Group Theoretical Structure of a Solution of the Unrestricted Hartree-Fock Equation in Molecular Systems with a Spatial Point Symmetry

Abstract

A theory is developed to determine the group theoretical structure of a UHF solution in molecular systems with a spatial point symmetry. It is shown that the invariance group G of a UHF solution has at least a series of halving subgroups G=Ho~H,···~H. such that H,+, is a halving subgroup of H, and H. is a group whose irreducible representations can be easily obtained or are available in standard text books. On the basis of this halving series, a general procedure is derived to obtain all the irreducible double valued representations of the invariance group of a UHF solution and their bases which provide a standard form of the orbitals of the UHF solution. The irreducible representations and their bases of the invariance groups of the seven classes of UHF solutions in spin and time reversal symmetry except the torsional spin wave (TSW) one are given in terms of those of the group of TSW type or the point group.