiabatic connection formula defines the exact electron-proton functional interms of an adiabatic scaling parameter that smoothly connects the noninteracting system with thefully interacting system. The virial expression provides the relation between the exact kinetic andpotential energy functionals for the ground state densities of multicomponent systems. Thesemathematical relationships provide insight into the fundamental properties of the exact universalmulticomponent density functional and serve as a guide for the development of approximateelectron-proton density functionals.