Predicting coriolis vibration-rotation coupling coefficients for analysis of rotational spectra, part 1: theory and implementation

Owen, Andrew N.

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https://hdl.handle.net/2142/107341 Copy

Description

Title

Predicting coriolis vibration-rotation coupling coefficients for analysis of rotational spectra, part 1: theory and implementation

Author(s)

Owen, Andrew N.

Contributor(s)

• McMahon, Robert J.
• Woods, R. Claude
• Esselman, Brian J.

Issue Date

2020-06-22

Keyword(s)

Theory and Computation

Abstract

The fitting and assignment of the rotational spectra of Coriolis-coupled distorted rotors is considerably more difficult than for isolated distorted rotors due to the sensitivity of a non-linear least-squares fit to the initial parameters and the lack of \textit{a priori} predictions of the Coriolis coupling coefficients for all but the simplest couplings. Herein, we present our efforts to automatically generate computational predictions of Coriolis coupling coefficients (\(G_{\alpha}\), \(F_{\beta\gamma}\), and their corresponding centrifugal distortion terms) using the outputs of Gaussian or CFOUR programs. The theory for deriving vibration-rotation couplings (through Van Vleck-style perturbation of the vibration-rotation Hamiltonian) and the formulas necessary for calculating a variety of coupling coefficients (\(G_{\alpha}\), \(F_{\beta\gamma}\) for \(\sum_{i}|\Delta v_{i}|\leq3\) and \(G_{\alpha}^{J}\), \(G_{\alpha}^{K}\), \(F_{\beta\gamma}^{J}\), \(F_{\beta\gamma}^{K}\) for \(\sum_{i}|\Delta v_{i}| = 2\)) have been known for some time, yet only predictions of \(G_{\alpha}\) for \(\sum_{i}|\Delta v_{i}| = 2\) have been used. Our implementation for predicting coupling coefficients of low order in rotation (\(G_{\alpha}\) and \(F_{\beta\gamma}\)) is straightforward. We found for terms of higher order (\(G_{\alpha}^{J}\), \(G_{\alpha}^{K}\), \(F_{\beta\gamma}^{J}\), \(F_{\beta\gamma}^{K}\)), however, that it is necessary to carry out reductions of the respective formulas. We therefore adapted the methodology used for reducing the centrifugal distortion to obtain predictions of the coupling coefficients that can be used for \textit{a priori} prediction and for post-fitting comparison directly to those determined experimentally.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

Text

Language

eng

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http://hdl.handle.net/2142/107341

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Copyright 2020 is held by the Author(s)

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