Effective-medium tight-binding model for silicon

A method for calculating the total energy of Si systems, which is based on the effective-medium-theory concept of a reference system, is presented. Instead of calculating the energy of an atom in the system of interest, a reference system is introduced where the local surroundings are similar. The energy of the reference system can be calculated self-consistently once and for all while the energy difference to the reference system can be obtained approximately. We propose to calculate it using the tight-binding linear-muffin-tin-orbital scheme with the atomic-sphere approximation (ASA) for the potential, and by using the ASA with charge-conserving spheres we are able to treat open systems without introducing empty spheres. All steps in the calculational method are ab initio in the sense that all quantities entering are calculated from first principles without any fitting to experiment. A complete and detailed description of the method is given together with test calculations of the energies of phonons, elastic constants, different structures, surfaces, and surface reconstructions. We compare the results to calculations using an empirical tight-binding scheme.