Orbital-free spherical density functional theory

Abstract

AbstractRecently, it has been proved that a set of spherically symmetric densities uniquely determines the Coulomb external potential. Utilizing this theorem, a previous method is extended to construct an orbital-free density functional theory. Auxilary spherical non-interacting systems and Kohn–Sham-like equations are constructed. A set of spherical generating functions are defined. These functions have two extra variables and are reduced to the set of spherically symmetric densities if the extra variables are equal to zero. Euler equations are rewritten as Schrödinger-like equations for the square root of the spherically symmetric generating functions. Generalized Pauli potentials are defined, and it is shown that these potentials can be calculated in the knowledge of the generating functions. The Euler equations can be solved with these Pauli potentials.