Fermi resonances approximation

The Spectral Density of Pure Fermi Resonance Beyond the Exchange Approximation... 

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). 

Applying the adiabatic approximation, we restrict the representation of the Hamiltonian to the reduced base (89). Within this base, the Hamiltonian that describes an undamped H bond involving a Fermi resonance may be split into effective Hamiltonians whose structure is related to the state of the fast and bending modes ... 

Figure 7. The Fermi resonance mechanism within the adiabatic and exchange approximations. F, fast mode S, slow mode B, bending mode.

We shall give here a brief summary of our previous work [71,72] that was concerned with the introduction of the relaxation phenomenon within the adiabatic treatment of the Hamiltonian (77), as was done in the undamped case by Witkowski and Wojcik [74]. Following these authors, we applied the adiabatic approximation and then we restricted the representation of the Hamiltonian to the reduced base (89). Within this base, the Hamiltonian that describes a damped H bond involving a Fermi resonance may be split into effective Hamiltonians whose structure is related to the state of the fast and bending modes ... 

The exchange approximation when dealing with Fermi resonance (A O)... 

We may finally conclude that, with the purpose of comparison with experiments, one has to be careful and must remember the following (i) Two sub-bands of the same intensity may not be the consequence of a resonant situation 0, (ii) The frequency of each submaxima is governed by the three parameters co0, o>0. and A, and (iii) The frequency of the Evans hole, which appears between the two sub-bands, is given within the exchange approximation by the average frequency j ( 0 + 2o>0), but it is dependent on A within the full treatment of Fermi resonances. 

Figure 12. Hydrogen bond involving a Fermi resonance damping parameters switching the intensities. The lineshapes were computed within the adiabatic and exchange approximations. Intensities balancing between two sub-bands are observed when modifying the damping parameters (a) with y0 =0.1, and y5 = 0.8 (b) with ya = ys = 0.8 (c) with yB — 0.8 and ys — 0.1. Common parameters oto = 1, A = 150cm, 2g)5 = 2850cm-1, and T = 30 K.

Fermi resonance physchem In a polyatomic molecule, the relationship of two vibrational levels that have In zero approximation nearly the same energy they repel each other, and the eigenfunctions of the two states mix. fer-me, rez-3n-3ns fermium chem Asynthetic radioactive element, symbol Fm, with atomic number 100 discovered in debris of the 1952 hydrogen bomb explosion, and now made in nuclear reactors. fer-me-3m )... 

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