Formulation of N‐ and v‐representable density functional theory. IV. Non‐Born–Oppenheimer approach

Local‐scaling transformations are employed in order to formulate a desity functional theory where both electrons and nuclei are treated quantum mechanically. Because of the properties of these transformations, the ensuing version of density functional theory is N‐ and v‐ representable. In particular, we study the effect of these transformations on both densities and generating wave functions, and as a result, a functional for the energy expressed in terms of the electronic and nuclear densities is constructed. Plausible physical approximations for simplifying this electronic‐nuclear functional are considered, and upon variation of the fuctional with respect to the electronic and nuclear densities, a system of coupled Euler–Lagrange equations is obtained.