Generalization of the basis functions of the LCAO method for band-structure calculations

A systematic discussion of various choices of the localized functions for constructing the bloch sums for LCAO calculations is presented. By generalizing the basis functions, improvement of efficiency and extension of the domain of applicability of the lcao method can be accomplished. The use of extended basis sets containing a series of single-gaussian bloch sums not only yields energy bands of accuracy comparable to those of the method of augmented plane waves, but also enables one to handle the highly excited states. For calculating the filled bands and lower conduction bands the basis functions formed by the optimized orbitals give considerably better results than those with the free-atom orbitals. To reduce the computational work, one can introduce the truncated orbitals by gradually damping the atomic wavefunctions beyond a certain distance, typically the mid-point to the second nearest neighbours. Specific calculations are given for the cases of lithium and diamond-type crystals.