Relaxation, vibrational dephasing time

The observations of vibrational coherence in optically initiated reactions described above clearly show that the standard assumption of condensed-phase rate theories—that there is a clear time scale separation between vibrational dephasing and the nonadiabatic transition—is clearly violated in these cases. The observation of vibrational beats has generally been taken to imply that vibrational energy relaxation is slow. This viewpoint is based on the optical Bloch equations applied to two-level systems. In this model, the total dephasing rate is given by... 

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-... 

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. 

For the moment, assume that the VE picture is correct and inertial solvent motion causes negligible dephasing. Diffusive motion must be the primary cause of coherence decay. In the VE theory, the diffusive motion is the relaxation of stress fluctuations in the solvent by viscous flow. The VE theory calculates both the magnitude Am and lifetime z0J of the resulting vibrational frequency perturbations. A Kubo-like treatment then predicts the coherence decay as a function of the viscosity of the solvent. Figure 19 shows results for typical solvent parameters. At low viscosity, the modulation is in the fast limit, so the decay is slow and nearly exponential. Under these conditions, the dephasing time is inversely proportional to the viscosity, as in previous theories [Equation (19)]. As the viscosity increases, the modulation rate slows. The decay becomes faster and approaches a... 

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-... 

Since the pulse time is so short (see Sec. 3.6.2.2.3) one can coherently excite many vibrational modes at a time and monitor relaxation processes in real time. The first reported femtosecond time-resolved CARS experiments (Leonhardt et al., 1987 Zinth et al., 1988) showed beautiful beating patterns and fast decays of the coherent signal for several molecular liquids. The existence of an intermolecular coherence transfer effect was suggested from the analysis of the beating patterns (Rosker et al., 1986). Subsequent studies by Okamoto and Yoshihara (1990) include the vibrational dephasing of the 992 cm benzene mode. A fast dephasing process was found that is possibly related to... 

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... 

The interaction with the fluctuating surrounding leads to an additional broadening of the individual lines by vibrational dephasing [22-25]. Nonlinear vibrational spectroscopy allows one to separate the different couplings in the nonlinear time-resolved response following femtosecond vibrational excitation. In particular, the coherent vibrational dynamics can be isolated from processes of population relaxation [26[ and energy redistribution. 

In Section II, we describe briefly the primary collisional effects, vibrational and rotational relaxation and dephasing processes, and discuss their influence on the time evolution of an electronically excited molecular system. 

Fujisaki, H. Zhang, Y. Straub, J. E., Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins. J. Chem. Phys. 2006, 124, 144910. 

Fluorescence and stimulated emission on transitions (p = 0 -> p" > 0) lead to a fast rise of the population densities A (p") of high vibrational levels in the Sq state. This would result in a self-termination of the laser oscillation if these levels were not depopulated quickly enough by collisions. The relaxation of N(v") toward the thermal equilibrium population No(v") can again be probed by a weak visible probe laser. Polarization spectroscopy (Sect. 2.4) with femtosecond pulses allows one to separately determine the decay times tvib of population redistribution and the dephasing times [814]. 

There have been limited attempts to correlate the spectrum of the random force responsible for vibrational dephasing with induced spectra. In the fast modulation limitthe dephasing time (t) is determined by the amplitude (< 5vp>)2and relaxation time of the solvent-induced fluctuations in the oscillator frequency... 

The duration of the pump pulse is ultrashort but it needs to be long enough that it does not create vibrational coherence, cf. Chapter 7, in the solute itself. This is possible because the dephasing time of the solute is usually (but not always) shorter than the relaxation time of the solvation shell. 

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