Effective Hamiltonian for degenerate vibrational states in symmetric top molecules |
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| Affiliation: | 1. School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Xi’an Shaanxi, 710 072, PR China;2. Institute of Information Theory and Automation of the CAS, Pod Vodárenskou věží 4, 182 08 Prague 8, Czech Republic;3. The Flinders University of South Australia, GPO Box 2100, Adelaide, SA, 5001, Australia;1. Department of Chemistry, Payame Noor University, P. O. Box, 19395-4697, Tehran, Iran;2. Departmen of Chemistry, North Tehran Branch, Islami Azad University, Po. Box: 1913674711, Tehran, Iran;3. School of Engineering Science, College of Engineering, University of Tehran, P. O. Box 11365-4563, Tehran, Iran;4. Department of Agriculture, Jouybar Branch, Islamic Azad University, Jouybar, Iran |
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| Abstract: | A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C3v or D3 molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels). |
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