Truncation-based energy weighting string method for efficiently resolving small energy barriers.

Abstract

The string method is a useful numerical technique for resolving minimum energy paths in rare-event barrier-crossing problems. However, when applied to systems with relatively small energy barriers, the string method becomes inconvenient since many images trace out physically uninteresting regions where the barrier has already been crossed and recrossing is unlikely. Energy weighting alleviates this difficulty to an extent, but typical implementations still require the string's endpoints to evolve to stable states that may be far from the barrier, and deciding upon a suitable energy weighting scheme can be an iterative process dependent on both the application and the number of images used. A second difficulty arises when treating nucleation problems: for later images along the string, the nucleus grows to fill the computational domain. These later images are unphysical due to confinement effects and must be discarded. In both cases, computational resources associated with unphysical or uninteresting images are wasted. We present a new energy weighting scheme that eliminates all of the above difficulties by actively truncating the string as it evolves and forcing all images, including the endpoints, to remain within and cover uniformly a desired barrier region. The calculation can proceed in one step without iterating on strategy, requiring only an estimate of an energy value below which images become uninteresting.