A naive look on the Hohenberg-Kohn theorem

Abstract

A generalised Hohenberg-Kohn theorem is described in terms of the sign of the second-order energy variation. Independently, it is also corroborated within the perturbation theoretical framework. An alternative formulation of the Hohenberg-Kohn theorem, based on the relationships involving the matrix representations of density functions and the Hamiltonian operator variations, is shown to extend the validity of the theorem to the excited states of the Hamiltonian operators possessing non-degenerate spectra. Finally, a connection with Brillouin's theorem when energy variation becomes stationary is also outlined.