Thomas-Fermi theory revisited

An exact Thomas-Fermi theory requires the existence of a Fréchet functional derivative of the Hohenberg-Kohn universal functional. Although, as recently shown, such a functional derivative cannot exist in quantum theory for more than two electrons, functional derivatives of the more general type defined by Gâteaux do exist. When the theory is reformulated in terms of Gâteaux derivatives, for noninteracting electrons, it is equivalent to the Schrödinger theory. For interacting electrons, it defines a generalized orbital-functional theory. The reformulated theory incorporates Fermi-Dirac statistics for electrons and deals correctly with atomic shell structure. © 2002 Wiley Periodicals, Inc. Int. J. Quantum Chem.