Optimization of hyperplanar transition states: Application to 2D test problems

The implementation of the WKE two step procedure for simulating slow, thermal transitions involving (1) a transition state theory approximation and (2) dynamical trajectories starting from the transition state is discussed, in particular the optimization of hyperplanar representations of the transition state dividing surface. A test problem involving a twisted reaction path is analyzed, and it is shown that the optimal hyperplanar transition state rotates abruptly from lying along the potential energy ridge at low temperature to an entropy dominated orientation at high temperature. The construction of more complex dividing surfaces using a set of intersecting hyperplanes is also illustrated. Finally, the use of the WKE procedure to enable long time scale simulations of systems undergoing activated, rare events is discussed.