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 $\eta \left(\frac{{\hslash }^2}{m{d}^2}\right)$, and for the diamond structure they are in good agreement with Harrison's earlier empirical results. For more closely packed structures the $\eta$ coefficients deviate from Harrison's values.