Conclusions

We have shown, with examples, how the potential energy surfaces of BzAr_n clusters may vary with changes in the Lennard-Jones parameters. For smaller n our surveys are quite systematic because low energy minima can be predicted due to the large influence the benzene molecule has on the ordering of the Ar atoms, and there are only a few degrees of freedom. For BzAr₁₉ we have discussed only general differences in the lower-lying minima and found that the lowest energy minima found in numerous Monte Carlo and Molecular Dynamics simulations are qualitatively the same for the two sets of parameters. We have also shown that the induction energy has little influence on the form of the potential energy surfaces and that its importance is reduced as n increases. For BzAr₁₉ we neglect this contribution to the energy for the purpose of simulations as it constitutes <1% of the total energy.

In the simulation of the canonical and the microcanonical ensembles we have shown how severely thermodynamic averages are affected by non-ergodic sampling. We combined the standard Monte Carlo method with the more ergodic Jump-Walking sampling and a histogram method to obtain a better understanding of the underlying non-ergodicity. Our implementation of Jump-Walking minimises correlation effects and storage problems. We find that the Jump-Walking approach provides much better sampling of configuration space. The `melting' process in BzAr₁₉ does not produce a clear feature in the canonical caloric curve.

We also employed a multiple histogram method and numerical convolution to generate the relative number of states in phase space in order to calculate thermodynamic functions in the canonical and the microcanonical ensembles. The numerical operations are accurate and the results for the microcanonical ensemble match well with estimates from direct MD simulations.

For describing finite time-scale experiments more insight might be gained from Molecular Dynamics simulations. For the important one-sided/two-sided transition the MC and MD results provide a consistent picture in which to estimate transition barriers and escape times. We employed the Bulirsch-Stoer integration scheme to integrate the MD trajectories. In general, for each kink in the canonical and the microcanonical caloric curve, signifying non-ergodicity, we are able to assign escape from a particular region of configuration space consistent with both MC and MD simulations. Our results suggest that BzAr_n clusters produced by pick-up experiments are likely to be found with the benzene molecule in a surface site on a timescale of tens of nanoseconds at temperatures below around 30K, providing some support for the recent interpretation of spectra by Adams and Stratt in terms of `non-wetting' isomers. [8]