THE SCALING OF THE TIGHT-BINDING HAMILTONIAN

We re-examine the variation of the Slater-Koster tight-binding (SKTB) parameters with the interatomic distance and the lattice structure. It is shown that when volume effects are separated from lattice (field) effects, the scaling with the volume can be described in terms of the electron density (or equivalently the parameter r(s)) while the scaling with the lattice structure can be described in terms of the number of nearest neighbours. The proposed scaling form appears to fit very accurately the SKTB parameters of Si obtained by the TB-LMTO method.