Statistical Adiabatic Channel Models

Quack M and Troe J 1998 Statistical adiabatic channel model Encyclopedia of Computational Chemistry vo 4, ed P von Rague Schleyer et a/(New York Wiley) pp 2708-26... 

Quack M and Troe J 1975 Complex formation in reactive and inelastic scattering statistical adiabatic channel model of unimolecular processes III Ber. Bunsenges. Phys. Chem. 79 170-83... 

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. 

SACM (statistical adiabatic channel model) method for computing reaction rates... 

For highly exothermic SN2 reactions, which have a central barrier significantly lower in energy than that of the reactants, association of the reactants may be the rate controlling step in TST.1 The SN2 rate constant can then be modeled by a capture theory9 such as VTST,10 average dipole orientation (ADO) theory,11 the statistical adiabatic channel model (SACM),12 or the trajectory capture model.13... 

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,... 

Figure 3. Thermal rate constants for capture of HC1 by H3 (PST locked-dipole capture corresponding to phase-space theory, Eq. (16) SACM statistical adiabatic channel model, Eqs. (26)-(34) [15] SACMci classical SACM, Eqs. (28H31) [15] CT classical trajectories, Eqs. (26) and (27) [1]).

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). 

Fig. 8. Variation of the rate coefficient with temperature as measured with the CRESU apparatus for the reaction of N+ with ammonia [50]. The open circles represent early CRESU (at Meudon) results [52] while the solid circles are newer CRESU (at Rennes) results [50]. The open square is a room-temperature result obtained by Adams et al. [53] with a SIFT apparatus. The solid line is a theoretical prediction by Troe using the statistical adiabatic channel model [54]...

This concludes the discussion of early theories of the reaction step. These have largely been superseded by RRKM theory and the Statistical Adiabatic Channel Model, which are discussed in the next two sections. 

Phase space theory, flexible RRKM theory, and the statistical adiabatic channel model... 

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.

The determination of the microcanonical rate coefficient k E) is the subject of active research. A number of techniques have been proposed, and include RRKM theory (discussed in more detail in Section 2.4.4) and the derivatives of this such as Flexible Transition State theory. Phase Space Theory and the Statistical Adiabatic Channel Model. All of these techniques require a detailed knowledge of the potential energy surface (PES) on which the reaction takes place, which for most reactions is not known. As a consequence much effort has been devoted to more approximate techniques which depend only on specific PES features such as reaction threshold energies. These techniques often have a number of parameters whose values are determined by calibration with experimental data. Thus the analysis of the experimental data then becomes an exercise in the optimization of these parameters so as to reproduce the experimental data as closely as possible. One such technique is based on Inverse Laplace Transforms (ILT). 

E.I.Dashevskaya, E.E.Nikitin, and J.Troe, Long-range nonadiabatic effects in statistical adiabatic channel models dynamic orientation of fiagments formed in the decompositi of long-lived triatomie eompexes, J. Chem. Phys. 93,7803 (1990)... 

Statistical Adiabatic Channel Model for low-temperature capture in open shell systems. Asymptotic interactions in H-K)2 and O+OH systems Manthe U. 

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.)...

E.LDashevskaya, E.E.Nikitin and J.Troe, Nonadiabatic effects in the statistical adiabatic channel model the atom + diatom case, J. Chem. Phys. 97, 3318 (1992)... 

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