Chemical reaction rates, collision transition probability

We consider an ensemble of reactant molecules with quantized energy levels to be immersed in a large excess of (chemically) inert gas which acts as a constant temperature heat bath throughout the reaction. The requirement of a constant temperature T of the heat bath implies that the concentration of reactant molecules is very small compared to the concentration of the heat bath molecules. The reactant molecules are initially in a MaxweD-Boltzmann distribution appropriate to a temperature T0 such that T0 < T. By collision with the heat bath molecules the reactants are excited in a stepwise processs into their higher-energy levels until they reach "level (2V+1) where they are removed irreversibly from the reaction system. The collisional transition probabilities per unit time Wmn which govern the rate of transfer of the reactant molecules between levels with energies En and Em are functions of the quantum numbers n and m and can, in principle, be calculated in terms of the interaction of the reactant molecules with the heat bath. 

This is integrated over the Q,Q2Q,-space. If the collision pair wave functions never overlap the vibration wave function Xiku(Qi>Q2>Q3 2Zu) of the QTS, there will be zero contribution to the cross section. In this case, the QTS defines the reaction domain. This is quantized by the corresponding vibration-rotation wave function. Therefore, from all possible collisions among the reactants, only those having a non-zero FC factor will contribute to the reaction rate. This is related to the steric factor, P, in elementary chemical kinetics theory. Selection rules for VR-transitions apply. The probability to find the system in one of the product channel states when starting from a QTS is controlled by the FC integral formed by the products of the type... 

The statistical adiabatic channel model (SACM) " is one realization of the laiger class of statistical theories of chemical reactions. Its goal is to describe, with feasible computational implementation, average reaction rate constants, cross sections, and transition probabilities and lifetimes at a detailed level, to a substantial extent with state selection , for bimolecular reactive or inelastic collisions with intermediate complex formation (symbolic sets of quantum numbers v, j, E,J. ..)... 

Because the total angular momentum and its component are conserved during a collision, we can study the reaction dynamics for each value of 7 and M, independently. Since the results are independent of M, we always set M, - 0, and we will not mention it again (but the existence of the Af, quantum number is the reason for the factor of 27 + 1 in the following sentence). In particular, we can study the 7-specific contributions to the rate constant, k (E) [with k(E) of Eq. (3) being a (27 + l)-weighted sum of individual k (E), to the cumulative reaction probability, N (E), and to the density of reactive states, pJ(E). The influence of quantized transition states on chemical reactivity will be analyzed through studies of k (E). 

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