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This work reports a combined experimental and computational study of the activation of an otherwise catalytically inactive cobalt complex, [Co(TIM)Br2]+, for aqueous nitrite reduction. The presence of phosphate buffer leads to efficient electrocatalysis, with rapid reduction to ammonium occurring close to the thermodynamic potential and with high Faradaic efficiency. At neutral pH, increasing buffer concentrations increase catalytic current while simultaneously decreasing overpotential, although high concentrations have an inhibitory effect. Controlled potential electrolysis and rotating ring-disk electrode experiments indicate that ammonium is directly produced from nitrite by [Co(TIM)Br2]+, along with hydroxylamine. Mechanistic investigations implicate a vital role for the phosphate buffer, specifically as a proton shuttle, although high buffer concentrations inhibit catalysis. These results indicate a role for buffer in the design of electrocatalysts for nitrogen oxide conversion. 

The combination of a boron Lewis acid and a decamethylsamarocene, specifically 9,10-Me 2 -9,10-diboraanthracene with (C 5 Me 5 ) 2 Sm II (THF) 2 , in toluene leads to cooperative reductive capture of N 2 . The product crystallizes as the salt, [(C 5 Me 5 ) 2 Sm III (THF) 2 ][(C 5 Me 5 ) 2 Sm III (η 2 -N 2 B 2 C 14 H 14 )], 1, which formally is comprised of an (NN) 2− moiety sandwiched between a [(C 5 Me 5 ) 2 Sm III ] 1+ metallocene cation and the diboraanthracene ditopic Lewis acid. 

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depends on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population, before outlining the various definitions of ‘diversity’ and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields, including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.