Classical dynamic studies were made of melting and diffusive behaviors in a Ar13 cluster. A comparison was made between the standard Einstein form for the diffusion constant (and the equivalent Green–Kubo form) and a theory for dynamics and diffusion in liquids which was based upon the dynamical Hessian matrix. Comparisons were also made to similar calculations on melting in bulk argon systems. In the molecular dynamics calculations, it was found that the onset of liquid-like behavior occurred rather suddenly across the transition region. Well‐defined Fick’s law diffusive behavior occurred in liquid-like clusters over time-scales which were long relative to the characteristic vibrational period. In studies involving the dynamical matrix, the distributions and numbers of positive and negative eigenvalues of the Hessian matrix were monitored as a function of energy and temperature, and the Einstein frequency of the cluster was computed.

Dynamics of Diffusion in Small Cluster Systems. Beck, T.L., Marchioro, T.L.: Journal of Chemical Physics, 1990, 93, 1347