Correlation effects in energy-band theory

Abstract

In this paper we study the effect of correlations on Hartree-Fock energy bands for solids. The band picture is retained, and we obtain rigorous and general expressions for the correlation corrections. These are then specialized to study insulators, and the range of validity of the approximations is discussed. Qualitative conclusions about the effects of correlation are obtained directly, without the need of model calculations. We recover the narrowing of the optical gap and the narrowing of the valence bands, which have been known through model calculations, and also show that the effect of correlation on x-ray-emission transition energies is less pronounced, almost negligible, due to a cancellation of correlation contributions. In the case of metals, we again obtain general results and discuss model calculations. We further address the problem of short-range correlations, which is best described in an alternative formalism, and give estimates of the corrections. We give specific and detailed results for MgO as illustration of all the concepts in this paper. Finally, we discuss the effect of correlation on wave functions and oscillator strengths, and, in an appendix, point out a comparison of correlation effects among free atoms, insulators, and metals.