  In metallic nanoparticles, the cluster geometric structures control the
particle's electronic band structure, polarizability, and catalytic properties.
Analyzing the structural properties is a complex problem; the structure of an
assembled cluster changes from moment to moment due to thermal fluctuations.
Conventional structural analyses based on spectroscopy or diffraction cannot
determine the instantaneous structure exactly and can merely provide an
averaged structure. Molecular simulations offer an opportunity to examine the
assembly and evolution of metallic clusters, as the preferred assemblies and
conformations can easily be visualized and explored. Here, we utilize the
adaptive biasing force algorithm applied to first principles molecular dynamics
to demonstrate exploration of a relatively simple system which permits
comprehensive study of the small metal cluster $\ce{Au4}$ in both neutral and
charged configurations. Our simulation work offers a quantitative understanding
of these clusters' dynamic structure, which is significant for single-site
catalytic reactions on metal clusters and provides a starting point for a
detailed quantitative understanding of more complex pure metal and alloy
clusters' dynamic properties.
