Non-Born–Oppenheimer density functional theory of molecular systems

It is shown that the Hohenberg–Kohn–Levy density functional theory of molecular structure is not restricted by the Born–Oppenheimer approximation. The existence of the corresponding ground-state density functionals for the case of the exact nonadiabatic, nonrelativistic, field-free Hamiltonian of a molecular system, in terms of the one-particle electronic and nuclear densities, is proven and the associated Euler equations are discussed. Extensions to the case of the system in an external electric field and to the bound excited states, are briefly examined. As an example the non-Born–Oppenheimer Hartree–Fock theory of Thomas is discussed from the density functional viewpoint. Possible applications of the theory in the analysis of molecular structure and chemical reactivity are identified.