Clebsch–Gordan coefficients for chains of groups of interest in quantum chemistry. II. The chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2

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Abstract
The formalism described in the first paper of this series is applied to the chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2, the covering of SO(3) ⊃ D∞ ⊃ D4 ⊃ D2. The state vectors (|αJaΓγ) adapted to each link of the chain under consideration and the corresponding coupling coefficients \documentclass{article}\pagestyle{empty}$ f\left( {\begin{array}{*{20}c} {J_1 } & {J_2 } & J \\ {a_1 \Gamma _1 \gamma _1 } & {a_2 \Gamma _2 \gamma _2 } & {a\Gamma \gamma } \\ \end{array}} \right) $ are given in analytical form. The material reported here is very convenient for a quantum‐mechanical description of molecular and nuclear systems with linear, tetragonal, or orthorhombic symmetry. In this respect, we present an outline for its applications to the electronic and vibrational–rotational spectroscopy of molecular aggregates and to the rotational spectroscopy of molecules or nuclei. In addition, we briefly show how the material may simplify the second–order non‐Lie subgroup type approach to the representation theory of SU(2).

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