Free energy and surface tension of arbitrarily large Mackay icosahedral clusters

We present a model for predicting the free energy of arbitrarily large Mackay icosahedral clusters, van der Waals clusters are experimentally observed to be particularly stable at magic numbers corresponding to these structures. Explicit calculations on the vibrational states were used to determine the spectrum of fundamental frequencies for smaller (≤561) icosahedral clusters. The scaled cumulative frequency distribution function rapidly approaches a limiting function for large clusters. This function was used to predict zero-point energies and vibrational free energies for larger clusters (>561 atoms). Combining these predictions with correlations for the moment of inertia and for the minimum potential energy of large clusters leads to free energies of arbitrary large clusters. The free energies are used to predict the chemical potential and surface tension as a function of size and temperature. This connects macroscopic properties to the microscopic atomic parameters.