General expressions for reducing the Slater-Koster linear combination of atomic orbitals integrals to the two-center approximation

This paper contains a derivation of general expressions for reducing Slater-Koster integrals Eᵢⱼ(l,m,n) to the two-center approximation for orbitals i (and j) having arbitrary angular momentum quantum numbers; l,m,n describe the location of one center relative to the other. This has allowed the author to check the entries in Table I of the Slater-Koster paper and provides a means for extending these entries to include states of higher angular momenta. The derived general expressions are especially useful for machine calculations when a large number of particular expressions are required to be evaluated. As a collateral result the missing factors in the energy matrix elements along the Δ line for the face-centered cubic structure given by Slater and Koster and reviewed by Reitz have been noted.