Generalized transition state dividing surface

Because the transition state geometry optimized in solution and the solution-path reacton path may be very different from the gas-phase saddle point and the gas-phase reaction path, it is better to follow the reaction path given by the steepest-descents-path computed from the potential of mean force. This approach is called the equilibrium solvation path (ESP) approximation. In the ESP method, one also substitutes W for V in computing the partition functions. In the ESP approximation, the solvent coordinates are not involved in the definition of the generalized-transition-state dividing surface, and hence, they are not involved in the definition of the reaction coordinate, which is normal to that surface. One says physically that the solvent does not participate in the reaction coordinate. That is the hallmark of equilibrium solvation. 

The generalized transition state number of states needed for microcano-nical variational theory calculations counts the number of states in the transition state dividing surface at s that are energetically accessible below an energy E. Consistent with approximations used in calculations of the partition functions, we assume that rotations and vibrations are separable to give... 

For 5 not equal to 0, a dividing surface is called a generalized transition state (to distinguish it from the conventional transition state where the gradient is zero). With this choice of dividing surface the generalized TST rate expression given by Eq. (11) reduces for a bimolecular reaction to... 

In principle the generalized transition state can be any hypersurface in phase space except for the constraint that it must divide reactants from products.However, in practice it would be difficult to calculate for arbitrary dividing surfaces as well as. to... 

For a reaction with a defined transition state and without recrossing, reaction rate can be well approximated by many methods. For such reaction, we can assume that there is a dynamics bottleneck located at the transition state (conventional transition state theory, TST) or at a generalized transition state obtained by a canonical (CTV) or microcanonical (/zVT) criterion. In the later cases, the dividing surface is optimized variationally to minimize the recrossing. Evans first proposed to place the transition state at the location that maximizes the free energy of activation which provides a key conceptual framework for modern variational transition state theory [33]. However, recrossing always possibly exists and only a full-dimensional reactive scattering dynamics calculations are able to provide us the exact rate constant on a defined PES. Eor a detailed discussion, one may refer to the reviews by Truhlar et al. [38,136]. 

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