TENSORIAL FORMALISM FOR ROVIBRONIC SPECTROSCOPY OF $C_{3v}$ MOLECULES SPECTROSCOPY OF XY$_{3}$Z (C$_{3v}$) MOLECULES WITH AN EVEN OR ODD NUMBER OF ELECTRONS: A TENSORIAL FORMALISM ADAPTED TO THE $SU(2)\otimes C_{I}\supset C_{\infty v}^{S}\supset C_{3v}^{S}$ GROUP CHAIN
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Date
2010
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Ohio State University
Abstract
In molecular spectroscopy, it is often considered that sophisticated group theoretical and tensorial formalism methods are only really useful for spherical top (\textit{i.e. }highly symmetrical) molecules, for which they have proven their high efficiency. Consequently, it is usually admitted that symmetric and asymmetric tops (\textit{i.e.}\ lower symmetry) species should be treated using more ``conventional'' methods. However, some key elements of the formalism developed in our group for tetrahedral or octahedral molecules can be used with great profit even for less symmetrical systems: the ability of performing systematic developments of all rovibrational interactions in case of complex polyads and the so-called ``vibrational extrapolation'' which makes global analyses much easier. Firstly, we present the development of a tensorial formalism adapted to the study of XY$_{3}$Z type molecules which possess integer angular momenta (\textit{i.e. }in a singlet electronic state) by using the $O(3)\supset C_{\infty v}\supset C_{3v}$ chain, {\bf 234}, 131--121 (2005).}$^,$, {\bf 234}, 176--181 (2005).}. We present also the $C_{3v}$\texttt{TDS}, {\bf accepted} (2010).}($C_{3v}$ Top Data System) software for spectrum simulation dedicated to the study of symmetric-top molecules belonging to the $C_{3v}$ point group. Secondly, we present the development of a tensorial formalism adapted to the study of XY$_3$Z type open-shell species which possess half-integer angular momenta by using the $SU(2)\otimes C_I\supset C_{\infty v}^{S}\supset C_{3v}^{S}$ group chain, {\bf 239}, 41--50 (2006).}$^,$, {\bf 253}, 92--98 (2009).}.
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Author Institution: LISA, CNRS/Universites Paris Est et Paris Diderot; 61 Avenue du General de Gaulle, 94010 Creteil, France; Laboratoire interdisciplinaire Carnot de Bourgogne; UMR 5209 CNRS--Universite de Bourgogne, 9, Avenue Alain; Savary, BP 47870, F-21078 Dijon Cedex, France