Rare Events, Transition Pathways and Reaction Rates

Introduction Zero-Temperature
String Method
String Method
String Method


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A major problem with the available algorithms to study rare events is slow convergence. Since the original and simplified string methods rely heavily on steepest descent minimization schemes, the convergence is exponential. This can become decisive when the system size is very large.

In order to overcome this problem, we propose an algorithm which borrows some ideas from String method and Locally Updated Planes (LUP) method proposed by Elber and co-workers : Reaction path study of conformational transitions and helix formation in a tetrapeptide, Proc. Natl. Acad. Sci. USA, 86, 6963 (1989).

The central idea is to start with a guess path (say N intermediate images) between the initial and final states. At each image (i), a hyperplane is determined which perpendicular to the tangent (t) at that point. Then each image is allowed to relax independently with their motion constrained on the hyperplane. However, to obtain a smooth path in the multi-dimensional energy landscape, we use a mixing procedure for the step length of individual images which preserves the continuity and at the same time prevents formation of kinks.Next, we use reparametrization of the images which helps to maintain a specified weight to the intermediate images along the minimum energy path.