Statistical vibrational energy redistribution

Computational Study of Many-Dimensional Quantum Vibrational Energy Redistribution. I. Statistics of the Survival Probability. 

Statistical theories would require decreases in reaction rates that are orders of magnitude larger than the modest differences noted. The key vibrational energy redistribution leading to the second ot-cleavage is restricted to modes near the acyl function and involved importantly in the reaction coordinate. These acylalkyl diradical intermediates do not achieve complete statistical redistributions of vibrational energy throughout all vibrational modes, and only then lose CO. The experimental results indicate non-RRKM behavior. 

Another important effect on the Norrish type I/II ratio is the occurrence of intramolecular vibrational energy redistribution (IVR). For short timescale processes shorter than 10 ps (such as the Norrish type I reaction), IVR is yet far from completed as assumed by statistical theories such as RRKM. The opposite is true for Norrish type II reaction. The reaction only starts after 20 ps, pointing out that IVR seems to be necessary for the reaction. The longer the cai bon chain (the larger... 

In order to remove the need for explicit trajectory analysis, one makes the statistical approximation. This approximation can be formulated in a number of equivalent ways. In the microcanonical ensemble, all states are equally probable. Another formulation is that the lifetime of reactant (or intermediate) is random and follows an exponential decay rate. But perhaps the simplest statement is that intramolecular vibrational energy redistribution (IVR) is faster than the reaction rate. IVR implies that if a reactant is prepared with some excited vibrational mode or modes, this excess energy will randomize into all of the vibrational modes prior to converting to product. 

Progress has been made in these areas of study, but challenges remain. For example, the problem of vibrational energy redistribution in large molecules, although critical to the description of rates, statistical or not, and to the separation... 

It has been found that IVR is in the statistical limit for a series of molecules with the general formula (0X3)37—C C—H, where 7 is C or Si and X is H, D, or F (Kerstel et al., 1991 Gambogi et al., 1993). The initially excited state is a fundamental or first overtone of the acetylenic C—H stretch. The spectra for the R 1) transitions of the fundamentals and the R 5) transitions of the overtones for 3,3-dimethylbutane, (CH3)3CC=CH, and (trimethylsilyl) acetylene (CH3)3SiC CH are shown in figure 4.16. The solid lines are Lorentzian fits, Eq. (4.34), to the spectra. In the statistical limit of intramolecular vibrational energy redistribution a Lorentzian line shape is... 

Of course, a proper description of the fragmentation of a van der Waals molecule must be based on quantum mechanics and must account for the competition between intramolecular vibrational energy redistribution and reaction. However, approximate statistical theories of the reaction rate based on classical mechanics can be very useful in the construction of a physical picture of the relevant molecular dynamics. For that reason we examine how the classical mechanical theory of... 

Reactions occurring via the formation of a long-lived intermediate complex. The long-lived intermediate complex usually corresponds to the strongly vibrationally excited molecule AB (e). This complex does not decompose within the time interval, which exceeds at least several rotation periods. Many vibrations occur in the complex during this time interval, so that the validity of the statistical description of the vibrational energy redistribution can naturally be assumed. 

These simulations show how the efficiency of intramolecular vibrational (energy) redistribution (IVR) and formation of a statistical reaction intermediate are intimately linked to the hierarchy of timescales for intramolecular motions and structural transitions on the PES. Inefficient formation of the CHsOH- -F reaction intermediate arises from rapid separation of the CH3OH - - F products in comparison to the longer timescale for C 0---F bending to form the intermediate. 

Furthermore, intermediates that lie in relatively deep wells will have a lifetime that allows for complete redistribution of vibrational energy. This allows for statistical interpretation of rates for reaction coming out of these intermediates. Generally, this would imply that intermediates would scramble whatever stereo- or regiochem-ical information that preceded its formation. In fact, this is one of the major distinguishing features among related classes of reactions. For example, the S 2 reaction proceeds without an intermediate and so stereochemistry is inverted, while the S l... 

Some years ago it was conventional wisdom to assert that for aromatic hydrocarbons Sx - S0 internal conversion was an improbable process compared with Sx - 7i non-radiative decay. However, it has recently been demonstrated that in naphthalene and related compounds the internal conversion can be the dominant decay process, particularly for vibrationally excited species.494 It is of interest to note that calculated rates for the internal-conversion process in naphthalene could only be made to fit experimental values if some redistribution of vibrational energy occurred, but not complete statistical distribution among normal modes. 

For these fast decompositions, the statistical energy redistribution over the vibrational degrees of freedom of the molecule has no time to occur. Therefore, the statistical theory is not applicable to these unimolecular reactions. The theoretical description of such a fast dissociation of electronically excited molecules requires dynamic calculations, which are very complicated and need the knowledge of the specific features of the potential energy surface of excited electronic states. 

As a rule, at the starting momentum after irradiation, the energy of vibrational excitation is localized. The statistical energy redistribution over all vibrational degrees of freedom occurs with time. The time of statistical energy redistribution depends on the number of atoms and frequencies of normal vibrations in the molecule and is approximately equal to 10-12 s. Therefore, rate constants of decomposition of molecules can be calculated using the statistical theory. 

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