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Uniform semiclassical theory of avoided crossings

Uzer, T. and Noid, D. W. and Marcus, R. A. (1983) Uniform semiclassical theory of avoided crossings. Journal of Chemical Physics, 79 (9). pp. 4412-4425. ISSN 0021-9606. doi:10.1063/1.446326.

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A voided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of avoided crossings is presented in this article for the case where that behavior is generated by a classical resonance. A low order perturbation theory expression is used as the basis for a functional form for the treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals) obtained from classical trajectory data. The results are compared with quantum mechanical results for the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are described.

Item Type:Article
Related URLs:
URLURL TypeDescription
Marcus, R. A.0000-0001-6547-1469
Additional Information:© 1983 American Institute of Physics. Received 25 May 1983; accepted 23 July 1983. We are pleased to acknowledge the support of the present research by the U.S. Department of Energy under contract W -7405-eng-26 with the Union Carbide Corporation (at Oak Ridge) and by a grant from the National Science Foundation (at the California Institute of Technology). We thank Dr. J. N. L. Connor for his helpful comments.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-eng-26
Union Carbide CorporationUNSPECIFIED
Subject Keywords:polarizability; dimers; van der waals forces; helium; hydrogen; neon; nitrogen; hartree−fock method
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Other Numbering System NameOther Numbering System ID
Caltech Arthur Amos Noyes Laboratory of Chemical Physics6837
Issue or Number:9
Classification Code:PACS: 31.15.A-; 33.15.Kr; 34.20.-b
Record Number:CaltechAUTHORS:20120712-144920694
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Official Citation:Uniform semiclassical theory of avoided crossings T. Uzer, D. W. Noid, and R. A. Marcus, J. Chem. Phys. 79, 4412 (1983), DOI:10.1063/1.446326
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32396
Deposited On:12 Jul 2012 23:16
Last Modified:09 Nov 2021 21:27

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