Liquid theory for band structure in a liquid

Abstract

When electron correlation effects are small, the set of energy levels available to both the localized and the delocalized individual electrons (the band structure) is the starting place for determining the macroscopic electronic properties of a substance. Calculating the band structure in any disordered medium, however, requires facing the problem that there will always be a distribution of geometries in the material—at least the local parts of which must be accounted for in order to get any reasonable results. In a liquid this requirement means that the liquid structure plays an important role. We show in this paper that the band structure in a liquid is completely and rigorously determined by the equilibrium behavior of an ‘‘effective’’ liquid with artificial internal degrees of freedom. This mapping implies that standard liquid theory methods (which automatically build in the correct liquid structure) can be used to find the electronic energy levels. As illustration, we use the mean-spherical approximation (MSA) to derive a simple expression for the density of states that is accurate at all but the lowest densities. We further show that this particular MSA theory is identical to an apparently different theory derived recently by Logan and Winn—which makes both theories identical to the so–called EMA theory of Roth. An even more general correspondence exists between our exact formalism and the exact formalism of Logan and Winn, though any given approximation might be more natural in one approach then in another.