Adiabatic-connection approach to Kohn-Sham theory

The Kohn-Sham method for energy calculation in inhomogeneous electron systems relies on a comparison of functionals describing interacting and noninteracting electrons. An alternate approach draws the link between interacting and noninteracting systems explicitly, via an adiabatic connection of eigenstates. This adiabatic-connection scheme eliminates the "Fermi-statistics" problem and provides partial answers to some other conceptual difficulties that arise when the Kohn-Sham method is applied in practice. In addition, dimensional arguments can be given that justify the use of local-density approximations for exchange and correlation within the adiabatic connection framework. These arguments do not involve a "slowly varying" assumption and are valid for any system, however inhomogeneous.