Viewpoint pubs.acs.org/acscatalysis Fluxionality of Catalytic Clusters: When It Matters and How to Address It Huanchen Zhai † and Anastassia N. Alexandrova* ,†,‡ Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90095, United States California NanoSystems Institute, Los Angeles, California 90095, United States 1. INTRODUCTION Small clusters secured at a given size, for example, via deposition on surfaces of semiconductors, can be remarkable catalysts. In the so-called “non-scalable” regime, where every atom and every electron counts in catalyst tuning, 1−4 the opportunities for design are vast and intellectually attractive. At the same time, these systems are incredibly complex to characterize. In particular, in the nonscalable regime, clusters have shapes that are far from being idealized cuts out of the bulk, especially in the presence of adsorbates (reactants, intermediates, products of the reaction) and the support. Instead, cluster shapes can be highly diverse and hardly ever obey our intuition, which is uncomfortably weak in this case. One problem then is to identify the most stable structure, the global minimum. Many efficient Global Optimization (GO) algorithms, including Generic Algorithm (GA), 5−8 Particle Swarm Optimization (PSO), 9,10 Simulated Annealing (SA), 11 and Basin Hopping (BH) 12,13 have been shown to be successfully applied to small cluster systems, when combined with different level ab initio electronic structure methods. In addition, the GO algorithms can be further accelerated by using potential energy surface fitting techniques 14−16 or empirical potentials, 17,18 where the latter can be particularly useful for significantly larger clusters. 19 However, even if the global minimum is found, just the global minimum may tell only part of the story. Potential energy surfaces of clusters are typically rich in low- energy local minima. Many of these isomers are energetically accessible at the elevated temperatures of catalysis, to the degree that thermodynamic equilibration is kinetically possible. For example, the gas-phase Pt 8 cluster has ca. 30 distinct isomers (local minima) within the vicinity of the global minimum that can be populated at 700 K. 14 Of course, it is possible that some isomers are protected kinetically by high barriers, especially when the supporting surface provides strong and selective interactions with certain isomers. Regardless, several isomers should be suspected to be present in the catalytic system. This calls for a statistical ensemble representation of the catalyst. Furthermore, the most stable isomer may not be the most catalytically active. After all, it is intuitive that less-stable species are more likely to be reactive. For example, consider catalytic Au clusters versus stable and inert bulk Au. Thus, if there exists a relationship between the catalytic efficiency of a cluster isomer and its relative stability, then it is more likely to be inversely proportional than otherwise. In summary, even if the global minimum of a cluster is found, the utility of this isomer alone in describing size- specific catalytic activities is likely limited. A cartoon illustration of this point is shown in Figure 1. © 2017 American Chemical Society Figure 1. Conditions of catalysis (A) do not imply a single rigid cluster isomer facilitating a single catalytic event in vacuum (B), but instead, realistic coverage, temperature T, pressure p, access to many cluster isomers (% in C indicating probabilities for occurrences), and fluxionality all have an influence on catalyst activity. Thus, a statistical ensemble representation of the catalyst isomers under catalytic thermal conditions is necessary. The situation is further complicated by the fact that isomers may interconvert from one to another under the influence of increased temperature and because of the changing amount and chemical nature of adsorbates 20,21 (for example, reactants versus reaction intermediates). This phenomenon is called fluxionality, and it is the topic of the present article. From our point of view, the most difficult question is that of the interdependence and the interaction between the catalyzed reaction and cluster isomer interconversion. Clusters covered with reactants may have a different preferred shape or an ensemble of shapes than those covered with reaction intermediates or products. However, does it mean that the cluster rearranges in the course of the reaction step, that is, part of the reaction coordinate? Alternatively, does it mean that the clusters interconvert from one to another within the given free- energy well (say that of the reactants) and, once a particularly catalytic isomer forms in this process of equilibration, the reaction proceeds with a very small barrier? If the latter is the case, then, once the next reaction intermediate is formed, the clusters may again re-equilibrate in the new free-energy well. The generally longer lifetime in the wells should allow for this. At the moment, there is a controversy and a general lack of clarity on this question. How can we begin thinking about it? Received: November 15, 2016 Published: January 27, 2017 DOI: 10.1021/acscatal.6b03243 ACS Catal. 2017, 7, 1905−1911
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Feb 14, 2024
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