Simulation of the band structure of liquids: Some calculation considerations and a test of the mean-spherical approximation

The discovery that simple classical liquid theories such as the mean-spherical approximation (MSA) provide a route for calculating electronic band structure opens up some interesting possibilities for investigating the interplay between liquid structure and electronic behavior. However, the MSA is better known for providing qualitative insights than it is for the accuracy of its quantitative predictions. In this paper we compare the MSA-computed band structure of a hard-sphere liquid with the exact band structure obtained from direct numerical diagonalization of the Hamiltonian at Monte Carlo–generated liquid configurations. In the medium dense to dense liquid range, the agreement is qualitatively reasonable with both s and p orbital basis sets, regardless of whether one includes nonorthogonality effects. Lower densities, as expected, are not as well treated. In the course of this comparison we also found it necessary to be aware of the limitations on computer-simulated band structures which are imposed by finite system size.