A Self-Consistent Procedure for the Linear-Combination-of-Atomic-Orbitals Method: Application to LiF

Abstract

An efficient method for computing self-consistent energy bands within the framework of the linear-combination-of-atomic-orbitals (LCAO) method is applied to LiF. Efficiency of the method is a result of characteristically small LCAO secular determinants, the ease with which energy bands may be computed at general points in the Brillouin zone, and a formalism which expresses iterated-Hamiltonian matrix elements in terms of LCAO integrals computed in the first step only. A study of the self-consistent procedure is presented, including an investigation of convergence and accuracy. On the basis of this study it is concluded that self-consistent calculations using small Brillouin-zone samplings of symmetry points to compute charge densities contain errors as large as 1 eV. Accurate self-consistent energy bands are computed for LiF in the Hartree-Fock-Slater approximation and compared with previous calculations and experimental data. While an initial linear combination of ionic potentials with an adjustable exchange potential yields reasonable agreement with optical data, only a self-consistent potential produces agreement with both optical and photoemission data. It is suggested that to obtain reliable spectra, even when using an adjusted exchange potential, it is necessary to compute optical properties with self-consistent energy bands and wave functions.