Spectroscopy of XY3Z (C3v) radicals with an odd number of electrons: A tensorial formalism adapted to the SU(2)⊗CI⊃C∞vS⊃C3vS group chain

A tensorial formalism adapted to the case of XY3Z symmetric tops with half integer angular momenta is proposed as an extension of the formalism for the group chain O (3) ⊃ C∞v ⊃ C3v developed in a recent paper [A. El Hilali, V. Boudon, M. Loëte, J. Mol. Spectrosc. 234 (2005) 113-121]. We use the chain SU(2)⊗CI⊃C∞vS⊃C3vS, where GS (G being C∞v or C3v) is the G point group with its spinorial representations. Coupling coefficients and formulas for the computation of matrix elements of the tensor operators are derived for this chain. A deduction of coupling coefficients (Clebsch-Gordan, 6C, 9C, …) and similar formulas is proposed for the group C3vS itself.