Electron correlations in narrow energy bands. II. The degenerate band case

TLDR

A prior study presented a theory of correlation effects in narrow s‑bands. This paper generalizes that theory to narrow degenerate electron bands. The theory focuses on intra‑atomic correlations in narrow bands and is illustrated using simplified models and implications for d‑band transition metals. The solution smoothly interpolates between ordinary band theory and the exact atomic limit, and its physical interpretation aligns with Van Vleck’s earlier theory.

Abstract

In a previous paper a theory of correlation effects in narrow s -bands was described. In this paper a generalization of that theory applicable to narrow degenerate electron bands is developed. The theory is based upon the notion that in the case of narrow bands the most important correlations are those between electrons on the same atom. The solution obtained has the important property of going over into the ordinary band theory solution in the appropriate limit (no interaction) and the exact atomic (Heitler-London) solution in the opposite limit (zero band-width). In order to elucidate the general properties of the solution some simplified models are discussed, and the more elementary implications of the theory when applied to the d -bands of transition metals are indicated. A physical interpretation of the results of the theory is given; the physical picture which emerges is found to be closely related to a theory discussed earlier by Van Vleck.