Principal component analysis of potential energy surfaces of large clusters: allowing the practical calculation of the master equation

Abstract

The number of variables in many-particle systems is typically unmanageably large; some way to reduce that number and still retain access to the important information about the system of interest is one of the great challenges in the broad topic of complexity. Principal components and principal coordinates provide a powerful means to extract—from unwieldy, large data sets—a reduced collection of variables that provide the information one needs, in a relatively efficient way and useful form. We investigate the application of principal components to the analysis of kinetics of the atomic motions in atomic clusters, particularly of clusters that are large enough so that a full description in terms of the entire high-dimensional potential surface is entirely impractical. A specific application is the use of principal components linking minima with their adjacent saddles, permitting the evaluation of rate coefficients (in the context of transition state theory) as ratios of partition functions of only one or two key variables.