Liquid theory for band structure in a liquid. III. The mean spherical approximation for p bands and the numerical solution of the mean spherical approximation for both s and p bands

Publisher Website
Google Scholar
Abstract
Formally, the problem of calculating the single‐electron energy levels for a liquid requires that one diagonalize a 1023×1023 matrix, but previous work has made it clear that precisely the same information is available from the solution of a simple classical liquid problem. We extend our previous applications of this idea in several ways here: (1) the mean spherical approximation (MSA) for liquids is used to provide an explicit route to the density of states for a band resulting from a basis of p orbitals, (2) the previous MSA solution for s bands and the new MSA solution for p bands are both generalized to allow for nonorthogonality in the basis, and (3) numerical procedures are described for solving the integral equations resulting from these MSA theories. These developments mean that it is now computationally feasible to find the band structure of almost any simple liquid within a tight‐binding model. We illustrate this point by computing the s and p bands expected from a hard‐sphere liquid with a minimal basis of hydrogenic orbitals on each atom.