Fermi resonance interaction

It is presently hard to give a definitive explanation of the unexpected appearance of the spectrum of slightly deuterated NMA, although one is tempted to suspect a Fermi resonance interaction giving rise to an Evans hole centered around 2300 cm-1. 

Fig. 9. The overtone spectrum of CHD3 in the gas phase at Ai ch 5. Note the well resolved P. Q, R branches. The presence of two Q branches is due to Fermi resonance interaction.

Overtone and combination bands are usually weak in comparison with the fundamentals. However, when the frequency of such a combination falls close to that of another fundamental of the same symmetry species, a Fermi resonance interaction occurs, which results in a sharing of intensity between the two modes as well as frequency shifts in both. This occurs, for example, in the interaction between the NH stretch mode, Pa, and overtones or combinations of amide II modes, (Miyazawa, 1960b). From measurements on the frequencies and intensities of the observed bands, pa and Pb. it is possible to obtain the frequencies of the unperturbed fundamental, p, and combination, p. The relation is given by (Miyazawa, 1960b)... 

The main perturbing influence on the amide I mode is TDC, although Fermi resonance interactions can occur in special cases (Dellapiane et al., 1980). For the structures analyzed thus far by normal-mode analyses, the calculated frequencies obtained with such coupling and their observed counterparts are collected together inTable XXXV. While there are common special features within structural groupings, small observed differences result from real structural differences, showing that generalized perturbation treatments (Miyazawa and Blout, 1961 Krimm, 1962) cannot provide a correct description of the actual situation. 

These expressions define the dispersion laws of normal modes arising from linear plane waves due to the nonlinear Fermi resonance interaction. It is important that the nonlinearity leads to the dependence of the dispersion laws on the intensity I of vibrations. Such a dependence gives rise to soliton solutions discussed in the following sections. 

Bistable energy transmission through the interface with Fermi resonance interaction... 

Interesting phenomena can take place in systems with Fermi resonance under the influence of an external electromagnetic field. Here we consider one example of such behavior - bistable energy transmission through the interface with the Fermi resonance interaction (14). To make the calculations easier, we shall consider the following simplified model. Let a monomolecular layer of a molecules be deposited on the plane surface of a crystal made of b molecules. For the ID case such a system is shown in Fig. 9.7. 

Now we have a driving force E(t) = Eq exp(—iu t) so that the molecule a oscillates with this laser field frequency u>l and due to the Fermi resonance interaction across the interface this leads to oscillations of molecules b with frequency 2ujl. As a result, we obtain an algebraic system of equations for the amplitudes A, B, Bu... ... 

The torsional motion of the two 0-H bonds relative to one another abont the 0-0 bond leads to a set of four torsional levels r= 1, 2, 3, 4 in order of ascending energy, within each fundamental torsional state n. The molecule exhibits also a cascading set of = 2 Fermi resonance interactions that connects the torsional levels (n, T ) -> ( 1, r). Moreover there is a Coriohs interaction between 03= 1 n = 0(l) and the ground vibrational v = On = 2(3) states. Hereby the torsional levels of different symmetry are coupled. 

For polymethylene chains, the origin of these complexities may be described in terms of the appropriate binary combinations involving methylene bending modes interacting with the infrared or Raman-active symmetric stretching fimda-mental (154,155). Two levels of Fermi resonance interactions, intramolecular and intermolecular, need be distinguished, however. Unexpectedly, the Raman-active bands observed for different intermolecular packings are quite different (Fig. 16). 

W,2 Fermi resonance interaction constant. Compare [55Tow, 82Pap]... 

Rotational constants, centrifugal distortion constants, rotation-vibration interaction constants, -type doubling constants, isotopic masses, Fermi resonance interaction constants, and references for structural data... 

We shall also discuss a perturbation which occurs between the combination band V2 + V5 and the fundamental V4. This is a Fermi resonance interaction and causes the combination band to be displaced from its normal position. 

In transition metal hydridocarbonyl complexes, Fermi resonance interaction occurs between the carbonyl and metal-hydride stretching vibration. Hence, a significant shift of the CO stretching frequency may be observed on deuteration of a complex, e.g. 30cm , and anomalous vm-h/i m-d ratios are observed instead of being [Pg.414]

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