Clebsch–Gordan coefficients for chains of groups of interest in quantum chemistry. III. The point symmetry groups

Abstract

AbstractThis work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch–Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch–Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU(2) ⊃ U(1). The Clebsch–Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch–Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU(2) ⊃ G through the resolving of a system of nonlinear equations.