Rigorous vibrational Fermi resonance criterion revealed: two different approaches yield the same resultстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 17 июля 2020 г.
Аннотация:Molecular vibrational resonances are manifest by abnormally small energy differences in denominators of anharmonic constants derived within the second-order vibrational perturbation theory (VPT2), or in abnormally large coefficients Ξ of unitary transformation generators in the canonical Van Vleck perturbation theory (CVPT). A quantitative measure of the vibrational resonance can be derived by assuming the perturbation parameter to be a complex variable λ, and the numerical analysis of the diverging high order Rayleigh-Schrödinger perturbation theory (RSPT) expansions for closely spaced states. The location of branch points for complex values of λ within the unit circle serves as the definitive evidence for a resonance. In practice, RSPT series for diverging resonant states can be treated by resummation using quadratic Padé-Hermite approximants. The critical values of λ can be further found and checked against the condition λ ≤ 1. A comparative analysis of selected resonances for some molecules (H2O, HDO, H2S and H2CO) revealed a threshold value of Ξ* = 0.076 that is equivalent to the RSPT parameter λ ≤ 1. The fundamentally different approach based on the polyad analysis of the resonance vectors spanning the (3Nat − 7)-dimensional subspace for the ethylene molecule led to nearly the same value for the resonance criterion.