A theoretical study of some molecular systems.

A united-atom approximation, employing one-centre wavefunctions, has been adopted in the investigations of the electronic distribution and physical properties of a number of XHn molecules. Calculations have been carried out on HF, H2O, NH3, NH4+, CH4, HCl, H2S, HS-, S--, PH3, PH+4, PH-2 and SiH4; and physical properties which have been computed include molecular energy, bond length, x-ray scattering factor, molar diamagnetic susceptibility, 'breathing' force constant, proton affinity and bond energy. The results of these calculations are, where possible, compared with existing experimental data. In general, the predictions of this simple approach are pleasing. Calculations have been preformed by Moccia on almost all of the systems mentioned above, using a one-centre expansion approximation with an extended set of basis functions. The reported results of Moccia have been analysed and as a result it has been possible to calculate the radial electron density distribution, the x-ray scattering factor, and the molar diamagnetic susceptibility of all the molecules he has considered. The results obtained from Moccia's work, together with the results of a similar analysis by Banyard and March of the work of Ellison and Shull on H2O, have boon compared with the united- atom predictions and with experiment. The comparison gives some indication of the relative merits of the different approximate treatments. A brief review of density matrix theory is presented with particular emphasis on its application to molecular problems. This review includes a discussion of the introduction of the density matrix, and a short account of McWeeny's formulation of the LCAO-MO-SCF theory in density matrix form. Finally, the Waller and Hartree theory of x-ray scattering by free molecules has been developed in terms of the one- and two-particle reduced density matrices.