Communication: Constrained search formulation of the ground state energy as a functional of an idempotent one-matrix

Despite the fact that idempotent one-particle reduced density matrices are pervasive in quantum chemistry, the understanding of a general energy functional of such idempotent density matrices for the ground state energy has been lacking. By a constrained search, we show the structure of the general functional, illuminating the contributions from various terms. For the examples of the "best idempotent density matrix" and Kohn-Sham idempotent density matrices, we contrast the functional forms and suggest how the best idempotent density matrix approach may be a good starting point for further development.