Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

Abstract

The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch between the initial and final state energy wells while the polymer beads undergo diffusive motion back and forth over the barrier. We present an efficient method for evaluating the correction factor by constructing a sequence of hyperplanes starting at the transition state and calculating the probability that the system advances from one hyperplane to another towards the product. This is analogous to what is done in forward flux sampling except that there

In silicosimulations of erythrocyte aquaporins with quantitativein vitrovalidation

“…However, the rate constant of IC-to-EC or EC-to-IC transition cannot be simply computed as the rate of water molecules crossing the dividing plane between the IC and the EC sides (z ¼ 0, Fig. 1) because the potential energy landscape of the waterprotein-membrane system is very rugged 58 and thus there are many recrossing events that need to be considered 59,60 in the application of the transition state theory (TST) to compute the transition rate constant. 61 Many of the events of a water molecule crossing the dividing plane actually end up recrossing the plane in the opposite direction and thus should be excluded from the counting of transitions between the IC and the EC sides.…”

A robust and memory-efficient transition state search method for complex energy landscapes

“…Meanwhile, single-ended methods can be inefficient because they are not well suited for identifying specific pathways and can spend a large amount of time searching for undesired transition states. Another major challenge in studying complex energy landscapes relates to the presence of locally flat or discontinuous regions, such as when considering patchy [42][43][44] and hard-body 8,45 interactions in atomistic simulations, systems of polymer chains 46 , or collision constraints for macroscopic objects 47 . Flat zero-modes in the landscape pose issues for single-ended search methods and current bracketing methods that rely only upon local information.…”

Multiscale modeling of reaction rates: application to archetypal SN2 nucleophilic substitutions

“…Finally, the total net flux is built from the collected probabilities. The method has been adapted to treat flat energy barriers, 21 and solvent restructuring. 15 The concepts of reaction coordinate and transition state are so intuitive and rooted into the chemist's view, that they are rarely abandoned even when they are ill-defined.…”