Fermi resonance coupling

Figure 10. Pure Fermi coupling within or beyond the exchange approximation. Left column spectra were obtained from expression (110) of the spectral density /sf (m, V. = 0) ex (a) Resonant case A — 0. A — 60 cm-1 (b) nonresonant case A — 120cm 1 with A — 60 cm-1 (dotted line),...

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. 

The idea of having two distinct quasi-Fermi levels or chemical potentials within the same volume of material, first emphasized by Shockley (1), has deeper implications than the somewhat similar concept of two distinct effective temperatures in the same block of material. The latter can occur, for example, when nuclear spins are weakly coupled to atomic motion (see Magnetic spin resonance). Quasi-Fermi level separations are often labeled as Im p Fermi s name spelled backwards. 

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 ... 

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