Marcus, R. A. (2001) Brief comments on perturbation theory of a nonsymmetric matrix: The GF matrix. Journal of Physical Chemistry A, 105 (12). pp. 2612-2616. ISSN 1089-5639. doi:10.1021/jp004164d. https://resolver.caltech.edu/CaltechAUTHORS:20150316-145509289
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Abstract
Perturbation theory for nonsymmetric matrices is discussed for the GF matrix for molecular vibrations. As a simple extension of early results, two approaches are given: one a direct diagonalization of the nonsymmetric matrix, the other a presymmetrization. Presymmetrization of the GF matrix, well known for ΔF, is also described here for ΔG. It permits the use of standard perturbation theory for symmetric matrices. Application of the second-order expression for the ΔG case to the determination of the frequencies of many ozone isotopomers is given elsewhere.
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| Additional Information: | © 2001 American Chemical Society. Received: November 10, 2000; In Final Form: December 20, 2000. Published on Web February 10, 2001. It is a pleasure to acknowledge the support of the National Science Foundation. It is a pleasure to congratulate Bill Miller on the occasion of his 60th birthday. Bill’s skill, insight, and mastery of mathematics and physics applied to chemical dynamics and collisions are a pleasure to behold and serve as a remarkable trademark of his work. There is perhaps also an added personal touch, in that these brief comments on GF perturbation theory deal with a tiny corner of the classic book by Bill’s eminent mentor, E. Bright Wilson, Jr., whose contributions have been a source of stimulation to numerous researchers. | |||||||||
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| Issue or Number: | 12 | |||||||||
| DOI: | 10.1021/jp004164d | |||||||||
| Record Number: | CaltechAUTHORS:20150316-145509289 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150316-145509289 | |||||||||
| Official Citation: | Brief Comments on Perturbation Theory of a Nonsymmetric Matrix: The GF Matrix R. A. Marcus The Journal of Physical Chemistry A 2001 105 (12), 2612-2616 DOI: 10.1021/jp004164d | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 55815 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 16 Mar 2015 22:01 | |||||||||
| Last Modified: | 10 Nov 2021 20:50 |
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