Fermi resonances dynamics

Ezra G S 1996 Periodic orbit analysis of molecular vibrational spectra-spectral patterns and dynamical bifurcations in Fermi resonant systems J. Chem. Phys. 104 26... 

The standard effective spectroscopic Fermi resonant Hamiltonian allows more complicated types of behavior. The full three-dimensional aspects of the monodromy remain to be worked out, but it was shown, with the help of the Xiao—KeUman [28, 29] catastrophe map, that four main dynamical regimes apply, and that successive polyads of a given molecule may pass from one regime to another. 

Note that Marechal [48,75] proposed an original peeling-off procedure, but in a very different perspective, whose purpose is to eliminate from a given experimental spectrum the features brought by multiple Fermi resonances, thus revealing the intrinsic informations on the hydrogen bond dynamics. 

Fermi resonance, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 710-711 Fermi s Golden Rule ... 

DCN in Two Lowest-Lying Singlet Excited States Effect of Fermi Resonances on Spectra and Dynamics. 

It has been shown recently that the vibrational spectra of HCP [33-36], HOCl [36-39], and HOBr [40,41] obtained from quantum mechanical calculations on global ab initio surfaces can be reproduced accurately in the low to intermediate energy regime (75% of the isomerization threshold for HCP, 95% of the dissociation threshold for HOCl and HOBr) with an integrable Fermi resonance Hamiltonian. Based on the analysis of this Hamiltonian, this section proposes an interpretation of the most salient feature of the dynamics of these molecules, namely the first saddle-node bifurcation, which takes place in the intermediate energy regime. 

Let us first neglect the Fermi resonance and analyze the dynamics of the uncoupled systems described by the Dunham expansion alone [Eq. (24)]. Because of the resonance condition co/ 2c0s, quantum states are organized in clumps, or polyads. Each polyad is defined by two quantum numbers, namely the number v of quanta in the uncoupled degree of freedom and the so-called polyad number P ... 

To conclude this analysis based on the Fermi resonance Hamiltonian, let us mention that HOCl, behaves very much like HOBr. Indeed, Fig. 10b of Ref. 36 shows that for this molecule the saddle-node bifurcation SNl takes place at P = 21.8, (for v = 0), the period-doubling bifurcation PD occurs at P = 24.6, and the second saddle-node bifurcation SN2 takes place at around P = 38, very close to the dissociation threshold. In contrast, the dynamics of HCP is somewhat simpler, in the sense that the first saddle-node bifurcation SNl is indeed observed at P = 14.3, but PD and SN2 do not take place (see Fig. 13 of Ref. 35 or Fig. 10a of Ref. 36). 

Most of the bifurcations, which take place in the high-energy regime, are however not reproduced by the Fermi resonance Hamiltonian, essentially because they result from the superposition of the 1 2 Fermi-resonance and higher-order ones. In order to gain information on the dynamics close to the reaction threshold, one therefore has to analyze the dynamics on the PES by... 

The relatively large number of experiments on vibrational relaxation compared to other means of access to the molecular dynamics (such as translational, rotational, or electronic relaxation) stems from the richness of vibrational structure. A molecule composed of N atoms presents 3N — 6 vibrational modes and still only three translational degrees of freedom. In addition the vibrational overtone manifold cannot always be ignored due to accidental (strongly size-dependent) degeneracy and Fermi resonance with fundamental modes. 

Although the spectroscopy of combination modes in molecular crystals has been studied in some detail, information on the decay times, and hence the dynamics, of these states is available only in a few cases and specifically in the Vi-2v2 region of CSj, NjO, and COj, three almost isomorphous crystals. Nevertheless the dynamics of the bound states, as exhibited by the temperature variation of their relaxation times, varies dramatically from one crystal to another. Thus while the decay time of the 2v2 mode of N2O is practically independent of temperature, the relaxation times of the two bound states 2 andfi" associated with the v,2v2 Fermi resonance in CO2 show a very strong temjjerature dependence (see Fig. 7). 3,144... 

Agranovich, V. M. (1983). Biphonons and Fermi resonance in vibrational spectra of crystals. In Spectroscopy and Excitation Dynamics of Condensed Molecular Systems. Edited by V. M. Agranovich and R. M. Hochstrasser. North-Holland, Amsterdam, pp. 83-138. 

High resolution spectroscopic measurements in the gas phase yield the most detailed structural information possible. For example, measurements of weakly-bound complexes in the far-IR [24, 25] and IR [26, 27] have provided the most exact information on their structure and steady-state dynamics. Of course, a much higher level of theory must be used than was presented in section Bl.2.2.1. Quite often the modes are so strongly coupled that all vibrational degrees of freedom must be treated simultaneously. Coriolis coupling and symmetry-allowed interactions among bands, i.e. Fermi resonances, are also quite significant, and must be treated explicitly. Direct measurement of the low frequency van der... 

It was also found, from the quantum calculations, that the short time dynamics (t < 0.5 psec) of the n = 3 overtone is accurately reproduced by reduced four- and fivemode models. In addition, only a small subset of states for these modes are significantly populated during the early decay of the = 3 overtone, even though the total density of states is very large. In the next section a Fermi resonance model is presented for the flow of energy from the excited C—H bond. 

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