Hathorn, B. C. and Marcus, R. A. (2001) Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules. Journal of Physical Chemistry A, 105 (23). pp. 5586-5589. ISSN 1089-5639. doi:10.1021/jp003849a. https://resolver.caltech.edu/CaltechAUTHORS:20150316-135714897
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Abstract
For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm^(-1). The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm^(-1). The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.
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| Additional Information: | © 2001 American Chemical Society. Received: October 19, 2000; In Final Form: January 25, 2001. Published on Web March 1, 2001. It is a pleasure to acknowledge the support of this research by the National Science Foundation and the award of a James W. Glanville Postdoctoral Fellowship in Chemistry at Caltech to one of us (B.C.H.). We thank Ian Mills and Lauri Halonen for their enlightening comments on current programs such as ASYM 20 and 40 for extracting frequencies. It is a pleasure also to dedicate this article to a long-time friend and colleague of one of us, Ed Schlag, on the occasion of his 68th birthday. R.A.M.’s first recollection of him is when Ed, his mentor Seymour Rabinovitch, and a fellow student, the late Wolfgang Michel, were pioneers in the application of RRKM theory to experiments on unimolecular reactions some four decades ago. He has made numerous pioneering developments since. | |||||||||
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| Issue or Number: | 23 | |||||||||
| DOI: | 10.1021/jp003849a | |||||||||
| Record Number: | CaltechAUTHORS:20150316-135714897 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150316-135714897 | |||||||||
| Official Citation: | Estimation of Vibrational Frequencies and Vibrational Densities of States in Isotopically Substituted Nonlinear Triatomic Molecules B. C. Hathorn and R. A. Marcus The Journal of Physical Chemistry A 2001 105 (23), 5586-5589 DOI: 10.1021/jp003849a | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 55803 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 16 Mar 2015 21:09 | |||||||||
| Last Modified: | 10 Nov 2021 20:50 |
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