Vibrational relaxation dephasing

Fig. 3.15, The CARS spectrum rotational width versus methane density for various values of parameter y (1) y = 0, (2) y = 0.3, (3) y = 0.5, (4) y = 0.7, (5) y = 0.75, (6) y = 0.9, (7) y = 0.95, (8) y = 1. Curves (4) and (6) are obtained by subtraction of the dephasing contribution from the line width calculated taking account of vibrational broadening. The other dependences are found assuming purely rotational broadening (vibrational relaxation neglected).

In [162] experiments on methane provided a linear pressure dependence of the contour width. This made it possible to find the dephasing cross-section and to discriminate between contributions of rotational and vibrational relaxation to the contour width. This was done under the above-mentioned simplifying assumption that they are additive. (Let us note that processing of experimental data on linear molecules was always performed under this assumption.) The points found by this method are shown in Fig. 3.15, curves (4) and (6). 

Valiev-Ivanov model 219, 275 vibrational broadening 123 vibrational dephasing 111, 113-15, 123 vibrational relaxation, and angular momentum relaxation 92 vibrational transition, adiabatic dephasing 92... 

From Eqs (7.5) and (7.6) we can deduce that the pure dephasing rate is Yio( ) = 0.2ps 1 and the vibrational relaxation takes place in the timescale of 0.5 ps for the 100-cm 1 mode. More results related to vibrational relaxation have been reported by Martin group [1-5], In this chapter we choose 0.3 ps for the 100-cm-1 mode, and the vibrational relaxation rates for other modes are scaled with their vibrational frequencies. 

From the above discussion, we can see that vibrational relaxation plays a very important role in ultrafast phenomena. In this appendix we shall present a model that can describe vibrational relaxation and dephasing (especially pure dephasing). Suppose that... 

Eq. (II.4) play different roles in vibrational relaxation and dephasing and in spectral shifts. The above treatment for vibrational relaxation can only be applied to the case where the system oscillator frequency 00 is not too much larger than the bath mode frequencies coFor the case where 00 00 multi-... 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

Coherent dissociation Geminate recombination Dephasing Proton transfer Electron transfer Vibrational relaxation 8arrierless reactions Bimolecular reactions Ionic reactions Solvation dynamics Friction dynamics Polarization (kerr)... 

A more general approach is required to interpret the current experiments, Jean and co-workers have developed multilevel Redfield theory into a versatile tool for describing ultrafast spectroscopic experiments [22-25], In this approach, terms neglected at the Bloch level play an important role for example, coherence transfer terms that transform a coherence between levels i and j into a coherence between levels j and k ( /t - = 2) or between levels k and l ( f - j - 2, k-j = 2) and couplings between populations and coherences. Coherence transfer processes can often compete effectively with vibrational relaxation and dephasing processes, as shown in Fig. 4 for a single harmonic well, initially prepared in a superposition of levels 6 and 7. The lower panel shows the population of levels 6 and 7 as a function of time, whereas the upper panels display off-diagonal density matrix ele-... 

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

Isotropic scattering In addition to the dephasing time T2, the correlation time rc of the purely vibrational relaxation process can be measured, providing quantitative information on the question of homogeneous/inhomogeneous line broadening. 

Intense picosecond pulses from free electron lasers, which are essentially freely tunable, have been used to study vibrational relaxation and dephasing of intense C=0 modes of metal carbonyls in the 2000 cur1 regime (73,75,98)... 

With IR light sources like this one, a technology is available which, in terms of day-to-day reliability and long-term and short-term stability, is entirely comparable with Ti sapphire regenerative amplifiers. As shown in this article, it was possible to perform femtosecond experiments on all kinds of condensed phase phenomena involving vibrational transitions (such as energy relaxation, dephasing, spectral diffusion, coupled systems) with essentially the same facility and accuracy as can be achieved in visible and near-infrared experiments. 

Hamm P. Lim M, Hochstrasser RM. Vibrational relaxation and dephasing of small molecules strongly interacting with water. In Elsaesser T, Fujimoto JG, Wiersma DA, Zinth W, eds. Ultrafast Phenomena. Berlin Springer-Verlag, 1998 514-516. 

Time resolved coherent anti-Stokes Raman spectroscopy of condensed matter has been recently extended to the femtosecond domain allowing direct and detailed studies of the fast relaxation processes of molecular vibrations in liquids. The vibrational phase relaxation (dephasing) is a fundamental physical process of molecular dynamics and has attracted considerable attention. Both experimental and theoretical studies have been performed to understand microscopic processes of vibrational dephasing. Developments in ultrafast coherent spectroscopy enables one now to obtain direct time-domain information on molecular vibrational dynamics. Femtosecond time-resolved coherent anti-Stokes Raman scattering measuring systems have been constructed (see Sec. 3.6.2.2.3) with an overall time resolution of less than 100 fs (10 s). Pioneering work has been per-... 

The use of an FPE, such as that developed in Section IIB, is not appropriate for the study of all aspects of vibrational relaxation, such as dephasing. Nevertheless it is not unrealistic to expect that the effective potential ( (P) of Eq. (2.26) and the relative friction of Eq. (2.34) will also characterize an appropriate three-dimensional formulation. In one dimension the energy diffusion equation of Zwanzig has been found to givea good... 

In Eqs (10.180) the terms that depend explicitly on time originate from cos((yZ)e " = (1/2)(1 + exp( 2z(z /)) and oscillate with frequency 2(7>. The other rates in the problem are the detuning frequency and the thennal rates (population relaxation and dephasing). For optical transitions these rates are usually much smaller than a>, for example typical room temperature vibrational relaxation rates are of order lO s while vibrational frequencies are in the range IO s . The effect of the fast tenns, exp( 2zrotating wave approximation (RWA)." Under this approximation Eqs (10.180) become... 

All theoretical studies on benzoic acid dimer underlined the need for a multidimensional potential surface. These studies have investigated the temperature dependence of the transfer process They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al. [26] have calculated the temperature dependence of the spin-lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be... 

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