Vibrational relaxation definition

Parker [198] has compared his classical theory with the experimental results on vibrational relaxation of hydrogen and deuterium. He finds satisfactory agreement for collisions with argon and krypton, but definite... 

From this state, ring strain facilitated predissociation to a "biradical-like" transition state [135] or vibrational relaxation (k ) to S may occur. It is also conceivable that transition state [135] could be produced directly from S °. Alternatively, molecules in the S ° state could intersystem cross (kST) to the triplet manifold (T ). For 2-alkylidenecyclobutanones, reactivity is manifested in isomerization about the exocyclic carbon-carbon double bond, while for the saturated cyclobutanone derivatives studied, definitive evidence for solution-phase reactivity is not available. If analogy is again made to the vapor-phase photochemistry of cyclobutanone [21], reactivity could conceivably result in decarbonylated products. Indeed, preliminary evidence has been obtained from sensitization experiments employing m-xylene as triplet sensitizer that decarbonylation of a saturated cyclobutanone is enhanced by selective population of its state (35). ... 

The competition between intramolecular vibrational relaxation and chemical reaction has been discussed in terms of the applicability of transition state theory to the kinetic analysis [6], If the environment functions mainly as a heat bath to ensure thermalization among the vibrational modes in the excited complex, then transition state theory is a good approximation. On the other hand, when the reaction is too fast for thermalization to occur the rate can depend upon the initial vibronic state. Prompt reaction and prompt intersystem crossing are, by definition, examples of the latter limit. 

In a stochastic approach the frequency-depiendent friction appears in the definition of the energy dependence of the relaxation rate P(E), defined by Eq. (4.12), and is evaluated for a Morse potential by Eq. (4.14). In this section the applicability of these relationships and the friction kernel B(d)( )) of Eq. (3.27) is tested in a variety of approaches for the case of u = 1, a diatomic. The use of frequency-dependent friction in the evaluation of D(E) for a system with many degrees of freedom is an area of ongoing activity. While many of the features of a stochastic approach to vibrational relaxation are found in inelastic scattering theories or master equation kernels, it is the characteristic of... 

Equation (6.70) results from Eq. (6.60) together with the definition of the vibrational relaxation rate kyg E) = dE/dt. 

By definition, this process involves no change in spin of the excited electron, only a conversion of excess electronic energy to excess vibrational energy. At the end of this process, the molecule arrives at the EVq sublevel of the Si state. The process is as rapid as vibrational relaxation indeed, if one assumes that electronic energy and vibrational energy are instantly interconvertible, then the slowest part of this process is vibrational relaxation from the EVn sublevel of the Si state to its EVq sublevel. 

The experimental results for the relaxation of internal energy in polyatomic gases have been well summarised in various places, see e.g. [61.C 77.L1]. The basic observations are as follows rotational relaxation rates appear to be commensurate with the collision rate itself and are in general rather poorly characterised, partly because of their great speed, but also because of the intrinsic ambiguity in their definition as I have just shown vibrational relaxation rates, on the other hand, are quite well defined and reasonably well understood [59.H 77.L1], and take place on time scales of from a few tens to a few thousands of collisions. 

Fluorescence Resonance Energy Transfer (FRET), Fig. 1 (a) Jablonski diagram illustrating FRET and related processes, including excitation of the donor, radiative (solid line) and non-radiative (dashed lines) relaxation on the donor and acceptor, vibrational relaxation (short curved arrows), and transitions associated with FRET (dotted lines). Processes that determine the FRET efficiency are indicated in bold, (b) Illustration of spectral overlap between Cy3 (donor) emission and Cy5 (acceptor) absorption, (c) Definition of the angles used to calculate... 

The vibrational relaxation time obtained corresponds to some average value of temperature T and pressure p, Tg < T < Ti, p2 < p < Pi Since Tyib markedly depends on T this may lead to inaccuracies due to unprecise definition of T. 

Whereas absorption spectra can be obtained at a given temperature via Monte-Carlo t q)e simulations, the reach of equilibrium in an excited state of an isolated cluster is less obvious, and even less is the definition of a relevant temperature. In any case, the final state may be strongly dependent on the excitation process. Here we will ignore the vibrations of the Na(3p)Arn cluster. We assume a Franck-Condon type approximation and that emission takes place from relaxed equilibrium geometry structures on the Na(3p)Arn excited PES. The Einstein coefficients of the lines of emission towards the ground state at energy AE are given by... 

In this case, as with all other hydrogen halide lasers, only P branch transitions are observed, indicating that only partial inversion is attained. The vibrational transitions observed are 1 - 0 and 2 -+ 1. There is a definite threshold flash energy, below which no laser action is observed because the chain decomposition is not fast enough. The development in time of the emission spectrum was observed and discussed in terms of rotational relaxation. 

These reactions are analogous to those of HSO, as proposed by Lovejoy et al. (20). The NO data were fitted by a non-linear least squares routine to an analytical solution. This yielded values for k4, the branching ratio of reaction (4) to give NO and the overall yield of NO. The fitted values were not definitive since some of the NO appears to be produced vibrationally excited, and relaxation may not have been complete on the time scale of the experiment Values of k4 fell in the range (8 4) x 10-12 cm3 molec-1 s-1. The overall yield of NO produced was around 1.5 per CH3S, and we suspect that the yields may actually be close to 1.0 for both reactions (2) and (4). Further experiments are in progress to elucidate the reaction sequence. More detailed accounts of both the 02 and NC reactions will be published shortly (21). 

To measure the departure from an Arrhenius-like behavior and to decrease the ambiguity in the use of fragility as a quantitative probe of the liquid state, the so-called F1/2 metric has been introduced. It is defined as the value of Tg/T at the midway of the relaxation time on a log scale, specifically, between the high-temperature phonon vibration lifetimes 10 14 s and the relaxation time at Tg, namely, i Tg), which is generally taken to be 102s [37], An advantage of this definition is that the midway values for the relaxation time are readily and accurately accessible by viscosimetric and by dielectric measurements [37,43], Let T /2 be temperature at which x = 10 6s. Now define a quantity Fx /2 as follows [37,43] ... 

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