Knowledge Bank

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$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$Z type molecules which possess integer angular momenta (\textit{i.e. }in a singlet electronic state) by using the $O(3)\supset C\infty v\supset C3v$ chain, {\bf 234}, 131--121 (2005).}$,$, {\bf 234}, 176--181 (2005).}. We present also the $C3v$\texttt{TDS}, {\bf accepted} (2010).}($C3v$ Top Data System) software for spectrum simulation dedicated to the study of symmetric-top molecules belonging to the $C3v$ 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 $SU(2)\otimes CI\supset C\infty vS\supset C3vS$ group chain, {\bf 239}, 41--50 (2006).}$,$, {\bf 253}, 92--98 (2009).}.