Local-density approximation, hierarchy of equations, functional expansion, and adiabatic connection in current-density-functional theory.

Abstract

Identities and approximations are proposed for the current-density-functional theory. Based on the virial theorem and the scaling properties of the kinetic and exchange energy density functionals, when local and variable-separation assumptions are made, local formulas for these functionals are obtained. One also obtains hierarchies of equations, which combine to give series expansions of the functionals in terms of their functional derivatives with respect to both the density and the paramagnetic current density. In addition, a general formulation is investigated in the form of the constrained search of a coupled Hamiltonian. Subject to the validity of a Taylor series, both the correlation energy density functional and its kinetic component can be expanded into series, each of which, if locality density approximations are assumed, consists of homogeneous functionals of degree (4{minus}{ital n})/3 in density scaling, (4{minus}{ital n})/2 with respect to {bold v}({bold r}), a gauge-invariant variable. {copyright} {ital 1996 The American Physical Society.}