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[v0] can be used directly with the external potential v0 of the interacting system, and (b) by employing the variational principle of density functional theory, the kinetic energy functional T s app[vs] is evaluated at the Kohn-Sham potential vs, which, in turn, is determined by an iterative procedure. Advantages and disadvantages of the two approaches are discussed.