Electron correlation effects in H₂ and H⁺₃ and a study of fluctuation potentials in atoms
Firstly, the origin of the electron correlation problem is outlined and some approaches to its solution are discussed. In Part I, the difference between the exact and Hartree Fock (HF) inter-electronic potentials experienced between a pair of electrons, known as the fluctuation potential, is used to investigate the effect of correlation on small atoms. They are analysed in terms of radial and angular components of correlation and the dominance of angular-based correlation for a large nuclear charge is seen. In Part II, a new technique for examining the effects of electron correlation on molecular systems is developed. This is subsequently used to investigate the ground states of the H2 and H+3 molecules in position and momentum-space. By employing a natural orbital analysis, it was found for molecules that correlation could be examined in terms of the redistribution in electronic probability parallel to the bond (z-correlation), axially around the bond (o-correlation) and perpendicular to the bond in all directions (p-correlation). The origins of these components were analysed mathematically and their effects on the two-particle electron density were displayed. In position-space, although z-correlation was found to be the most dominant, all types of correlation were seen to increase the mean inter-electronic separation. In momentum-space, however, o and p-correlation acted to increase the mean inter-electronic momentum whereas z-correlation acted in opposition to this and had the effect of increasing the probability of locating both electrons travelling parallel to the bond in the same direction. This was compared with the work performed on atomic systems and the HeH+ molecular ion. For the electron-deficient, the investigation provided evidence to suggest that there are three distinct 'bonding regions' bent towards the centre of the molecule.