Spectroscopy of XY3Z (C3v) molecules: A tensorial formalism adapted to the O (3) ⊃ C∞v ⊃ C3v group chain

A tensorial formalism adapted to the case of XY3Z symmetric tops has been developed. We use the O (3) ⊃ C∞v ⊃ C3v group chain. All the coupling coefficients and formulas for the computation of the matrix elements are given for this chain. Such relations are also deduced in C3v group itself.