Spectroscopy of XY3Z (C3v) radicals with an odd number of electrons: A tensorial formalism adapted to the SU(2) Ci Civ(S) C3v(S) group chain

• Published in: Journal of molecular spectroscopy Vol. 239; pp. 41 - 50
• Main Authors: El Hilali, A., Boudon, Vincent, Loete, Michel
• Format: Journal Article
• Language: English
• Published: Elsevier 2006
• Subjects: Atmospheric and Oceanic Physics; Physics; group theory; free radicals; tensorial formalism; rovibronic spectroscopy
• ISSN: 0022-2852; 1096-083X
• DOI: 10.1016/j.jms.2006.05.016

A tensorial formalism adapted to the case of XY(3)Z symmetric tops with half integer angular momenta is proposed as an extension of the formalism for the group chain O(3) C-infinity v superset of C-3v developed in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 234 (2005) 113-121]. We use the chain SU(2) circle times C-I superset of D C-infinity v(S) superset of C-3v(S), where G(S) (G being C-infinity v or C-3v) 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 C-3v(S) itself.