Fractional occupation numbers in density-functional theory

Density-functional theory for ensembles defined by fixed weights and fractional occupation numbers is derived using a Lagrange-multiplier version of the constrained-search procedure. This is related to an adiabatic connection between a generalized Kohn-Sham ensemble for noninteracting electrons and a minimum-energy ensemble including the electronic Coulomb interaction. Using this formalism, it is shown that discontinuous changes of the chemical potential of a finite electronic system result from constraints on density variations imposed by Fermi statistics. Such discontinuities do not exclude the possibility of defining an exchange-correlation energy functional that is free of derivative discontinuities for unconstrained density variations.