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Testing transition state theory on KacZwanzig model
 J. Stat. Phys
"... A variant of the KacZwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a doublewell external potential and coupled to N free particles through linear s ..."
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A variant of the KacZwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a doublewell external potential and coupled to N free particles through linear springs. While the KacZwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a twostate Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems. 1
Molecular Dynamics and Stochastic Simulations of Surface Diffusion
, 2007
"... Despite numerous advances in experimental methodologies capable of addressing the various phenomenon occurring on metal surfaces, atomic scale resolution of the microscopic dynamics remains elusive for most systems. Computational models of the processes may serve as an alternative tool to fill this ..."
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Despite numerous advances in experimental methodologies capable of addressing the various phenomenon occurring on metal surfaces, atomic scale resolution of the microscopic dynamics remains elusive for most systems. Computational models of the processes may serve as an alternative tool to fill this void. To this end, parallel molecular dynamics simulations of selfdiffusion on metal surfaces have been developed and employed to address microscopic details of the system. However these simulations are not without their limitations and prove to be computationally impractical for a variety of chemically relevant systems, particularly for diffusive events occurring in the low temperature regime. To circumvent this difficulty, a corresponding coarsegrained representation of the surface is also developed resulting in a reduction of the required computational effort by several orders of magnitude, and this description becomes all the more advantageous with increasing system size and complexity. This representation provides a convenient framework to address fundamental aspects of diffusion in nonequilibrium environments and an interesting mechanism for directing diffusive motion along the surface is explored. In the ensuing discussion, additional topics including transition state theory in noisy systems and the construction of a checking function for protein structure validation are outlined. For decades the former has served as a cornerstone for estimates of chemical reaction rates. However, in complex environments transition state theory most always provides only an upper bound for the true rate. An alternative approach is described that may alleviate some of the difficulties associated with this problem. Finally, one of the grand challenges facing the computational sciences is to develop methods capable of reconstructing protein structure based solely on readilyavailable sequence information. Herein a checking function is developed that may prove useful for addressing whether a particular proposed structure is a viable possibility.