All-electron self-consistent variational method for Wannier-type functions: Applications to the silicon crystal

A new iterative algorithm is introduced that enables the direct calculation of Wannier-type functions. These functions are practically identical to the Wannier functions except for a minor difference in the structure of the Lagrange multiplier matrix. With this method, multiband systems are as easy to study as single-band systems. This method is used to carry out fully self-consistent local-spin-density (LSD) calculations on the silicon crystal. The resulting Wannier-type functions are guaranteed to satisfy the site othogonality constraints to the arbitrarily chosen value of 0.000 01. The LSD band centroids and band structures which are obtained within the Wannier-type formulation are in excellent agreement with those obtained using the usual Bloch formulation.