Direct calculation of Slater-Koster parameters: Fourfold-coordinated silicon/boron phases

The need for tight-binding total-energy representations of interatomic forces has renewed interest in Slater-Koster parametrization of electron band structure. For larger numbers of parameters, as in multicomponent systems, and to truly test issues of transferability, it is advantageous to have means of directly calculating these parameters. Here we derive analytic expressions for the two-center Slater-Koster hopping parameters, effective site energies, and effective crystal-field parameters in terms of the one-electron Hamiltonian matrix elements in any localized minimal basis, and analogous quantities for the overlap. We apply these expressions to the cubic diamond phases of Si and B, and the zinc-blende phase of SiB at three volumes each, using $\mathrm{spd}$, nonorthogonal full potential linear muffin-tin orbital matrix elements calculated with a linked or contracted minimal basis.