Point-group symmetries on the spherical shell. New perspectives in the generation of symmetry-adapted LCAO functions

Abstract

The formalism underlying recently proposed new techniques in group theory and qualitative molecular-orbital theory is given and the relation with other theories and methods established. It is shown that the higher-order π- and δ-representations of a set of ligand functions in a point structure follow directly from the easily determined σ- or permutation representation. Symmetry-adapted LCAO functions (group orbitals) are generated using the tensor harmonic technique and it is shown that this procedure is directly applicable to the qualitative molecular-orbital theory of, for example, the closo-boranes exemplified by the B₁₂H^2–₁₂ anion.