Statistical interpretation of topographies and dynamics of multidimensional potentials

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Abstract
A statistically based method of characterizing the topography of a multidimensional potential surface classifies not only local minima and saddles but entire basins containing many minima, and divides separating basins and monotonic sequences of local minima within each basin. The data, so classified, fold readily into the formalisms of chemical kinetic isomerization theory and master equations to provide a connection between that topography and the dynamics on the surface. This analysis, in particular, permits an interpretation of the glass-forming or ‘‘focusing’’ character of the surface. The method is illustrated with a model system derived, with simplifications, from the 19-atom Lennard-Jones cluster. The method also leads naturally to control problems including the determination of optimum conditions for forming glasses or selected structures, such as particular crystal structures or folded protein structures.