Wannier Representation of Energy in Metals

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Abstract
A method is given for representing the energy of a metal as sums of one-, two-, three-, and four-body atomic interactions in the Hartree-Fock approximation by the use of Wannier functions. This method puts the energy in a form well suited for cohesive and structural studies. The differential equation that must be satisfied by the Wannier functions for the Hartree-Fock approximation is shown to be a generalization of that previously obtained by Koster, and explicit relations are obtained among localization of the Wannier functions, bandwidth, and effective mass. For full bands, it is shown that only pairwise forces exist, so that three- and four-body forces arise only from interactions involving partially full bands. An extension of Wannier-Bloch theory is outlined for elastically strained systems, showing that the quantum theory of perfect crystals can be adapted to strained crystals by a proper choice of coordinates.