An energy study of the ground state of some four electron complexes.

The work of Banyard and Shull on a series of two-electron pseudomolecular ions ZHZ+2Z-1 has been extended to four electron systems of the form ZHZH+2Z-2. These systems may be regarded as an approximate representation of a fragment of a more complex molecule, therefore, noninteger Z values were used in an attempt to make some allowance for the nuclear shielding caused by the presence of other electrons which were otherwise unaccounted for in the calculations. The effective nuclear charge Z was allowed to take values of 1.0, 1.2, 1.4, 1.8 and 2.2 and the optimum bond angle ZHZ was studied as a function of Z. Within a limited basis set of Slater-type 1s orbitals, the calculations were complete configuration interaction treatments. The C.I. wave functions were reformulated in terms of natural spin orbitals. Consequently, changes in the electron density distributions have been investigated as a function of Z and bond angle. For Z = 1.0, 1.4, 1.8 and 2.2, and ZHZ = 100° and 120°, the electron densities of the ZHZH+2Z-2 ion have been compared with those of the ZHZ+2Z-1 systems. The nuclear framework of the diborane "bridge" was adopted for a second series of four-centre, four-electron calculations: a similar investigation has been carried out by Hamilton. Once again an allowance was made for nuclear shielding by using effective nuclear charges - the boron nuclear charge, BZ, was given values of 2.0, 2.5 and 3.0. Slater-type 1s orbitals were centred on the hydrogen nuclei and 2s orbitals on the boron nuclei. For each value of BZ the energy was minimized with respect to the orbital exponents. The electron density at points along the internuclear axes was then evaluated for the optimized systems.