ANALYTIC EXPRESSIONS OF BAND-STRUCTURE POTENTIALS AND TRANSFERABILITYSTUDIES

We performed a least-squares fit for crystal potentials derived by APW band structure calculations for monatomic, as well as diatomic, struc tures. The potential is described by an eighth order polynomial multip lied by an exponential function. The fitted potentials yield eigenvalu es, for a variety of k points, within 2-3 mRyd of the first-principles APW results. We have also discovered that starting with the fitted po tential at a given lattice constant and using the potential in the int erstitial region (muffin-tin zero) as a single parameter, we are able to accurately reproduce the band structure at another lattice constant . The relationship between the muffin-tin zero and the lattice paramet er is very nearly linear. The linear relationship allows us to use the se modified potentials for 'one-shot' total energy calculations which given an equilibrium lattice parameter and a bulk modulus in very good agreement with the self-consistent calculations. We believe that thes e findings may be of importance in the search for transferable potenti al energy functions that can be used in calculating the band structure and the total energy of large systems.