A rigorous modified Thomas–Fermi theory for atomic systems

Recently Parr and Ghosh [Proc. Natl. Acad. Sci. USA 83, 3577 (1986)] proposed a variant of the classical Thomas–Fermi theory of electrons in an atom. They produced a continuous electron density by introducing the constraint that the integral ∫R3 e−2k‖x‖ Δρ(x)dx exists, where k is determined by the nuclear cusp condition. Their results give improved calculations of ground state electron densities and energies. The present paper provides a rigorous mathematical foundation for the work of Parr and Ghosh and converts their results into theorems. Some generalizations are also obtained.