Collisional vibrational relaxation processes

E.E.Nikitin, Optimal trajectory approach in the theory of collisional vibrational relaxation of diatomic molecules, in Dynamical Processes in Moleailar Physics, First EPS Southern European School of Physics, ed. G. Delgado-Barrio, Bristol and Philadelphia, Institute of Physics Publishing Ltd, 1993, p. 55... 

Tusa, Sulkes, and Rice have also obtained data for the zero-energy collisional relaxation of the levels l , P, 6a, and 12 of Rj aniline. In each case only a very few of the energetically accessible levels are coupled to the initial level by the coUision, so the selectivity of the vibrational relaxation process is retained in the zero-energy mechanism. 

Vibrational Relaxation. Stochastic processes, including vibrational relaxation in condensed media, have been considered from a theoretical standpoint in an extensive review,502 and a further review has considered measurement of such processes also.503 Models have been presented for vibrational relaxation in diatomic liquids 504 and in condensed media,505 using a master-equation approach. An extensive development of quantum ergodic theory for relaxation processes has been published,506 and quantum resonance effects in electronic to vibrational energy transfer have been considered.507 A paper has also considered the coupling between vibrational relaxation and molecular electronic transitions.508 A theory has also been outlined for the time-resolved electronic absorption spectrum of a molecule undergoing collisional vibrational relaxation.509... 

The possibility of deactivation of vibrationally excited molecules by spontaneous radiation is always present for infrared-active vibrational modes, but this is usually much slower than collisional deactivation and plays no significant role (this is obviously not the case for infrared gas lasers). CO is a particular exception in possessing an infrared-active vibration of high frequency (2144 cm-1). The probability of spontaneous emission depends on the cube of the frequency, so that the radiative life decreases as the third power of the frequency, and is, of course, independent of both pressure and temperature the collisional life, in contrast, increases exponentially with the frequency. Reference to the vibrational relaxation times given in Table 2, where CO has the highest vibrational frequency and shortest radiative lifetime of the polar molecules listed, shows that most vibrational relaxation times are much shorter than the 3 x 104 /isec radiative lifetime of CO. For CO itself radiative deactivation only becomes important at lower temperatures, where collisional deactivation is very slow indeed, and the specific heat contribution of vibrational energy is infinitesimal. Radiative processes do play an important role in reactions in the upper atmosphere, where collision rates are extremely slow. 

An aspect of 12(A) collisional energy transfer that complicated the data analysis is apparent in Fig. 4. While it was obvious that rotational energy transfer was much faster than vibrational transfer (e.g. compare the intensities of the t = 23 and t = 22 rotational lines in Fig. 4), vibrational energy transfer was fast enough to be detectable well before rotational thermaliza-tion of the initially excited vibrational level had been achieved (with the exception of I2-I2 collisions). Therefore, in constructing kinetic models of the relaxation processes, rotational and vibrational energy transfer could... 

Collision-induced vibrational excitation and relaxation by the bath molecules are the fundamental processes that characterize dissociation and recombination at low bath densities. The close relationship between the frequency-dep>endent friction and vibrational relaxation is discussed in Section V A. The frequency-dependent collisional friction of Section III C is used to estimate the average energy transfer jjer collision, and this is compared with the results from one-dimensional simulations for the Morse potential in Section V B. A comparison with molecular dynamics simulations of iodine in thermal equilibrium with a bath of argon atoms is carried out in Section V C. The nonequilibrium situation of a diatomic poised near the dissociation limit is studied in Section VD where comparisons of the stochastic model with molecular dynamics simulations of bromine in argon are made. The role of solvent packing and hydrodynamic contributions to vibrational relaxation are also studied in this section. 

Consider a closed system characterized by a constant temperature T. The system is prepared in such a way that molecules in energy levels are distributed in departure from their equilibrium distribution. Transitions of molecules among energy levels take place by collisional excitation or deexcitation. The redistribution of molecular population is described by the rate equation or the Pauli master equation. The values for the microscopic transition probability kfj for transition from ith level toyth level are, in principle, calculable from quantum theory of collisions. Let the set of numbers vr be vibrational quantum numbers of the reactant molecule and vp be those of the product molecule. The collisional transitions or intermolecular relaxation processes will be described by ... 

Chemical lasers are complex nonequilibrium molecular systems governed by an intricate interplay between a variety of chemical, radiative, and collisional relaxation processes. Many of their kinetic properties are reflected by the temporal, spectral, and power characteristics of the out-coupled laser radiation. For example, threshold time measurements and other gain experiments have provided detailed information on vibrational distributions of nascent reaction products. Another, more qualitative, example Single-line and simultaneous multiline operation indicate, respectively, whether the lasing molecules are rotationally equilibrated or not. Besides their practical applications, chemical lasers are widely used as means of selective excitation in state-to-state kinetic studies. On the other hand, many experimental and theoretical studies have been motivated by the wish to understand and improve the mechanism of chemical laser operation. 

Considerable experimental effort has been aimed at elucidating the collision-free unimolecular dynamics of excited molecules. Processes of interest include the dynamics of highly excited vibrational states, which have been reached by multiphoton absorption, and the various electronic relaxation processes that can occur in electronically excited states of moderate to large molecules, etc. The idealized collision-free limit is approached either by extrapolating data to the limit of zero pressure or by performing experiments in molecular beams. Alternatively, estimates of expected collisional effects are made by using collision cross-sections that are computed from hard-sphere collision rates. These estimates are then utilized to determine whether the experiments are performed in the collision-free domain. 

Such a mechanism has been proposed by Slanger and observed for the first time by Bondybey et al. in the case of diatomic molecules inbedded in rare-gas matrices. In their subsequent work, similar effects have been found for collisional processes in the gas phase. The vibrational relaxation of CO excited to the v = 3 and c = 2 levels of the A w state induced by collisions with He is more efficient by 4-5 orders of magnitude than in the ground-state CO + He system.Moreover, the form of the fluorescence decay from the o = 1 level observed under v = 2 excitation cannot be fitted if a direct v = 2 v=l relaxation path is assumed the induction time of the relaxed emission being much longer than the decay of the resonance fluorescence. 

A recent study on the rate of formation of products from excited hexafluoro-acetone in the presence of a vibrational relaxer and azoalkanes as triplet quenchers has produced data which the authors use to support the notion that vibrational relaxation in the singlet manifold is a multistep collisional process.75 76 The reaction between excited perfluoroacetone and ethane78 and the photochemistry of hexafluorobiacetyl vapour77 have also been discussed. 

On the basis of all the then available data, Campbell and Thrush proposed the following mechanism for the nitrogen afterglow. The A SJ state is populated by three body combination. Measurements of absolute afterglow intensities were combined with quenching data, as described for O - - NO H- M, to show that formation of A SJt by three body recombination accounted for about 50% of the total rate of recombination of N atoms. The vibrational energy distribution in A SJ is governed by the population process, by collisional redissociation, and by vibrational relaxation. Several types of collision-induced... 

On the theoretical front, it is possible to make a few simple assertions. We have already seen that a collisional component to the randomisation process may become faster the more dense are the states of the molecule. It is also obvious that the first order component will become slower as the states become further apart, but the molecular level density where this begins is not known a cut-off at about 1000 states per wavenumber has been suggested [82.S2] for intramolecular vibrational relaxation of isolated molecules in one kind of experiment. It is also obvious that there must be propensity rules for the occurrence of randomising transitions within any grain [81.P2] for example, transitions between states of... 

For larger molecules M two different collisional relaxation processes have to be distinguished collisions M 4- AB may transfer the internal energy of M to AB (mr rmolecular energy transfer), or may redistribute the energy among the different vibrational modes of M (m ramolecular transfer)... 

The process of vibrational excitation and deexcitation of a diatom in a collision with an atom represents a simplest example from the host of processes which are relevant to gas-phase chemical kinetics. Experimental techniques available now allow one to measure directly state-to-state energy transfer rate coefficients. Theoretically, it is possible to accomplish completely ab initio calculation of these coefficients. One can therefore, regard the existing models of the vibrational relaxation from a new standpoint as a means for helping to understand more clearly the dynamics of the energy transfer provided that all the models are related to a single fundamental principle. This is the Ehrenfest adiabatic principle as formulated by Landau and Teller in the application to the collisional vibrational transitions of diatomic molecules. 

The first, involving a spin change, is called inter system crossing, the second, conserving spin, is internal conversion. Since vibrational relaxation from highly excited vibrational states is relatively efficient (the separation of adjacent levels being small), collisional deactivation rapidly makes the reverse processes nonresonant. Both processes of (6.13) compete with fluorescence and reduce cpf. 

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