Determination of fragment orbitals and LCFO MO's in semiempirical methods with overlap matrices

We propose a technique for a fragment stage solution of the Roothaan equations, allowing us to obtain fragment orbitals (FO's) and to form molecular orbitals (LCFO MO'S) for the molecule from them. As an example, in the Mulliken-Wolfsberg-Helmholtz (MWH) approximation we obtain the orbitals for fragments of the simplest hydrocarbon molecules and we compare them with the FO's found in the CNDO/2 approximation. We discuss the possibilities in perturbation theory for joining the fragments and for study of the properties of the molecules in the FO basis.