Molecular orbital wave functions for methane and silane are set up as harmonic expansions about the central nucleus as origin. This method avoids the many-centred integrals of the l. c. a. o. theory. Energies, bond lengths and force constants are obtained quite accurately using only the first term in each expansion. In this case the radial wave functions may be calculated by the Hartree s. c. f. method as for atoms. Scale-factor methods are developed to obtain the bond length and force constant from the s. c. f. wave functions calculated for a single internuclear distance, and to determine the approximate effect of exchange terms. It is shown that higher terms in the expansions of the m. o. ’s are important in the calculation of some molecular properties, particularly angular momentum and diamagnetic susceptibility.