Kinetic Analysis of Discrete Path Sampling Stationary Point Databases

Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem. First, we show how the original rate constant prescription within the discrete path sampling approach can be rewritten in terms of committor probabilities. Two alternative formulations are then derived in which the steady-state assumption for intervening minima is removed, providing both a more accurate kinetic analysis, and a measure of whether a two-state description is appropriate. The first approach involves running additional short kinetic Monte Carlo (KMC) trajectories, which are used to calculate waiting times. Here we introduce `leapfrog' moves to second-neighbour minima, which prevent the KMC trajectory oscillating between structures separated by low barriers. In the second approach we successively remove minima from the intervening set, renormalising the branching probabilities and waiting times to preserve the mean first-passage times of interest. Regrouping the local minima appropriately is also shown to speed up the kinetic analysis dramatically at low temperatures. Applications are described where rates are extracted for databases containing tens of thousands of stationary points, with effective barriers that are several hundred times kT.Comment: 28 pages, 1 figure, 4 table

A simple and effective relevance-based point sampling for 3D shapes

The surface of natural or human-made objects usually comprises a collection of distinct regions characterized by different features. While some of them can be flat or can exhibit a constant curvature, others may provide a more mixed landscape, abundant with high frequency information. Depending on the task to be performed, individual region properties can be helpful or harmful. For instance, surface registration can be eased by a set of non-coplanar smooth areas, while distinctive points with high curvature can be key for object recognition. For this reason, it is often critical to perform a surface sub-sampling that is suitable to the actual processing goal. To this end, most of the shape processing pipelines found in literature come bundled with one or more sampling rules, designed to boost their performance and accuracy. In this paper we introduce a sampling method for 3D surfaces that aims to be general enough to be useful for a wide range of tasks. The main idea of our method is to exploit the extent of the region around each point that exhibits limited local changes, granting higher relevance to points contained in compact neighborhoods. The effectiveness of the proposed method is experimented through its adoption as a point sampler within three very different shape processing scenarios