Adiabatic channel statistical calculations

Qei and Qvtbrot denote electronic and rovibrational partition fimctions, respectively. In general, the contributions of the internal degrees of freedom of A and B cancel in g and gviiroXA)gv iro((B ), such that only contributions Irom the external rotations of A and B and the relative motion, summarized as "transitional modes", need to be considered. Under low temperature quantum conditions, these can be obtained by statistical adiabatic channel (SACM) calculations [9],[10] while classical trajectory (CT) calculations [11]-[14] are the method of choice for higher temperatures. CT calculations are run in the capture mode, i.e. trajectories are followed Irom large separations of A and B to such small distances that subsequent collisions of AB can stabilize the adduct. 

Rather than using transition state theory or trajectory calculations, it is possible to use a statistical description of reactions to compute the rate constant. There are a number of techniques that can be considered variants of the statistical adiabatic channel model (SACM). This is, in essence, the examination of many possible reaction paths, none of which would necessarily be seen in a trajectory calculation. By examining paths that are easier to determine than the trajectory path and giving them statistical weights, the whole potential energy surface is accounted for and the rate constant can be computed. 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

Our application of this approach to the benzene ion dissociation in collaboration with Klippenstein was noted in Section II. When it can be carried out, this is by far the most satisfactory way currently available for extrapolation to E. The necessary VTST calculations, whether by way of the Marcus variational RRKM approach or other approaches (e.g., statistical adiabatic channel theory ) are laborious, involving the quantum chemical construction of large potential maps for the interaction of the separating fragments and extensive statistical calculations for the dissociation process. Application of this approach to a variety of interesting systems is one of the outstanding opportunities for future work. 

Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics 819... 

RECENT ADVANCES IN STATISTICAL ADIABATIC CHANNEL CALCULATIONS OF STATE-SPECIFIC DISSOCIATION DYNAMICS... 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Another advantage of the quantum calculations is that they provide a rigorous test of approximate methods for calculating dissociation rates, namely classical trajectories and statistical models. Two commonly used statistical theories are the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and the statistical adiabatic channel model (SACM). The first one is thoroughly discussed in Chapter 2, while the second one is briefly reviewed in the Introduction. Moreover, the quantum mechanical approach is indispensable in analyzing the reaction mechanisms. A resonance state is characterized not only by its position, width and the distribution of product states, but also by an individual wave function. Analysis of the nodal structure of resonance wave functions gives direct access to the mechanisms of state- and mode-selectivity. 

Figure 20 Overview of the calculated dissociation rates of HOCl as function of the excess energy. The solid line is the prediction of the statistical adiabatic channel model (SACM). Adapted from Ref. 67.

A.I. Maergoiz, E.E. Nikitin, and J. Troe, Statistical adiabatic channel calculation of accurate low-temperature rate constant for the recombination of OH radicals in their ground rovibronic state. J. Chem. Phys. 103,2083 (1995)... 

One version of the statistical adiabatic channel models, i.e. the maximum free energy method,20 was applied in the theoretical analysis of Fagerstrom et al,203 The calculated high-pressure limiting rate constant... 

The model of Quack and Troe,18 the statistical adiabatic channel model (SACM), is an approximate prescription for calculating the number of open adiabatic channels. A universal function g(R) is assumed for interpolating between all eigenvalues of reactants and products,19... 

Figure 5. Comparison of the observed product rotational state distributions (solid bars) and the results of two statistical models the statistical adiabatic channel model (SACM, open bars) and phase space theory (PST, hatched bars). The distributions are an average of those observed, or those calculated, at several excitation wavelengths in the region of (a) the 5tbu main band, (b) the 5voh combination band, (c) the 6vOH main band, and (d) the 6v0H combination band of HOOH. (Reproduced with permission from Ref. 41.)...

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