Anharmonic coupling theory Fermi resonance

As a consequence of the above equations, the full Hamiltonian describing the fast mode coupled to the H-bond bridge (via the strong anharmonic coupling theory) and to the bending mode (via the Fermi resonance process) may be written within the tensorial basis (222) according to [24] ... 

Fig. 10. Fermi resonance within the strong anharmonic coupling theory.

This section now deals with H-bonded species, where together with the strong anharmonic coupling and the quantum indirect damping, Davydov coupling and Fermi resonances may occur, that is, centrosymmetric H-bonded cyclic dimers the theory of which, for situations without damping,was first performed by Marechal and Witkowski [18]. 

Figure 19. Davydov coupling and 1 Fermi resonance, for centrosymmetric cyclic dimer within the strong anharmonic coupling theory. (The subscripts 1 and 2 refer, respectively, to the a and b moieties of the centrosymmetric cyclic dimer).

Another manifestation of vibrational anharmonicity occurs in Fermi resonance [8]. When two vibrational states of the same overall symmetry are accidentally degenerate, they can become strongly mixed by the anharmonic coupling terms between them. Their energies may be repelled considerably (in the language of degenerate perturbation theory), and the intensities of the spectroscopic transitions to these levels may be redistributed by the mixing. 

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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