ANZIAM J. 45(E) ppC534--C550, 2004.

Long time scale molecular dynamics using least action.

Abstract

We present here an efficient method for evaluating molecular trajectories over long time scales. The method is based on optimisation of the path action defined by classical mechanics. We test the technique on non-trivial examples drawn from the literature and discuss the effectiveness of this approach in the study of molecular processes. Many of the present techniques for calculating molecular trajectories are limited computationally. Standard forward integration of Newton's equations of motion yields accurate results for a range of systems whose transition times are many orders of magnitude less than most biologically interesting processes. If one wants to extend these calculations to biologically relevant time scales, it is necessary to develop methodologies which avoid this limitation. The process outlined in this paper has been tested on simple systems using harmonic and Lennard--Jones potential energy functions. The algorithm yields stable trajectories and is adjustable to suite available computational resources. In theory, this algorithm is applicable to any molecular system where the initial and final states are known. This could include investigation of chemical reactions, ligand/receptor binding and work cycles of molecular machinery.

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Authors

B. A. Gladwin

Department of Mathematics, University of Queensland, Brisbane, Australia. mailto:gladwin@maths.uq.edu.au

T. Huber

Department of Mathematics, University of Queensland, Brisbane, Australia

Published 26 June 2004, amended July 8, 2004. ISSN 1446-8735