Quantum mechanical integrated reaction probability

I 6 Single and Multiple Hydrogen/Deuterium Tranter Reactions in Liquids and Solids the quantum mechanical integrated reaction probability by... 

Theresultsgivenbelowarebasedonstandardparametervalues Vq = 1-56 x 10 a.u., fl = 1.36 a.u., mass m = 1060 a.u., and reaction coordinate = x. The exact quantum mechanical (QM) rate constant kq for this reaction can be obtained by integrating the exact quantum mechanical cumulative reaction probability, which is known analytically [30,78]. 

Finally, we note that although all of the discussion in this section has applied to a completely classical mechanical treatment of the reaction, the expression for the cumulative reaction probability can be quantized in the usual ad hoc fasion in statistical theory by replacing the classical flux of equation (21) by the quantum mechanical integral density of states... 

Figure 1 H + H2, J = 0. (a) Cumulative reaction probability. The solid curve is a spline fit to the accurate quantal results, and the dashed curve was obtained by integrating the synthetic density in b. (b) Density of reactive states. The solid curve is obtained by analytically differentiating a cubic spline fit to the accurate quantum mechanical CRPs. The heavy dashed curve is the fit of Eqs. (14) and (15). The arrows are positioned at the fitted values of T, and the feature numbers and assignments above the arrows correspond to Table 2. (Reprinted with permission from Ref. 8, copyright 1991, American Chemical Society.)...

Here, we report the results of quantum mechanical close coupling calculations of reaction probabilities on the ah initio surface of Walch et at. and the DIM one of Whitlock et The integration... 

For another perspective we mention a second approach of which the reader should be aware. In this approach the dividing surface of transition state theory is defined not in terms of a classical mechanical reaction coordinate but rather in terms of the centroid coordinate of a path integral (path integral quantum TST, or PI-QTST) [96-99] or the average coordinate of a quanta wave packet. In model studies of a symmetric reaction, it was shown that the PI-QTST approach agrees well with the multidimensional transmission coefScient approach used here when the frequency of the bath is high, but both approaches are less accurate when the frequency is low, probably due to anharmonicity [98] and the path centroid constraint [97[. However, further analysis is needed to develop practical PI-QTST-type methods for asymmetric reactions [99]. 

---