Method of local-scaling transformations and density-functional theory in quantum chemistry

The method of local-scaling transformations is developed with a view to applications of the nonrelativistic quantum mechanical variational principle in quantum chemistry. Some properties of local-scaling transformations are studied. The method presented links local-scaling transformations and one-electron densities via the ordinary differential equation that provides a proof of the theorem on the existence of the energy density functional within any given orbit and its universality in a sense of the general theory of ordinary differential equations, and allows the construction of this functional explicitly.