Non-Empirical Molecular Orbital Theory for Molecular Crystals

The theory discussed in these lectures is based on single determinant SCF (Self-Consistent-Field) molecular orbital theory. It differs from the conventional tight binding approach only in the method used to solve the crystal SCF matrix equation. The usual approach (1,2) is to factorize the crystal Fock operator by the introduction of translational symmetry adapted basis functions. This procedure is relatively straightforward and works well for polymers and one-dimensional crystals but is rather complicated when applied to three-dimensional crystals. The approach under discussion here attempts to side-step these problems by directly calculating the crystal density matrix(3,8). It uses the molecular character of molecular crystals to advantage by means of matrix partitioning methods and SCF perturbation theory.(9)