Vibrational lifetime and Fermi resonance in polyatomic molecules

Abstract

The energy decay of CH-stretching modes of the molecules CHCl 3 ,CH 2Cl 2, CH 3COCH 3, CH 3OH, and CH 3CH 2OH is measured in the liquid state. The observed lifetime very between 1.5 and 65 ps. A theoretical analysis points to the importance of Fermi resonance in the vibrational relaxation process. Quantitative comparison between theory and experiments is presented for the individual molecules. The strong variation of the lifetime for CH-stretching modes of various molecules may be understood if several effects are taken into account. First and most important is the influence of the Fermi resonances. Without the anharmonic mixing of the initial state, the overtone of the CH-bending modes and/or a higher order combination tone, one would predict lifetimes which are more than an order of magnitude longer than the observed lifetimes. This effect has been discussed earlier in detail for methylhalides by Zygan-Maus and Fischer [11] and, more recently, it has been incorporated in elaborate discussions for triatomic molecules like CO 2 by several authors [12]. A second factor to be considered for the interpretation is the rapi energy redistribution between different CH-stretching states was found theoretically to be faster than the further decay process by an order of magnitude [6, 11]. Experimentally, this effect was verified in this note for CH 2Cl 2 by the observation that the decay time was the same regardl whether the symmetric or the asymmetric CH-stretching mode was excited. This effect leads to a lengthening of the observed decay process. There is a bottleneck effect. Finally, we have shown that location and width of the final state are important parameters for the interpretation of the depopulatio lifetime. The empirical determination of these effects is not free of uncertainties. Very strong Fermi resonance can lead to rapid energy exchange during the exc process. In this case there is no bottleneck effect and it is difficult to detect the pathway of the energy flow. If the Fermi resonance is weak it is to assess quantitatively its magnitude, because — independently of Fermi resonances — there exist small intensities and shifts of the combination m overtones due to diagonal anharmonicities. Nevertheless, the examples show that eq. (15) provides a useful estimate. While the lifetime depends critica upon the individual molecule, some general predicitions are possible. For instance, if the CH-bending modes are high, around 1450 cm −1, there wil strong Fermi resonance of the overtones with the CH-stretching modes and the lifetime would be short.