Multiphonon vibrational relaxation states

This relative ease of electronic relaxation as compared with multiphonon vibrational relaxation was qualitatively interpreted using phonon Franck-Condon arguments. Change in the vibrational state of the guest molecule requires in general very little change in the equilibrium positions of the lattice atoms, and this results in poor Franck-Condon factors for multiphonon vibrational relaxation. Electronic transitions, on the other hand, are often accompanied by considerable changes in electron density distri-... 

Matrix-isolated molecules exhibit a surprising facility for interelectronic relaxation processes. Vibrational relaxation in excited electronic states is often dominated by interstate cascades involving other electronic states. The rates of the individual steps of such a cascade are modulated by the intramolecular Franck-Condon factors and exhibit qualitatively an exponential dependence on the size of the energy gap expected by multiphonon relaxation theories. 

In rare gas crystals [77] and liquids [78], diatomic molecule vibrational and vibronic relaxation have been studied. In crystals, VER occurs by multiphonon emission. Everything else held constant, the VER rate should decrease exponentially with the number of emitted phonons (exponential gap law) [79, 80] The number of emitted phonons scales as, and should be close to, the ratio O/mQ, where is the Debye frequency. A possible complication is the perturbation of the local phonon density of states by the diatomic molecule guest [77]. 

Here, p = AEq o/ eff is the dimensionless energy gap between the upper state and the closest lower-energy state in units of the effective vibrational energy, Veff (cm ). C is the electronic factor, and S is the Huang-Rhys dimensionless excited-state distortion parameter in units of vibrational quanta v ff. As shown in Eq. (2), /c ,p is strongly dependent onp. Additionally, for a given reduced energy gap p, the introduction of even small excited-state distortions, S, can rapidly enhance the radiationless multiphonon relaxation rate such that this dominates the total 0 K relaxation. This model is easily extended to elevated temperatures, where substantial increases in may be observed [7,8]. 

Fig. 13.2 The relaxation of different vibrational levels of the ground electronic state of 2 in a sohd Ar matrix. Analysis of these results indicates that the relaxation of the v < 9 levels is dominated by radiative decay and possible transfer to impurities. The relaxation ofthe upper levels probably takes place by the multiphonon mechanism discussed here. (From A. Salloum and H. Dubust, Chem. Phys. 189, 179 (1994).)...

The observation that the reaction requires an induction time of tens of picoseconds can be used to differentiate between proposed mechanisms of how shock wave energy localizes to cause chemical reaction. This induction time is expected for mechanisms that involve vibrational energy transfer, such as multiphonon up-pumping [107], where the shock wave excites low frequency phonons that multiply annihilate to excite the higher frequency modes involved in dissociation. It is also consistent with electronic excitation relaxing into highly excited vibrational states before dissociation, and experiments are underway to search for electronic excitations. On the other hand, prompt mechanisms, such as direct high frequency vibrational excitation by the shock wave, or direct electronic excitation and prompt excited state dissociation, should occur on sub-picosecond time scales, in contrast to the data presented here. 

Most of the earlier theoretical studies dealt with the simplest relaxation mechanism where the internal vibrational energy of the guest is dissipated directly into the delocalized and harmonic lattice phonons. The common results of these works " were, as we mentioned above, predictions of a strong temperature dependence for the relaxation and an exponential decrease in the rates with the size of the vibrational frequency. The former result has its origin in stimulated phonon emission the conversion of vibrational energy into lattice phonons is greatly facilitated if some excited phonon states are thermally populated. The energy-gap law is due to the fact that the order of the multiphonon relaxation increases with the size of... 

The constants W (0) and a are dependent on the host and strength of the ion-lattice coupling but not on the specific rare earth ion or electronic state. Data for multiphonon relaxation in several different crystals and in a glass are summarized in fig. 35.7. Experimental points correspond to different electronic states and ions. The numbers in parentheses are the phonon energies which, based upon the temperature dependence of multiphonon rates and vibronic spectra, appear to be most important for relaxation. In general, the major contribution to multiphonon processes involves the highest energy vibrations... 

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