SIGNIFICANCE OF MODEL HAMILTONIANS IN ENERGY-BAND THEORY

The results of recent ab initio calculations of energy bands are compared with interpolation schemes in order to assess the significance of the latter. When the parameters in the interpolation scheme are required to correspond to those obtainable by an ab initio calculation based on a reasonable one-electron potential, we describe the scheme as a model Hamiltonian. The analytic character of model Hamiltonians for s–p bands (pseudopotential case) or for d bands interacting with s–p bands (resonance case) is summarized. The compatibility of the results of several workers with these analyticity requirements is considered. It is shown that if the empirically-motivated adjustments of parameters are to be regarded as physically significant, these adjustments must satisfy rather strict conditions. © 1968 Taylor & Francis Group, LLC.