Population relaxation

Oxtoby D W 1981 Vibrational population relaxation in liquids Photoselective Chemistry Part 2 (Advances in Chemical Physics 47) ed J Jortner, R D Levine and S A Rise (New York Wiley) pp 487-519... 

Jiang Y J and B G 1994 Vibrational population relaxation of perylene in its ground and exoited eleotronio states J. Phys. Chem. 98 9417-21... 

Interference in the Q-branch and population relaxation are ruled by the operator... 

One would prefer to be able to calculate aU of them by molecular dynamics simulations, exclusively. This is unfortunately not possible at present. In fact, some indices p, v of Eq. (6) refer to electronically excited molecules, which decay through population relaxation on the pico- and nanosecond time scales. The other indices p, v denote molecules that remain in their electronic ground state, and hydrodynamic time scales beyond microseconds intervene. The presence of these long times precludes the exclusive use of molecular dynamics, and a recourse to hydrodynamics of continuous media is inevitable. This concession has a high price. Macroscopic hydrodynamics assume a local thermodynamic equilibrium, which does not exist at times prior to 100 ps. These times are thus excluded from these studies. 

The determination of the laser-generated populations rij t) is infinitely more delicate. Computer simulations can certainly be applied to study population relaxation times of different electronic states. However, such simulations are no longer completely classical. Semiclassical simulations have been invented for that purpose, and the methods such as surface hopping were proposed. Unfortunately, they have not yet been employed in the present context. Laser spectroscopic data are used instead the decay of the excited state populations is written n (t) = exp(—t/r ), where Xj is the experimentally determined population relaxation time. The laws of chemical kinetics may also be used when necessary. Proceeding in this way, the rapidly varying component of AS q, t) can be determined. 

If the system under consideration is chemically inert, the laser excitation only induces heat, accompanied by density and pressure waves. The excitation can be in the visible spectral region, but infrared pumping is also possible. In the latter case, the times governing the delivery of heat to the liquid are those of vibrational population relaxation. They are very short, on the order of 1 ps this sort of excitation is thus impulsive. Contrary to a first impression, the physical reality is in fact quite subtle. The acoustic horizon, described in Section VC is at the center of the discussion [18, 19]. As laser-induced perturbations cannot propagate faster than sound, thermal expansion is delayed at short times. The physicochemical consequences of this delay are still entirely unknown. The liquids submitted to investigation are water and methanol. 

The system of dilute HOD in H20 is equally good for probing the structure and dynamics of water with an isolated chromophore (in this case the OD stretch), and it may be even better for two reasons. First, in this case the solvent is water, not heavy water and second, the excited state vibrational lifetime of the OD stretch is somewhat longer (1.45 ps [55]) than that of the OH stretch in HOD/ D20, providing a wider dynamic window before effects of local heating due to energy deposition from population relaxation occur. 

Thus, we generally expect only very small values of t to contribute significantly to the transition probability. There are some exceptions to this. Population relaxation between degenerate or nearly degenerate vibrational states is an example of this, since the pre-hop and post-hop momenta are nearly the same and the two branches of the combined trajectoiy can separate quite slowly in this case. ... 

Fermi resonances of the v0H=l state with over- and combination tones of modes in the fingerprint region are considered a key element determining the spectral envelope of the O-H stretching bands of cyclic carboxylic acid dimers. In principle, such Fermi resonances open up channels for population relaxation of the O-H stretching modes through the O-H bending... 

From the steady state fluorescence spectrum of indole in water a fluorescence quantum yield of about 0.09 is determined. Since the cation appears in less than 80 fs a branching of the excited state population has to occur immediately after photo excitation. We propose the model shown in Fig. 3a). A fraction of 45 % experiences photoionization, whereas the rest of the population relaxes to a fluorescing state, which can not ionize any more. A charge transfer to solvent state (CITS), that was also introduced by other authors [4,7], is created within 80 fs. The presolvated electrons, also known as wet or hot electrons, form solvated electrons with a time constant of 350 fs. Afterwards the solvated electrons show no recombination within the next 160 ps contrary to solvated electrons in pure water as is shown in Fig. 3b). 

Equation (33) assumes that IV// is large compared to 2J (i.e., no electronic and vibrational recurrences). In addition, Eq. (33) deals only with population dynamics Interferences between different Franck-Condon factors are neglected. These interferences do influence the rate, and the interplay between electronic and vibrational dynamics can be quite complex [25], Finally, as discussed by Jean et al. [22], Eq. (33) does not separate the influence of pure dephasing (T-T) and population relaxation (Ti). These two processes (defined as the site representation [22]) can have significantly different effects on the overall rate. For example, when (T () becomes small compared to Eq. (33) substantially overestimates the rate compared to... 

As a result of ion-phonon interaction, the population of the excited state decreases via nonradiative transition from the excited state to a lower electronic state. The energy difference between the two electronic states is converted into phonon energy. This process of population relaxation is characterized by a relaxation time, xj, which depends on the energy gap between the two electronic states, the frequencies of vibration modes, and temperature (Miyakawa and Dexter, 1970 Riseberg and Moos, 1968). At room temperature, the excited state lifetime is dominated by the nonradiative relaxation except in a few cases such as the 5Do level of Eu3+ and 6P7/2 level of Gd3+ for which the energy gap is much larger than the highest phonon frequency of the lattice vibrations. 

Figure 3.20. Population relaxation at A (0) = l,iVg(0) = 0, xB = oo, ka = 5kp, and ckaid = 1.0 (a) decay of A with its own lifetime xa = 2xj (thick straight line) accompanied by the intersystem crossing at kb = 5kD (dotted line), kb = kD (dashed-dotted line), and kj, = 0 (dashed line) (b) accumulation and dissipation of the initially empty state B, which decays through A faster, when kb is higher. (From Ref. 45.)...

If the excited molecules undergo disorienting collisions before emitting light, then the bpQ of various rank K relax at different rates T/c. The anisotropy of polarization % permits us to find the ratio between the population relaxation rate To and that of the alignment relaxation r2 ... 

Table 2.2. Cross-sections of population relaxation cto in collisions with an atom A for NaK DlTlu, (o = 17, J = 94) excited by 476.5 nm Ar+ laser line [24] and for K2, (v = 8, J = 73) excited by 632.8 nm He-Ne laser line [312]...

The Molecular Mechanisms Behind the Vibrational Population Relaxation of Small Molecules in Liquids... 

Mizutani and Kitagawa measured the time-dependent Stokes and anti-Stokes Raman intensities of the heme v4 band after photoexcitation and used the relative intensities to estimate its temperature and thermal relaxation dynamics (30). They found the population relaxation to occur biexponen-tially with 1.9 ps (93%) and 16 ps (7%) time constants. The dominant 1.9 ps population relaxation correlates with a 3.0 ps thermal relaxation, which is a factor of 2 faster than the ensemble averaged temperature relaxation deduced from the near-IR study of band III. The kinetic energy retained within a photoexcited heme need not be distributed uniformly among all the vibrational degrees of freedom, nor must the energy of all vibrational modes decay at the same rate. Consequently, a 6.2 ps ensemble-averaged estimate of the heme thermal relaxation is not necessarily inconsistent with a 3 ps relaxation of v4. 

Fortunately in a number of cases there is experimental information on these points from broad band pump/probe experiments when the anharmonicity A is larger than the linewidth but much smaller than the bandwidth 8(o of the laser. Then the 0-1 transition is seen as a bleaching signal and the 1-2 (66,67,71) as well as the 2-3 and often higher quantum number transitions (68,95) appear as new absorptions to an extent that depends on the pump intensity. A direct comparison of the total linewidths (1/T2) of these transitions, and the population relaxation times for the v = 1, v = 2 and perhaps higher levels can be obtained from such data. For N3 we found that ratio of the state to state relaxation from v = 2 to v = 1 was 1.8 times that for v = 1 to v = 0, not far from the harmonic value of 2 (50,95). However, the bandwidth of both transitions was roughly the same. 

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