Dividing hypersurface

Attention should be drawn to the fact that thermal energy randomization occurring after a particle has crossed the activation barrier is not perfect, so that return jumps may not be neglected. This can be taken into account by introducing a curved dividing hypersurface S which the jumping particle crosses more than once. Corrections (backjumps) of up to 10% are predicted [C.P. Flynn (1987)]. 

How can we extract a dividing hypersurface as free as possible from recrossings between the reactant and product states And what is the physical foundation of why the reacting system can climb through the saddles ... 

For analyses of the infrequent saddle crossings, we employed a modified Keck-Anderson method [40] to generate the microcanonical ensemble of well-saddle-well trajectories. We generated 10,000 well-saddle-well trajectories for both the saddles, which were found to be enough to yield statistical convergence in calculating the transmission coefficients in terms of many-body phase-space dividing hypersurfaces q) = 0) (i = 0,1,2) at... 

In other terms, almost nonreactive recrossings initiated from the CTBP state occur because the real dividing surface mainly distributes outwards to the OCT side from the Siq = 0), while the less frequent nonreactive recrossings from the other OCT state occur when the system finds an edge of the reaction bottleneck, that is, a tiny part of the dividing hypersurface in the phase space. 

Fortunately, if one s objective is to determine only rate constants, one can employ transition state theory (TST), which has been comprehensively reviewed by Fernandez-Ramos et a/. In TST, attention is focused on the flux of trajectories through a critical dividing surface (or strictly, critical dividing hypersurface), S, which divides the phase space associated with reactants from that associated with products. In most cases, the location of S can be defined by just the positional co-ordinates of the system that is, in our example involving just three atoms rc )- For reactions involving IV atoms and... 

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