Adiabatic Connection and the Kohn-Sham Variety of Potential-Functional Theory

In potential-functional theory the total electronic energy is expressed as a functional of the external potential. We discuss how approximations, T-s(app)[V] of the noninteracting kinetic energy functional can be exploited for interacting systems. Two possibilities are discussed: (a) Via an adiabatic connection formula, T-s(app)[V-0] can be used directly with the external potential V-0 of the interacting system, and (b) by employing the variational principle of density functional theory, the kinetic energy functional T-s(app)[V-s] is evaluated at the Kohn-Sham potential V-s, which, in turn, is determined by an iterative procedure. Advantages and disadvantages of the two approaches are discussed.