SYMMETRY BEYOND PERTURBATION THEORY: FLOPPY MOLECULES AND ROTATION-VIBRATION STATES

Schmiedt, Hanno

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Description

Title

SYMMETRY BEYOND PERTURBATION THEORY: FLOPPY MOLECULES AND ROTATION-VIBRATION STATES

Author(s)

Schmiedt, Hanno

Contributor(s)

• Jensen, Per
• Schlemmer, Stephan

Issue Date

22-Jun-15

Keyword(s)

Ions

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.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

text

Language

English

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