Beyond Boltzmann: thermalization of cluster catalyst ensembles can extend beyond reaction timescales

The fluxionality of subnanocluster catalysts is essential for understanding their be- havior at an atomistic level. Up until now, when it is at all considered, fluxionality has been treated primarily thermodynamically, representing relevant isomer populations as their Boltzmann populations. Previous work supported this, suggesting that the Pt7/Al2O3 ensemble should be kinetically accessible within ns, based on the barrier heights for isomerization. In the current work, we explore the isomerization kinetics of gas-phase and surface-supported Pt4Hx clusters, using kMC to explore the evolution of isomer populations with time as a function of temperature. We additionally revisit the previously-obtained Pt7/Al2O3 network. This allows us to determine the temperature- dependent timescales at which the ensembles of these subnanoclusters reach thermal equilibirum. Gas-phase clusters readily thermalize by 350 K, while surface-supported clusters require temperatures between 500-700 K. These thermalization timescales de- pend on how structurally distinct the cluster isomers are within their ensemble. The greater the structural difference there is between low-energy structures, the longer it requires to reach thermal equilibrium. We show that it is essential to compute the barriers for isomerization between low-lying isomers in order to accurately determine either thermalization timescales, or non-equilibrium steady-state populations. Finally, we find that these thermalization timescales can extend to longer than catalytically- relevant timescales, depending on the reaction in question, indicating that isomerization is an essential feature of the reaction coordinate of a catalytic reaction