Potential functionals: dual to density functionals and solution to the v-representability problem.

A functional of external potentials and its variational principle for the ground-state energy is constructed. This potential functional formulation is dual to the density functional approach and provides a solution to the v-representability problem in the original Hohenberg-Kohn theory. A second potential functional for Kohn-Sham noninteracting systems establishes the foundation for the optimized effective potential approach and results in efficient approaches for ensemble Kohn-Sham calculations.