Symmetry Simplifications of Space Types in Configuration Interaction Induced by Orbital Degeneracy

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types wherein all the space types in the same equivalence class with identical spin coupling make identical contributions to correlation. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group S , if n is the n number of electrons. Method is illustrated with CI using the localized Lowdin orbitals of polyenes and CI in benzene for several reference states. 2