Dynamics of diffusion in small cluster systems

Classical dynamical studies are presented of melting and diffusive behavior in the Ar₁₃ cluster. A comparison is made between the standard Einstein form for the diffusion constant (and the equivalent Green-Kubo form) and a recently developed theory for dynamics and diffusion in liquids based on the dynamical Hessian matrix. Comparisons are also made to similar calculations on melting in bulk argon systems. In the molecular dynamics calculations, it is found that the onset of liquidlike behavior occurs rather suddenly across the transition region. Well-defined Fick's Law diffusive behavior occurs in liquidlike clusters over time scales 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 are monitored as a function of energy and temperature, and the Einstein frequency of the cluster is computed.