The Low Temperature Specific Heat of Au

The calculated specific heat for Aujj at temperatures between 2K and 60 K, based on this model, is shown in Fig. 6. Almost equally good agreement has been obtained for the specific heats and the f-factors for the cluster compounds Au Lg and AU11L7X3 (with X = SCN) [25]. 

Note that the full curve drawn in the figure corresponds to the specific heat calculated with no free parameters. While the agreement of this model to the specific heat is rather impressive, it is in fact the 3 inter-cluster degrees of freedom, i.e. motion of the whole cluster, which govern the phonon contribution to the specific heat at temperatures below about 15-20 K [99]. 

This in itself is proof of the importance of the center-of-mass motion in treating the thermal properties of small particles at low temperature. 

An additional piece of information provided by this calculation is that the mean square displacement of the gold atoms on all the sites except for the PPhj-coordinated sites are primarily, though not exclusively, radial. The mean square displacement of the gold atoms on the PPh 3-coordinated sites, on the other hand, have an in-plane (i.e. tangential) mean-square displacement which is not only larger than in the radial direction [94, 100], but also exhibits significant inplane anisotropy. This may be related to an incompletely developed soft mode in the cluster [101], which might be considered as a precursor to a transition from the observed close-packed structure to the icosahedral structure, predicted theoretically by Sawada et al. [102]. 

The site f-factors are strongly sensitive to the details of the structure of the cluster. The fact that a model which completely ignores the type of ligand and 

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