Kinetic restructuring of catalyst active sites: a MACE-APE study of fluxional Pd_n/MgO (n = 3-11) clusters

The role of dynamic restructuring of catalytic interfaces under reaction conditions is of unquestionable importance. Sub-nanocluster catalysts, consisting of just a few atoms on a metal oxide support, are known to be highly fluxional. They are able to populate and interconvert between multiple isomers with similar energies. Computational cost has hitherto restricted first-principles treatment of sub-nanocluster fluxionality to the assumption of thermodynamic equilibrium, where the relative isomer populations are Boltzmann distributed. Here, we exploit the advent of fast and accurate machine-learned interatomic potentials (MLIPs), coupled with an automatic process explorer (APE) approach, to systematically evaluate the kinetics of fluxional behavior of sub-nanoclusters. Specifically, we explore the size-dependent restructuring kinetics of Pd₃-Pd₁₁ clusters on a fixed MgO(100) support. Propagation of the constructed comprehensive isomerization networks shows that the timescale for relaxation to thermodynamic equilibrium can vary by several orders of magnitude upon changing the number of Pd atoms in the cluster by only one. There is also no simple correlation between the overall relaxation timescale and the amount of time spent in individual (metastable) isomers. Comparison of the timescales of cluster restructuring to a typical rate-limiting catalytic barrier of 1 eV shows that typical fluxional restructuring occurs on comparable to (much) faster timescales, depending on cluster size and specific isomer geometry. Thus, it becomes clear that explicitly resolving the state-to-state dynamics of fluxional sub-nanoclusters is essential for the development of mechanistic understanding of their catalytic performance.