Potential functionals versus density functionals

TL;DR

This paper explores potential functional approximations as an alternative to density functionals, analyzing their properties, limits, and response functions, highlighting both advantages and limitations in semiclassical contexts.

Contribution

It defines the dual potential functional to the Lieb density functional, examines its properties, and compares semiclassical potential functionals to density functionals, especially in large particle number limits.

Findings

Potential functionals have no ambiguity in energy density.

Semiclassical potential functionals approach classical limits.

Response functions can violate symmetry conditions.

Abstract

Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between Thomas-Fermi theory as a density functional and as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially in their approach to the large particle number and classical continuum limits. The lack of ambiguity in the energy density of potential functional approximations is demonstrated. The density-density response function of the semiclassical approximation is calculated and shown to violate a key symmetry condition.