How to tell when a model Kohn–Sham potential is not a functional derivative

Abstract

A model exchange-correlation potential constructed with Kohn-Sham orbitals should be a functional derivative of some density functional. Several necessary conditions for a functional derivative are discussed including: (i) minimization of the total-energy expression by the ground-state solution of the Kohn-Sham equations, (ii) path independence of the van Leeuwen-Baerends line integral, and (iii) net zero force and zero torque on the density. A number of existing model potentials are checked for these properties and it is found that most of the potentials tested are not functional derivatives. Physical properties obtained from potentials that have no parent functionals are ambiguous and, therefore, should be interpreted with caution.