Kenneth Mednick

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 ...

On the cluster approach for calculating electronic energies of solid surfaces

Abstract A scheme for calculating electronic energy states of infinite solid surface systems by a cluster approach under the framework of the method of linear combinations of atomic orbitals is presented. The basis functions consist of atomic-like orbitals confined within a cluster whereas the Hamiltonian is that of the infinite solid. The latter circumvents the difficulty arising from the auxiliary boundary of the cluster which is not the true surface of the solid. All the multicenter integrals appearing in the Hamiltonian matrix can be evaluated exactly by means of the technique of Gaussian orbitals. This cluster-basis method is applied to the chlorine-adsorbed silicon (111) surface using several different clusters. The results are compared with those of the same Hamiltonian with basis functions extending over the entire solid in the Bloch-sum form. Criteria for optimal selection of clusters are suggested.