Isomerization is a fundamental process in chemistry. We use a two-dimensional Coulomb crystal to emulate molecular isomerization and characterize its physical mechanisms. In our molecular analogue, the externally controlled confining potential determines the crystal’s potential energy surface (PES), thereby playing the role that the molecular electronic state plays in determining the PES in a molecule. We focus on a crystal of six ${}^{138}$Ba${}^{+}$ ions exhibiting a region of bistability, and use a Monte Carlo simulation to extract the PES as a function of the trap aspect ratio. Experimentally, we prepare the ions in a stable isomer, quench the PES to populate a metastable isomer, and use a configuration-resolved imaging to detect isomerization in real time. We measure isomers’ populations in the bistability region and compare them with a theoretical model to extract the crystal’s temperature. Moreover, we derive the transition rates from the measured transient times, thus providing a full characterization of the isomerization process. Our work sets a new platform for emulating molecular processes, paving the way to study quantum superpositions of crystal configurations and control isomeric excitations in two-dimensional Coulomb crystals.