Reduction of nearest neighbours L.C.A.O. Hamiltonians for systems with equivalent bonds

Abstract

The nearest neighbor's L.C.A.O. approximation is applied to systems having equivalent bonds. This is first done for a sp basis in a two-center tight-binding approximation which yields in general five independent interatomic parameters β ss, β sσ, β σs, β σσ, β ππ of which the last one is usually much smaller. It is demonstrated that the Hamiltonian corresponding to the inclusion of the first four parameters can quite generally be reduced to a one band Hamiltonian. An application is made to the case of group IV elements. An extension to more complicated symmetrically bonded systems such as SiO 2 is also presented. It is shown that a nearest neighbors' tight binding approximation cannot give an accurate description of these systems. The method is then extended to include nearest neighbors overlap integrals, which allows a much better fit to the band structure of SiO 2.