The Kohn variational method to study Wannier functions has been rewritten in a new form that makes it suitable for numerical calculations. Thus, using a Wannier-function scheme, we have been able to perform an ab initio self-consistent calculation of the charge density and band structure of silicon. The interactions between the Wannier functions are calculated as well. The Hamiltonian has been built up with a local approximation for the screening potential and a bare ionic potential taken from a fit to atomic properties. Our charge density and band structure are in good agreement with previously reported pseudopotential results. This is the first time that the Wannier functions for connected bands have been calculated. We have verified that satisfactory results are obtained when starting with a simple trial set of localized orbitals.

• Received 23 December 1977

DOI:https://doi.org/10.1103/PhysRevB.19.2283