Cluster-type calculations of electronic structures of crystals by the method of linear combinations of atomic orbitals

First-principle cluster-type calculations of the electronic energy structures for the silicon and lithium fluoride crystals by the method of linear combinations of atomic orbitals (LCAO) are presented. The Hamiltonian is that of the infinite crystal (with a Slater-type approximation for electron exchange) and the basis functions are linear combinations of localized functions centered at the atomic sites within a cluster. By means of the Gaussian technique all the multicenter integrals associated with the Hamiltonian and overlap matrix elements are readily evaluated. For the localized functions in the basis set, we use (i) atomiclike orbitals, expanded in terms of the Gaussian-type orbitals, corresponding to the core and valence states of the free atoms and (ii) single Gaussians with various exponents. With exclusively atomiclike basis orbitals we show that one can reproduce the valence bands of the infinite crystals reasonably well using a cluster of eight or ten shells. However, to obtain representative conduction bands, particurly energy band gaps, we find it necessary to supplement the atomiclike orbitals by a few single Gaussians. In these cluster calculations, no energy levels are found in the crystal band gap region because the Hamiltonian is that of an infinite crystal with no physical surfaces present.