Simple Model and Spectral Analysis for a Fluxional Catalyst: Intermediate Abundances, Pathway Fluxes, Rates, and Transients

The fluxional interconversion of a catalyst between forms with different structures and properties complicates mechanistic analyses and kinetic modeling efforts. We construct a simple model for a catalyst with two fluxionally interconverting forms, inspired by the interconverting flat (*) and stacked (▴) forms of noble metal sub-nanoclusters. Using a detailed balance, free energy relations, non-dimensionalization, and representative equilibrium constants from ab initio calculations in the literature, ten initial rate parameters are reduced to two. The two remaining parameters control the fluxional interconversion rate and the reactant concentration. For a wide range of these two parameters, we compute the steady-state turnover frequencies, pathway fluxes, intermediate abundances, as well as transient intermediate relaxation rates. The results demonstrate how steady-state abundances and dominant pathways can change with the degree of fluxionality, even when equilibrium constants are unchanged. We conclude that accurate rate expressions must account for non-equilibrium steady-state abundances and fluxes, beyond equilibrium populations. Furthermore, in contrast to the short-lived transients for a non-fluxional catalyst, we show that non-steady transients may persist through many turnovers when fluxional interconversion is slow.