Free energy landscapes and transition rates of dynamic properties of Au₄ neutral and charged clusters at finite temperature

In the assembly of nanoscopic and mesoscopic materials, clusters form as important precursors to larger aggregates. Long lived stable, and metastable states within these assemblies determine the structure and dynamics of subsequent assembly. In metallic nanoparticles, specific cluster geometries are sought to control the particle's catalytic properties. Predicting long-lived aggregates is a complex problem, and conventional structural analyses based on spectroscopy or diffraction provide only averaged and not instantaneous structures. Molecular simulations offer an opportunity to examine the formation and fluctuation of metallic clusters in a highly controlled environment where the preferred conformations can be determined. In this work, we use advanced sampling algorithms coupled with ab initio molecular dynamics to estimate cluster conformations' free energy. We explore the conformational free energy landscape of the small metallic cluster Au₄, a simplified system enabling comprehensive study in neutral and charged configurations. We analyze the thermodynamics of conformational isomerization and predict transition rates with transition state theory. These simulations offer a quantitative understanding of the fluxionality of cluster structures.