|Rare Events, Transition Pathways and Reaction Rates|
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.