Single-site approximations in the electronic theory of liquid metals

Abstract

The electronic structure of liquid metals is described by a multiple scattering formalism. Alternate methods based on a single site description of the liquid are developed and compared. The first method, the quasicrystalline approximation of Lax, is used to interpret and extend the work of Ziman and Anderson and McMillan. The second method, discussed here for the first time, extends the coherent potential theory of binary substitutional alloys to the liquid problem. Formally, this method is based on the introduction of a local self-energy operator associated with each site, and the subsequent self-consistent decoupling of the multiple scattering hierarchy. The lowest-order effects of one and two atom clusters are then discussed in connection with the expansion of the total scattering operator. It is shown that in the liquid, as in the alloy, these effects are treated more accurately by the self-consistent methods than by their non-self-consistent counterparts, the quasicrystalline and average t matrix approximations. It is in fact possible to establish a parallel between the self-consistent and coherent potential approximations on the one hand and the quasicrystalline and average t matrix approximations on the other. In the evaluation of second-order corrections to the work of Anderson and McMillan, unitarity requirements suggest an expansion in terms of the reaction matrix rather than the scattering matrix. This procedure treats the damping of electrons more carefully, eliminating spurious contributions. These formal considerations are illustrated by a calculation of the complex band structure and density of states for liquid Cu.