Fermi resonances exchange 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). 

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

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

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),...

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.

F. Fermi Resonance Within Adiabatic and Exchange Approximations... 

SD With Fermi Resonance, Beyond Adiabatic, Harmonic and Exchange Approximations [59]... 

Here, co is the angular frequency of the bending mode involved in the Fermi resonance. Next, within the exchange approximation [69], the coupling Hamiltonian (220) involved in the Fermi resonance is... 

In conclusion, note that the quality of the theoretical SD with respect to the experimental line shape is not as good for crystalline adipic acid as for the gaseous and liquid carboxylic acids studied above. The reason is that if Fermi resonances seem to be unavoidable in order to reproduce all features of the experimental line shapes and to conserve a good stability of the basic physical parameters when changing the temperature, however, the way in which the Fermi resonances are taken into account is very sentitive to the used adiabatic and exchange approximations [82]. 

The extraction of numerical values for the local densities of state at the Fermi energy from NMR resonance position and relaxation rate requires of course a number of hypotheses. Some of them (such as knowledge of the resonance position corresponding to zero total shift the breakup of the density of states into parts of different symmetry, etc.) already come into play when we try to parameterize data for the bulk metal [58]. Here we mention only the additional ones used to go to the local version of the equations. It is assumed that the hyperfine fields and exchange integrals are a kind of atomic properties that do not vary when the atom is put in one environment or another, whether it is deep inside the particle or on its surface. The approximation is probably reasonable when the atomic volume stays approximately... 

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