Unraveling mechanisms from waiting time distributions in single-nanoparticle catalysis

The catalytic conversion of substrates to products at the surface of a single nanoparticle cluster can now be resolved at the molecular scale and the waiting time between individual product turnovers measured with precision. The distribution of waiting times and, in particular, their means and variances can thus be obtained experimentally. Here, we show how theoretical modeling based on the chemical master equation (CME) provides a powerful tool to extract catalytic mechanisms and rate parameters from such experimental data. Conjecturing a family of mechanisms that both include and exclude surface restructuring, we obtain the mean and variance of their waiting times from the CME. A detailed analysis of the link between mechanism topology and waiting time dispersion, then, allows us to select several candidate mechanisms, with branched topologies, that can reproduce experimental data. From these, the least complex model that best matches experimental data is chosen as the minimum model. The CME modeling extracts the Langmuir-Hinshelwood mechanism for product formation and two-pathway mechanism for product dissociation, with substantial off-pathway state fluctuations due to surface restructuring dynamics, as the minimal model consistent with data. Our work, thus, provides a mechanistic origin of the coupling between the kinetics of catalytic turnovers and surface restructuring dynamics and yields a systematic way to compute catalytic rates from distributions of waiting times between product turnovers in the presence of surface restructuring.