Introduction

As the dynamical behaviour of a system is determined by the PES, characterization of the topography and topology of the PES is a prerequisite for understanding the dynamics. For example, to apply the master equation approach that we used for our model PES's in the previous chapter, one would need a complete sample of minima and transition states on the PES. Such sampling is only possible for very small clusters (up to $N\approx 13$) because of the exponential increase in the number of minima with size[64,65,162]. For larger clusters one would need some way to statistically characterize the PES in order to compensate for the incompleteness of any sample of stationary points. This would be akin to the method we used in §3.4 to reproduce the thermodynamics from an incomplete sample of minima.

Here we use the eigenvector-following method to obtain a comprehensive characterization of the M₁₃ PES and its dependence on the range parameter, $\rho_0$ (§6.3), and to provide some typical downhill pathways for LJ clusters (§6.4). These surveys of the PES allow qualitative predictions of the effects of the range on the dynamics, and insight into the known relaxation behaviour of LJ clusters. Quantitative predictions await the application of the master equation method.