The Intriguing Fbc(pbpc+pcpb) Term In The Interaction Hamiltonian For Tunneling Between Equivalent Gauche Conformers

Groner, Peter

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https://hdl.handle.net/2142/116665 Copy

Description

Title

The Intriguing Fbc(pbpc+pcpb) Term In The Interaction Hamiltonian For Tunneling Between Equivalent Gauche Conformers

Author(s)

Groner, Peter

Issue Date

2022-06-21

Keyword(s)

Comparing theory and experiment

Abstract

This study was triggered by the results of the microwave investigation of triflic acid (TA), \chem{CF_3-SO_2-OH}, and its deuterated (TA-d) and $^{34}$S (TA-S) isotopologues by Huff et al.\footnote{A.K. Huff, N. Love, C.J. Smith, K.R. Leopold, (2022) submitted for publication.} To fit the observed transitions split by gauche-gauche tunneling due to the CS-OH internal rotation, the interaction Hamiltonians for TA and TA-S required the term $F_{bc}(P_{b}P_{c}+P_{c}P_{b})$. In contrast, the Coriolis term $g_{a}P_{a}$ had to be used for TA-d. The $F_{bc}$ term results from two facts: 1) The moment of inertia tensor $I$ and its inverse, the $\mu$-tensor, of both the right- and left-handed forms of the gauche conformers need to be expressed in the same molecule-fixed axis system; 2) The Cartesian coordinates of some or all atoms and the components of $I$ depend on the internal rotation coordinate $\tau$. If we define a Cartesian axis system with two of the axes in the symmetry plane of the transition state between the two conformers, the third axis is perpendicular to it. When $\tau$ changes, the moving atoms will eventually cross the symmetry plane and their 3rd Cartesian coordinate will change its sign and with it also the signs of two off-diagonal components of $I$ and the $\mu$-tensors. The rotational Hamiltonian in a 2-by-2 block format contains the contributions of the right and left gauche conformers ($H_{R}$ and $H_{L}$, respectively) on the diagonal and the Coriolis interactions in the off-diagonal blocks. If the internal rotation wave functions $\phi_{R}$ and $\phi_{L}$ are symmetrized to $\phi_{A'}$ and $\phi_{A''}$ to conform with $C_{s}$ symmetry, the diagonal blocks of the Hamiltonian become $H_{A'}$ and $H_{A''}$. The off-diagonal blocks contain now the Coriolis terms and the contributions from the sign-changing $\mu$-tensor components. Detailed explanations and a demonstration that this particular interaction may be especially important for $K_{a}=1$ energy levels will be presented.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

text

Language

eng

Handle URL

https://hdl.handle.net/2142/116665

DOI

https://doi.org/10.15278/isms.2022.TF01

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Copyright 2022 held by the authors

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