Elementary prediction of linear combination of atomic orbitals matrix elements

For solids in the diamond structure there is a close resemblance between the true bands, the nearest-neighbor linear combination of atomic orbitals (LCAO) bands, and the free-electron bands. Making use of the similarity of the last two we have derived universal LCAO parameters for the interatomic matrix elements between s- and p-like states. They are all of the form η(²md²), and for the diamond structure they are in good agreement with Harrison's earlier empirical results. For more closely packed structures the η coefficients deviate from Harrison's values.