A super-linear minimization scheme for the nudged elastic band method

In this article, we present a superlinear minimization scheme for the nudged elastic band (NEB) method, which determines a minimum-energy path (MEP) of a reaction via connecting intermediate replicas'' between the reactant and the product. The minimization scheme is based on a quasi-Newton method: the adopted basis Newton-Raphson (ABNR) minimization scheme. In each step of ABNR minimization, the Newton-Raphson procedure is performed in a subspace of a user-defined dimension. The tangent directions of the path at a new Newton-Raphson step are determined self-consistently in the subspace. The acceleration of the proposed scheme over the quenched molecular-dynamic minimization, the current practice for minimizing a path using NEB, is demonstrated in three nontrivial test cases: isomerization of an alanine dipeptide, alpha-helix to pi-helix transition of an alanine decapeptide, and oxidation of dimethyl sulfide. New features are also added such that the distances between replicas can be defined in the root of mean squared (RMS) best-fit space with flexible weighting options. This offers a way to incorporate the effects of a mobile solvent in the process with a finite number of replicas. MEPs obtained from various initial structures can be used to investigate different proposed reaction mechanisms, and the speedup of minimizing a path enhances the applicability of the NEB method. The combination of NEB force projection procedures, the flexible distance definition in the RMS best fit space with arbitrary weighting options, and the superlinear minimization scheme provides a framework to aid in the study of transition processes of biological molecules as such proteins. (C) 2003 American Institute of Physics.