Intramolecular vibrational energy relaxation theory

However, the chromophoies used in SD experiments imdergo small changes in the solute intramolecular potential. Fmthermore, since they are large polyatomics with many intramolecular vibrational modes, vibrational energy relaxation is expected to be very rapid. Thus, AE = AE. In all theories and in most simulations of SD, with a few exceptions, the intramolecular contribution to AE is neglected. 

In this chapter we have reviewed the general theory of vibrational energy relaxation for a single oscillator coupled to a bath, and we have discussed the application of these results to three specific systems iodine in xenon, neat liquid oxygen, and W(CO)6 in ethane. In the first case the bath is the translations of the solute and solvent molecules, in the second case it is the translations and rotations of solute and solvent molecules, and in the third case it is the solute s other intramolecular vibrations and the translations of solute and solvent molecules. 

There is a general view that, for most molecules of intermediate and large sizes, decay rates may be described by a statistical theory, such as the RRK.M model. However, modern experiments on decay rates of single vibronic levels (SVL) often show serious deviations from statistical behavior, even at energies where fast intramolecular vibrational relaxation (IVR) is presumed to exist. This suggests that apparent statisticality in previous experiments may have resulted from poor resolution. However, further work is necessary, since few SVL experiments have been performed thus far. 

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. 

Pump-probe experiment is an efficient approach to detect the ultrafast processes of molecules, clusters, and dense media. The dynamics of population and coherence of the system can be theoretically described using density matrix method. In this chapter, for ultrafast processes, we choose to investigate the effect of conical intersection (Cl) on internal conversion (IC) and the theory and numerical calculations of intramolecular vibrational relaxation (IVR). Since the 1970s, the theories of vibrational relaxation have been widely studied [1-7], Until recently, the quantum chemical calculations of anharmonic coefficients of potential-energy surfaces (PESs) have become available [8-10]. In this chapter, we shall use the water dimer (H20)2 and aniline as examples to demonstrate how to apply the adiabatic approximation to calculate the rates of vibrational relaxation. 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

This asymptotic form is plotted in Fig. 5. A feature of BBM(d>) is that it decreases asymptotically with frequency to zero. If the atom B is involved in vibrational motion at frequency oo (Oq, the coupling with the bath through binary collisions is small and the slow dissipation is the stochastic manifestation of slow vibrational relaxation. The most significant feature of Eq. (3.17) is that the dependence in the exponent of Eq. (3.17) is equivalent to an exponent This is just the form of the Landau-Teller theory of vibration-translation (V-T) energy transfer in atom-diatom collisions, and this form is almost universally used to fit vibrational relaxation rates in such systems. This will be dealt with in more detail in Section V C. The utility of BBM(d>) is that it pertains to atom-atom collisions in which the atom B is bonded to the other atoms by arbitrary potentials. No assumptions have been made about the intramolecular motions, although the use of BBM(d)) implies linear coupling to the displacements of atom B. Grote et al. have alluded to the form of Eq. (3.20) for di = 0 in a footnote. 

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