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Author(s):Schmiedt, Hanno
Contributor(s):Jensen, Per; Schlemmer, Stephan
Abstract:In the customary approach to the theoretical description of the nuclear motion in molecules, the molecule is seen as a near-static structure rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction, which fails in fluxional molecules, where textit{all} vibrational motions are large compared to the linear extension of the molecule. An example is protonated methane (CH$_5^+$)~footnote{P. Kumar and D. Marx, Physical Chemistry Chemical Physics textbf{8}, 573 (2006); Z. Jin, B. J. Braams, and J. M. Bowman, The Journal of Physical Chemistry A textbf{110}, 1569 (2006); A. S. Petit, J. E. Ford, and A. B. McCoy, The Journal of Physical Chemistry A textbf{118}, 7206 (2014).}. For this molecule, customary theory fails to simulate reliably even the low-energy spectrum. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions can be symmetry classified separately in the molecular symmetry (MS) group~footnote{P.R. Bunker and P. Jensen, textit{Molecular Symmetry and Spectroscopy} (NRC Research Press, Ottawa, Canada, 1998).}. In the present contribution we discuss a fundamental group theoretical approach to the problem of determining the symmetries of molecular rotation-vibration states. We will show that all MS groups discussed so far are subgroups of the special orthogonal group in three dimensions SO(3)footnote{Being precise, we must include O(3) and SU(2), but our theory can be easily extended to these two groups.}. This leads to a group theoretical foundation of the technique of equivalent rotations~footnote{H. Longuet-Higgins, Molecular Physics textbf{6}, 445 (1963).}. The MS group of protonated methane (G$_{240}$) represents, to the best of our knowledge, the first example of an MS group which is not a subgroup of SO(3) (nor of O(3) nor of SU(2)). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. We want to discuss the consequences of this. In conclusion, we show that the prototypical floppy molecule CH$_5^+$ represents a new class of molecules, where usual group theoretical methods for determining selection rules and spectral assignments fail so that new methods have to be developed.
Issue Date:22-Jun-15
Publisher:International Symposium on Molecular Spectroscopy
Citation Info:ACS
Genre:Conference Paper / Presentation
Date Available in IDEALS:2016-01-05

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