Two-electron bond-orbital model I

Abstract

Harrison's one-electron bond-orbital model of tetrahedrally coordinated solids is generalized to a two-electron model, using an extension of the method of Falicov and Harris for treating the hydrogen molecule. The six eigenvalues and eigenstates of the two-electron anion-cation Hamiltonian entering this theory can be found exactly even in the most general case. In this first paper, however, the nonorthogonality of the anion and cation $s{p}^{3}$ hybrids is neglected to simplify the treatment and to emphasize the most essential features of the model. The two-electron formalism is shown to provide a useful basis for calculating both nonmagnetic and magnetic properties of semiconductors in perturbation theory. As an example of the former, we calculate expressions for the electric susceptibility and the dielectric constant. In the limit of no electron correlation, our expression for the susceptibility agrees with that found by Harrison and by Harrison and Ciraci. As an example of the latter, we calculate new expressions for the nuclear exchange and pseudodipolar coefficients. A simple theoretical relationship between the dielectric constant and the exchange coefficient is also found in the limit of no correlation. The expressions for the exchange and pseudodipolar coefficients are quantitatively evaluated in the limit of no correlation for twenty elemental and binary semiconductors, and the results are compared with existing experimental data. Preliminary studies on the quantitative effects of correlation on the various quantities considered here are also discussed.