Vibrational excitation Vibrationally adiabatic

A. H. Zewail For vibrational adiabaticity we must complete the study of correlation of reaction product distribution to the nature of the initial excitation (see reply to Prof. Marcus below). You may be interested to know that for a given energy within our pulse we see tra-... 

Figure 8.2. Vibrationally adiabatic potential for formaldehyde conversion in excited electronic (a) A A2 and (b) a3A2 states. The levels of the vt vibration are indicated. (From Jensen and Bunker [1982].)...

The idea that the vibrational enhancement of the rate is due to the attraetive potential for excited vibrational states of the reactant is closely related to the observation made long ago based on transition state theoiy [25,26]. Poliak [25] found that for vibrationally highly excited reactants the repulsive pods (periodic orbit dividing surface) is way out in die reactant valley, and the corresponding adiabatic barrier is shallow. Based on this theory one can explain why dynamical thresholds are observed in reactions with vibrationally excited reactants. The simplicity of the theory and its success for mostly collinear reactions has a real appeal. However, to reconcile the existence of a vibrationally adiabatic barrier with the capture-type behavior - which seems to be supported by the agreement of the calculated and experimental rate coefficients [23] -needs further study. 

The results of the present calculations that the zero-point vibrational energy of the reactants can pass smoothly into that of the intermediate complexes is entirely consistent with the basic postulate of Eyring s theory that activated complexes are created from the reactants in equilibrium states. It is easy to show that the vibrationally adiabatic model, coupled with the assumption that collision cross sections are the same for all vibrational levels, leads to the conclusion that there is a Boltzmann distribution between the vibrational levels in the activated state. Thus, consider the situation represented by the energy diagram shown in Fig. 6 two levels are shown for the initial and activated states— the ground level and the nth vibrationally excited... 

In reactions with vibrationally excited reagents additional shape effects may thns arise for two reasons [22]. First, the energies and form of the critical dividing surface for each vibrationally adiabatic state of the system will be different. Second, the physical shape of the reagent molecule may also depend on its vibrational states. In case of A + BC(v =... 

With all of the v, and v2 assignments made, some interesting trends in the fitted parameters kt and W7 appear. From Table 2, we see that the significant deviations of kt from unity are generally found for the highly bend excited transition state levels. Therefore, most of the breakdown of transition state theory appears to be associated with only those few levels. In addition, we see in Table 2 that W7 becomes larger as v2 is increased from 0 to 2 for a given value of v,. This is consistent with the discussion below Eq. (13) since the vibrationally adiabatic potentials become narrower as v2 increases (8,16). This same trend in W7 is even more apparent in the results discussed below for H + H2, 7=1, where both even and odd values of v2 are allowed. 

B. C. Garrett and D. G. Truhlar, WKB approximation for the reaction-path Hamiltonian Application to variational transition state theory, vibrationally adiabatic excited-state barrier heights, and resonance calculations,/. Chem. Phys. 81 309 (1984). 

When the frequency of a normal mode decreases dramatically (which corresponds to breaking of a chemical bond) during the reaction, the square bracket becomes negative. This means that an excitation of the bond, before the reaction, decreases the (vibrational adiabatic) reaction barrier and the reaction rate will increase. 

D.C. Clary and J.N.L. Connor. Vibrationally adiabatic distorted wave calculation for the rotationally excited reaction H+H2(v=0,/> ->... 

Figure 3.9 shows the resonance-mediated reaction mechanism. The HF(v = 3)-H VAP on the new PES is very peculiar with a deeper vibrational adiabatic well close to the reaction barrier and a shallow van der Waals (vdW) well. The ID wave function for the ground resonance state in Fig. 3.9 shows that this state is mainly trapped in the inner deeper well of the HF(v = 3)-H VAP with a considerable vdW character, whereas the excited resonance wave function is mainly a vdW resonance. Because of the vdW characters, these two resonance states could likely be accessed via overtone pumping from the HF(v = 0)-H vdW well. 

Fig. 14.10. The reaction H2 + OH H2O + H (within the vibrationally adiabatic approximation). Three sets of the vibrational numbers (i>oh- fHH) = fO. 0). 11.0). 10.1) were chosen. Note, that the height and position of the barrier depend on the vibrational quantum numbers assumed. An excitation of H2 considerably decreases the barrier height. The small squares on the right show the limiting values. According to T Dunning, Jr. and E. Kraka, from Advances in Mokcular Electronic Structure Theory , ed. T. Dunning, Jr., JAI Press, Greenwich, CN (1989), courtesy of the authors.

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