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Recent experiments indicated that nanoparticles (NPs) might efficiently catalyze multiple chemical reactions, frequently exhibiting new phenomena. One of those surprising observations is intra-particle catalytic cooperativity, when the reactions at one active site can stimulate the reactions at spatially distant sites. Theoretical explanations of these phenomena have been presented, pointing out the important role of charged hole dynamics. However, the crucial feature of nanoparticles that can undergo dynamic structural surface rearrangements, potentially affecting the catalytic properties, has not yet been accounted for. We present a theoretical study of the effect of dynamic restructuring in NPs on intra-particle catalytic cooperativity. It is done by extending the original static discrete-state stochastic framework that quantitatively evaluates the catalytic communications. The dynamic restructuring is modeled as stochastic transitions between states with different dynamic properties of charged holes. Our analysis reveals that the communication times always decrease with increasing rates of dynamic restructuring, while the communication lengths exhibit a dynamic behavior that depends on how dynamic fluctuations affect migration and death rates of charged holes. Computer simulations fully support theoretical predictions. These findings provide important insights into the microscopic mechanisms of catalysis on single NPs, suggesting specific routes to rationally design more efficient catalytic systems. 

Modern chemical science and industries critically depend on the application of various catalytic methods. However, the underlying molecular mechanisms of these processes still remain not fully understood. Recent experimental advances that produced highly-efficient nanoparticle catalysts allowed researchers to obtain more quantitative descriptions, opening the way to clarify the microscopic picture of catalysis. Stimulated by these developments, we present a minimal theoretical model that investigates the effect of heterogeneity in catalytic processes at the single-particle level. Using a discrete-state stochastic framework that accounts for the most relevant chemical transitions, we explicitly evaluated the dynamics of chemical reactions on single heterogeneous nanocatalysts with different types of active sites. It is found that the degree of stochastic noise in nanoparticle catalytic systems depends on several factors that include the heterogeneity of catalytic efficiencies of active sites and distinctions between chemical mechanisms on different active sites. The proposed theoretical approach provides a single-molecule view of heterogeneous catalysis and also suggests possible quantitative routes to clarify some important molecular details of nanocatalysts. 

Catalysis is a method of accelerating chemical reactions that is critically important for fundamental research as well as for industrial applications. It has been recently discovered that catalytic reactions on metal nanoparticles exhibit cooperative effects. The mechanism of these observations, however, remains not well understood. In this work, we present a theoretical investigation on possible microscopic origin of cooperative communications in nanocatalysts. In our approach, the main role is played by positively charged holes on metal surfaces. A corresponding discrete-state stochastic model for the dynamics of holes is developed and explicitly solved. It is shown that the observed spatial correlation lengths are given by the average distances migrated by the holes before they disappear, while the temporal memory is determined by their lifetimes. Our theoretical approach is able to explain the universality of cooperative communications as well as the effect of external electric fields. Theoretical predictions are in agreement with experimental observations. The proposed theoretical framework quantitatively clarifies some important aspects of the microscopic mechanisms of heterogeneous catalysis.