Adiabatic channels

Quack M and Tree J 1974 Specific rate constants of unimolecular processes. II. Adiabatic channel model Ber. Bunsenges. Phys. Chem. 78 240-52... 

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,... 

The reason for this difference is very simple. It is that the density functional approach calculates the rate for the adiabatic channel. For AG x> this will proceed via an activated complex with successor-state formal electron density parameter A = 1 for AGq <-x, it will proceed via an activated... 

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... 

V. Comparison of Statistical Adiabatic Channel and Variational Transition-State Treatments... 

The complete adiabatic channel potentials are finally obtained by adding a centrifugal energy term Ecent(r). As long as channel maxima are located at comparably large values of r, the quasi-diatomic expression... 

Figure 1. Adiabatic channel potential curves V,(r) for the interaction between Hj and HC1 (calculations for (j,m,l) = (0, 0, /) with / = 0, 40, 60 from Ref. 15 full curves real potential dashed curves locked-dipole potential used in PST).

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]).

V. COMPARISON OF STATISTICAL ADIABATIC CHANNEL AND VARIATIONAL TRANSITION-STATE TREATMENTS... 

In the following we elaborate VTST expressions for various charge-dipole potentials. For demonstrative purposes, we further consider the isotropic locked permanent-dipole case where SACM and PST are identical. We also consider the real anisotropic permanent-dipole case in the quantum low-temperature and classical high-temperature oscillator limits. Finally we show comparisons for real permanent and induced-dipole cases. We always employ explicit adiabatic channel eigenvalues for calculating partition functions or numbers of states. 

The locked permanent-dipole capture system may serve as our first example for an isotropic potential where SACM and PST coincide. In this case, the adiabatic channel potential curves have the form... 

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