From crystal orbitals to strange electronic states. I. Crystal orbitals by direct recursion (transfer matrix) method (DRM)

Abstract

The history of Bloch's and Tamm's states is sketched. The present stage in the theory of the bounded infinite polymers and crystals and strange electronic states is outlined. To lay the foundations of the SCF LCAO bounded crystal orbital (BCO) method applicable for surface electronic problems, the direct recursion (transfer matrix) method (DRM) is formulated for perfect cyclic polymers and crystals. A simple combination of block-decomposition and matrix transpositions is applied to calculate U−1 directly from the blocks of U, the similarity transformation bringing the recursion matrix T into its normal form. Several forms are given for the auxiliary and fundamental equation of the DRM. The crystal orbitals are derived by the DRM. Full matrix expression is presented for the resolvent (Green) matrix of perfect cyclic polymers, the unperturbed system in the SCF local-density approach of Ladik and Seel. The formulae of the charge-bond order matrix are derived both by the DRM and the indirect (Green matrix) recursion method (IRM).