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Learning the science of heterogeneous catalysis and electrocatalysis always starts with the simple case of a flat, uniform sur-face with an ideal adsorbate. It has of course been recognized for a century that real catalysts are more complicated. For the increasingly complex catalysts of the 21st century, this Perspective argues that surface heterogeneity and non-ideal binding isotherms are central features, and their implications need to be incorporated in current thinking. A variety of systems are described herein where catalyst complexity leads to broad, non-Langmuirian surface isotherms for the binding of hydrogen atoms – and this occurs even for ideal, flat Pt(111) surfaces. Modern catalysis employs nanoscale materials whose surfaces have substantial step, edge, corner, impurity, and other defect sites, and they increasingly have both metallic and non-metallic elements MnXm, including metal oxides, chalcogenides, pnictides, carbides, doped carbons, etc. The surfaces of such catalysts are often not crystal facets of the bulk phase underneath, and they typically have a variety of potential active sites. Catalytic surfaces in operando are often non-stoichiometric, amorphous, dynamic, and impure, and often vary from one part of the surface to another. Understanding of the issues that arise at such nanoscale, multi-element catalysts is just beginning to emerge. Yet these catalysts are widely discussed using Brønsted/Bell-Evans-Polanyi (BEP) relations, volcano plots, Tafel slopes, the Butler-Volmer equation, and other linear free energy relations (LFERs), which all depend on the implicit assump-tion that the active sites are all “similar” and that surface adsorption is close to ideal. These assumptions underly the ubiqui-tous intuition based on the Sabatier Principle, that the fastest catalysis will occur when key intermediates have free energies of adsorption that are not too strong nor too weak. Current catalysis research often aims to minimize the complexity of non-ideal isotherms through experimental and computational design (e.g., the use of single crystal surfaces), and these studies are the foundation of the field. In contrast, this Perspective argues that the heterogeneity of binding sites and binding energies is an inherent strength of these catalysts. This diversity makes many nanoscale catalysts inherently a high-throughput screen wrapped in a tiny package. Only by making the heterogeneity part of the foundation of catalysis models, sorting the types of active sites and dissecting non-ideal binding isotherms, will modern catalysis learn to harness the inherent diversity of real catalysts. Controlling rather than avoiding diversity is needed to optimize complex modern catalysts and catalytic condi-tions. 

Cerium oxide (ceria, CeO 2−x ) has been traditionally used as a catalyst support functionalized with metal nanoparticles or synthesized with metal dopants for a variety of applications ranging from catalytic converters to solid oxide fuel cells. In a departure from these typical heterogeneous motifs, we explore the interactions of nano-CeO 2−x systems with organometallic oxidation catalysts in organic solvents. Ceria is used here both as an organically-capped colloid and as an uncapped insoluble nanopowder. Both the colloid and nanopowder act as terminal oxidants by accepting hydrogen atoms from a ruthenium Noyori–Ikariya hydride complex. To our knowledge, this is the first demonstration that CeO 2−x can oxidize an organometallic hydride. Building on this concept, we show the uncapped CeO 2−x powder also acts as the terminal acceptor in catalytic alcohol dehydrogenation reactions, utilizing iridium pyridine sulfonamide catalysts under anaerobic and aerobic conditions. The coupling of homogeneous oxidation catalysts with cerium oxide demonstrates the versatility of CeO 2−x and a bridging of concepts in homogeneous and heterogeneous catalysis. 

Stoichiometric reduction reactions of two metal–organic frameworks (MOFs) by the solution reagents (M = Cr, Co) are described. The two MOFs contain clusters with Ti 8 O 8 rings: Ti 8 O 8 (OH) 4 (bdc) 6 ; bdc = terephthalate (MIL-125) and Ti 8 O 8 (OH) 4 (bdc-NH 2 ) 6 ; bdc-NH 2 = 2-aminoterephthalate (NH 2 -MIL-125). The stoichiometry of the redox reactions was probed using solution NMR methods. The extent of reduction is greatly enhanced by the presence of Na + , which is incorporated into the bulk of the material. The roughly 1 : 1 stoichiometry of electrons and cations indicates that the storage of e − in the MOF is tightly coupled to a cation within the architecture, for charge balance.