On the self-consistent-field linear combination of atomic orbitals for bounded crystal orbitals (SCF-LCAO-BCO) method

Abstract

The self-consistent-field linear combination of atomic orbitais for bounded crystal orbitais (SCF-LCAO-BCO) method can be used to study the electronic structure of bounded polymers and crystals if they have a significant amount of internal translational symmetry, at the ab initio Hartree-Fock level. The direct recursion (transfer matrix) method (DRM) is applied to its derivation, here only for certain simpler models. It is shown that the application of the free boundary condition instead of the periodic (Born-von Kármán) one halves the conventional one-dimensional Brillouin zone and resolves the double degeneracy of the Bloch states. A longitudinal bulk-state distortion (LBSD) is demonstrated for a linear bounded polymer model possessing perfect translational symmetry and symmetrical intercell interaction matrices. The block diagonalizability is discussed when free boundary conditions are applied. The non-existence of limit wave functions in the overlapping regions of bands is shown for the infinite size limit. The use of certain averaged wave functions is proposed for the calculation of the charge-bond order matrices in order to resolve the above difficulty.