Thesis Overview

The work described in this thesis is theoretical and its aim is to help provide a fundamental understanding of three of the most important properties of clusters, their structure, thermodynamics, and dynamics. Rather than attempting to model accurately a specific substance, I choose to study homogeneous atomic clusters for which the interactions are described by simple potentials. Only with this simplicity does the main theme of the thesis--the relationship between the form of the potential and the behaviour of the cluster--become tractable. To attempt this task I focus on the potential energy surface (PES), because it allows the elucidation of this relationship to be broken down into two steps: firstly, how the potential determines the topographical features of the PES, and then how these in turn determine the behaviour of the cluster. In the analyses of the PES performed here, the stationary points (at which $\nabla V=0$ where V is the potential energy) will be particularly important, since the minima on the PES represent locally stable structures, and the transition states characterize the possible rearrangement paths between minima.

The thesis progresses in the following way. In Chapter 2, I show how the range of attraction of the potential affects the structures of the global minima. In Chapter 3, I extend a statistical method to incorporate anharmonicity so that the thermodynamic properties of clusters can be accurately calculated from a representative sample of minima. In Chapter 4, I attempt to provide a microscopic explanation of the range-dependence of the stability of the liquid phase. In Chapter 5, by examining model PES's I seek to elucidate the topographical features which significantly affect relaxation to the global minimum. In Chapter 6, I outline and apply methods by which to characterize the topology of the PES, particularly the network of connections between the minima, in order to provide insights into the dynamics. Finally, in the conclusion I attempt to summarize the achievements of the work described in this thesis, and suggest some possible future directions. Comprehensive introductions into each area will be given at the beginning of each chapter.

As I hope the interdependence of the chapters in this thesis will illustrate, structure, thermodynamics and dynamics are intimately connected. For example, only once liquid structure is characterized can the range-dependence of the liquid phase thermodynamics be explained. Furthermore, to be able to predict whether a cluster is likely to adopt the structure of the global minimum, one must first know whether the minimum is kinetically accessible, which in turn depends on whether there are free energy barriers to this relaxation process.

Although the approach of this work is unashamedly fundamental, throughout the thesis I shall attempt to relate the findings to experiment and other more specific theoretical calculations. Indeed, the hope is that the results for these simple systems can begin to provide a framework for understanding the diverse behaviour of real clusters.