Path sampling methods

The basis of the transition path sampling method is the statistical description of dynamical pathways in terms of a probability distribution. To define such a distribution consider a molecular system evolving in time and imagine that we take snapshots of this system at regularly spaced times fj separated by the time step At. Each of these snapshots, or states, consists of a complete description z of the system in terms of the positions q = <71, <72, , [Pg.252]

In the transition path sampling method we are interested in trajectories that start in a certain region of configuration space, which we will call region si, and end in another region, 38. We call such trajectories reactive. Accordingly, we restrict the probability distribution from (7.3) to reactive trajectories only (see Fig. 7.2)... 

Note that the transition path sampling method can be also used for the calculation of activation energies (as opposed to activation free energies) [29]. This approach is useful for systems in which it is not possible to identify transition states. 

The calculation of reaction rate constants with the transition path sampling methods does not require understanding of the reaction mechanism, for instance in the form of an appropriate reaction coordinate. If such information is available other methods such as the reactive flux formalism are likely to yield reaction rate constants at a lower computational cost than transition path sampling. 

Dellago, C. Bolhuis, P. G. Geissler, P. L. Transition path sampling methods. In Computer Simulations in Condensed Matter From Materials to Chemical Biology Lecture Notes in Physics (2006), Ciccotti, G. Binder, K., Eds., vol. 703, Springer Berlin,... 

C. Dellago et al. Transition Path Sampling Methods, Lect. Notes Phys. 703, 349—391 (2006) DOI 10.1007/3-540-35273-2 10 Springer-Verlag Berlin Heidelberg 2006... 

Transition Path Sampling Methods 367 4.1 Reaction Coordinate vs. Order Parameter... 

It is obvious that the results of the two numerical methods are indistinguishable. Note that the procedure we outlined requires separate calculation at different times. An efficient method for calculating the probability at any other time f from the probability at a single time t is the transition path sampling method, which was developed by Dellago et al. [24]. We have employed that procedure to complete graph in Fig. 11. 

---