Correlation effects and electron densities in some two-electron systems.

The first section of this work consists of an analysis of three wave-functions for the ground state of the two-electron series which begins with H-. Two of the wave-functions include electron correlation. One does so by means of superposition of configurations and the other by the inclusion of explicit correlation factors. For comparison, the third function is of the Hartree-Fock type. The correlation within the wave-functions is demonstrated by presenting various density functions and density difference maps relative to the uncorrelated approach. Expectation values and physical properties such as X-ray scattering factors, diamagnetic susceptibilities and nuclear diamagnetic shielding factors are also presented. By this means it is possible to assess the correlation predicted by the wave-functions, with comparison being made where possible with results from a more accurate wave-function. In addition, the production of the natural expansion for one of the correlated functions gives extra information about the effects of radial and angular correlation. The second part consists of a study of a good one-centre treatment of the diatomic molecular ion HeH+. Both the molecular formation and the electron correlation in the system are studied by means of density differences and expectation values. Natural orbitals are used to enable comparison to be made with another HeH+ wave-function. This comparison shows that the two calculations are similar, even though conceived quite differently. A development of the general theory of natural spin orbitals is given as an appendix. Special emphasis is given to this technique as regards two-electron systems.