Fermi resonance, resonantly coupled

The Fermi resonance Hamiltonian consists of two terms. The first one, Ho, is the Dunham expansion, which characterizes the uncoupled system, while the second term, Hp, is the Fermi resonance coupling, which describes the energy flow between the reactive mode and one perpendicular mode. For the three systems, HCP CPH, HOCl HO - - Cl and HOBr HO + Br, the reactive degree of freedom is the slow component of the Fermi pair and will therefore be labeled s, while the fast component will be labeled /. Thus, the resonance condition writes co/ w 2c0s. More explicitly, for HCP the slow reactive mode is the bend (mode 2) and the fast one is the CP stretch (mode 3), while for HOCl and HOBr the slow mode is the OX stretch (X = Cl,Br) (mode 3) and the fast one is the bend (mode 2). The third, uncoupled mode— that is, the CH stretch (mode 1) for HCP and the OH stretch (mode 1) for HOCl and HOBr—will be labeled u. With these notations, the Dunham expansion writes in the form... 

Fermi resonance coupling between molecular vibrations leads to the interaction of these linear modes with each other, which gives rise to mixed waves. To obtain their dispersion law, we again introduce the intensity... 

The ideas fundamental to an understanding of infrared spectroscopy were introduced in this chapter. The electromagnetic spectrum was considered in terms of various atomic and molecular processes and classical and quantum ideas were introduced. The vibrations of molecules and how they produce infrared spectra were then examined. The various factors that are responsible for the position and intensity of infrared modes were described. Factors such as combination and overtone bands, Fermi resonance, coupling and vibration-rotation bands can lead to changes in infrared spectra. An appreciation of these issues is important when... 

A similar reasoning can be applied to the intensity of the peaks assigned to the methyl group, although it is usually more difficult to draw conclusions based on these peaks due to the Fermi resonance coupling [49] and because of their placement at an interface [49, 56, 57]. It has been observed that, when the substrate metal is Au, the... 

From an energetic point of view, the bands at higher wavenumbers can be assigned to the Ss rings. However, the intensities were found as ca. 0.65 1 (pure infected) instead of 2.8 1 which would be expected from the natural abundance of the isotopomers. These discrepancies were solved by applying the mathematical formalism utilized in the treatment of intramolecular Fermi resonance (see, e.g., [132]). Accordingly, in the natural crystal we have to deal with vibrational coupling between isotopomers in the primitive cell of the crystal [109]. 

In this section we shall give the connections between the nonadiabatic and damped treatments of Fermi resonances [53,73] within the strong anharmonic coupling framework and the former theory of Witkowski and Wojcik [74] which is adiabatic and undamped, involving implicitly the exchange approximation (approximation later defined in Section IV.C). 

Several studies of Fermi resonances in the absence of H bond have been made [76-80]. We shall account for this situation by simply ignoring the anharmonic coupling between the fast and slow modes (a = 0). The theory then describes the coupling between the fast mode and a bending mode through the potential Htf, with both of these modes being damped in the same way. Because aG = 0, the slow mode does not play any role, so that the total Hamiltonian does not refer to it ... 

Besides, we have shown elsewhere [22,23,71,72] that the term Fermi resonances is not fully adequate because noticeable perturbations of the vs (X-H Y) bandshape may be obtained in nonresonant cases—that is when the Fermi coupling takes place between the fast mode (of frequency 0)o) and a bending mode whose overtone frequency 2g>s may be very far from 0)o (see Section IV.B.3). 

As a consequence of the wide frequency range over which Fermi resonances may be effective, let us conclude that, in practical situations, several Fermi couplings may be involved in a spectrum, which must lead to puzzling spectral lineshapes. 

Fermi resonance is a common phenomenon in IR and Raman spectra. It requires that the vibrational levels be of the same symmetry species and that the interacting groups be located in the molecule so that mechanical coupling is appreciable. 

---