Calculations of k2 T

The activated complex theory provides a link which connects the potential-energy surface with the chemical rate constant. To apply the theory requires knowing the structure of the potential-energy surface near the saddle point. As discussed in Section 9.2 accurate determination of the surface is a difficult problem. Instead of computing the properties of the 

Here we treat two specific examples. First we consider the hard-sphere model for chemical reaction and show that activated complex theory leads to a k2, T) identical with that calculated using kinetic theory arguments in Section 8.4. We then consider the molecular example 

We assume that only one electronic state of the complex is important in thermal reactions. 

It might seem that this assumption of separability implies that knowledge of the saddle point structure can be used to characterize the reactants and products. If each degree of freedom were strictly independent then precise description of the saddle point structure would specify the molecular properties of both reactants and products. Since separability is only approximate, no such extrapolation is possible. In fact, the reaction coordinate evolves from a molecular vibration in a manner unspecified by knowledge of the saddle point region. 

Introduction to Statistical Thermodynamics (Reading, Mass. Addison-Wesley, 1960), Chapters 4, 8, and 9 or see Appendix A. 

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