Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory

Journal Article · Sun Dec 21 04:00:00 EST 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4903927· OSTI ID:22413330

Krasnoshchekov, Sergey V.; Isayeva, Elena V.; Stepanov, Nikolay F. ^[1]

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1. Chemistry Department, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.

• OSTI ID: 22413330
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 23 Vol. 141; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
74 ATOMIC AND MOLECULAR PHYSICS
ANNIHILATION
COUPLING
ENERGY LEVELS
EVALUATION
FERMI RESONANCE
HAMILTONIANS
INTERFERENCE
MOLECULES