Path sampling

Dellago C, Boihuis P G, Csajka F S and Chandler D 1998 Transition path sampling and the calculation of rate constants J. Chem. Phys. 108 1964-77... 

We recently received a preprint from Dellago et al. [9] that proposed an algorithm for path sampling, which is based on the Langevin equation (and is therefore in the spirit of approach (A) [8]). They further derive formulas to compute rate constants that are based on correlation functions. Their method of computing rate constants is an alternative approach to the formula for the state conditional probability derived in the present manuscript. 

C. Dellago, P.G. Bolhuis, F.S. Csajka, and D. Chandler, Transition path sampling and the calculation of rate constants , a preprint. 

P. G. Bolhuis, D. Chandler, C. Dellago, and P. Geissler, Transition path sampling throwing ropes over mountain passes, in the dark, Arum. Rev. Phys. Chem. 53, 291 (2002). 

Dellago C, Bolhuis PC (2007) Transition Path Sampling Simulations of Biological Systems. 268 291-317... 

The Crooks relation follows from an elegant derivation of Jarzynski s identity using path-sampling ideas [18], For instructive purposes, that derivation is briefly summa-rized here. Consider generating a discrete trajectory z0 - z i . .. z v, where... 

One of the major advances in the application of Jarzynski s identity to the calculation of free energies came from coupling it to path sampling [46, 47]. In a typical application with fast switching, the system is rapidly driven out of equilibrium as the coupling parameter is changed, and nearly all trajectories are essentially... 

Sun, S. X., Equilibrium free energies from path sampling of nonequilibrium trajectories, J. Chem. Phys. 2003,118, 5769-5775... 

Ytreberg, F. M. Zuckerman, D. M., Single-ensemble nonequilibrium path-sampling estimates of free energy differences, J. Chem. Phys. 2004,120,10876-10879... 

Transition Path Sampling and the Calculation of Free Energies... 

Transition path sampling can also be helpful in the calculation of free energies in the context of fast-switching methods described in Chap. 5. As shown by Jarzynski [12], equilibrium free energies can be computed from the work performed on a system in repeated transformations carried out arbitrarily far from equilibrium. From a computational point of view, this remarkable theorem is attractive because it promises efficient free energy calculations due to the reduced cost of... 

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)... 

The efficiency of a transition path sampling simulation crucially depends on how new pathways are generated from old ones. Various schemes to do that are possible. 

Free Energies from Transition Path Sampling Simulations... 

In most applications of transition path sampling it is sufficient to define the stable regions si and 88 in terms of configurational coordinates without reference to the momenta. The transition path sampling formalism, however, can be also applied to situations in which si and 88 also depend on the atomic momenta. 

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. 

Free energy profiles can also be evaluated within the partial path transition interface sampling method (PPTIS), a path sampling technique designed for the calculation of reaction rate constant in systems with diffusive barrier-crossing events [31,32], In this approach, the reaction rate is expressed in terms of transitions probabilities between a series of nonintersecting interfaces located between regions. c/ and... 

The Jarzynski Identity Path Sampling of Nonequilibrium Trajectories... 

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