Electronic structure of SiO2. I. Theory and sample calculations

Abstract

An LCLO (linear combination of localized orbitals) cluster method using a small basis set is developed to calculate the electronic structure of Si${\mathrm{O}}_2$. The localized orbitals are obtained by Kunz's approach to the Adams-Gilbert equation. The matrix elements of the Fock operator $F_{a\beta }$ are evaluated in Gilbert's version of extended Húckel theory, which involves expanding $F_{a\beta }$ in powers of overlap integrals and keeping only terms of first order. Molecular orbitals and energy levels for a chosen cluster representing the solid system are then calculated by solving a secular equation. This paper discusses our approach, which involves no disposable parameters, compares it with other recent modifications to extended Hückel theory, and presents results of sample calculations on ${\mathrm{H}}_2$ and ${\mathrm{H}}_2$O molecules for the purpose of testing our method and computer programming.