Extensions to the instantaneous normal mode analysis of cluster dynamics: Diffusion constants and the role of rotations in clusters

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Abstract
For the instantaneous normal mode analysis method to be generally useful in studying the dynamics of clusters of arbitrary size, it ought to yield values of atomic self-diffusion constants which agree with those derived directly from molecular dynamics calculations. The present study proposes that such agreement indeed can be obtained if a sufficiently sophisticated formalism for computing the diffusion constant is adopted, such as the one suggested by Madan, Keyes, and Seeley [J. Chem. Phys. 92, 7565 (1990)]. In order to implement this particular formalism, however, we have found it necessary to pay particular attention to the removal from the computed spectra of spurious rotational contributions. The utility of the formalism is demonstrated via a study of small argon clusters, for which numerous results generated using other approaches are available. We find the same temperature dependence of the Ar13 self-diffusion constant that Beck and Marchioro [J. Chem. Phys. 93, 1347 (1990)] do from their direct calculation of the velocity autocorrelation function: The diffusion constant rises quickly from zero to a liquid-like value as the cluster goes through (the finite-size equivalent of) the melting transition.