Two-electron bond-orbital model. II

Abstract

The two-electron bond-orbital model of tetrahedrally-coordinated solids is generalized and its application extended. All intrabond matrix elements entering the formalism are now explicitly retained, including the direct overlap $S$ between the anion and cation $s{p}^{3}$ hybrid wave functions. Complete analytic results are obtained for the six two-electron eigenvalues and eigenstates of the anion-cation bond in terms of $S$, one-electron parameters ${V}_{2}$ and ${V}_{3}$, and the two-electron correlation parameters ${V}_{4}$, ${V}_{5}$, and ${V}_{6}$. Refined formulas for the dielectric constant and the nuclear exchange and pseudodipolar coefficients, as well as new expressions for the valence-electron density, polarity of the bond, and the cohesive energy, are then derived. A scheme for evaluating the basic parameters of the model is established, in which ${V}_{2}$ is fit to the optical-absorption peak of group-IV elements in the manner of Harrison and Ciraci and the remaining quantities are calculated using Hartree-Fock free-atom wave functions and term values. For the 20 group-IV and III-V semiconductors, we find ${V}_{5}\ensuremath{\sim}{V}_{6}\ensuremath{\sim}0$, but $\frac{{V}_{4}}{{V}_{2}}\ensuremath{\sim}\frac{1}{2}$, leading to significant correlation effects in most properties. The theory gives a good account of the experimentally observed trends in all properties considered and approximate quantitative agreement is achieved for the pseudodipolar coefficient. Good agreement is also obtained for the ${E}_{2}$ optical-absorption peak, the dielectric constant, the nuclear exchange coefficient, and the cohesive energy of the binary compounds by scaling to experiment for the group-IV elements. Our calculations on the cohesive energy suggest that the intrabond overlap energy, discarded by Harrison and Ciraci, is an essential source of positive cohesion and probably rules out any major role by the interbond Van der Waals interaction suggested by them. The valence-electron density is found to be dominated by the polarity and the shape of the $s{p}^{3}$ hybrids. The preliminary indication is that the long-range tails of the free-atom $s$ and $p$ wave functions must be contracted to account for the observed bond density in Si.