Statistical Methods of Chemical Reactivity

Statistical methods are based on a microscopic view of the reacting system. In this respect we consider it reasonable to discuss them briefly in this review. Moreover, the statistical treatment consists of several steps, some of them closely related to the microscopic characteristics of a reacting system. 

Statistical methods represent a background for, e.g., the theory of the activated complex (239), the RRKM theory of unimolecular decay (240), the quasi-equilibrium theory of mass spectra (241), and the phase space theory of reaction kinetics (242). These theories yield results in terms of the total reaction cross-sections or detailed macroscopic rate constants. The RRKM and the phase space theory can be obtained as special cases of the single adiabatic channel model (SACM) developed by Quack and Troe (243). The SACM of unimolecular decay provides information on the distribution of the relative kinetic energy of the products released as well as on their angular distributions. 

Generally, the statistical methods assume that in the course of an elementary process a special state of the reacting system is reached where one of the internal degrees of freedom is changed into the translation along the reaction path. Hence, the statistical methods have two features in common. 

It is assumed that there is a point on the reaction path, the attainment of which leads necessarily to the formation of products. This point on the reaction path from which no backward motion is possible is called the critical configuration the state of the microscopic system at the critical configuration is referred to as the transition state and the corresponding species is called the activated complex. 

The rate of the transformation of reactants into products depends on the amount of energy in the different degrees of freedom of the activated complex. However, the distribution of energy is not a priori known and it is necessary to make an assumption concerning the energy distribution in the degrees of freedom of the activated complex. From the theory of information 

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