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This paper provides a theoretical analysis of three alternative auto ownership rationing schemes, including lottery, auction and the hybrid scheme. The city's residents are differentiated by their income level, which is assumed to follow a uniform distribution. Expected social cost minimization models are proposed for determining the optimal auto quota for these schemes and the optimal proportion allocated to the lottery and auction in the hybrid scheme. The solution properties of the proposed models are analytically explored, and a comparison of these schemes is made. The results show that the auction scheme is most efficient and the lottery scheme is most inefficient in terms of the expected social cost. The optimal auto quota increases with degraded transit services, but decreases with increased auto travel time/cost. Increasing the proportion of allocation to the lottery in the hybrid scheme may lead to an increased or a decreased optimal auto quota, depending on the road service level. Residents' income gap can significantly affect the optimal quota solution: widening the income gap via raising the income of the rich pushes the government to increase the quota to be provided. However, narrowing the income gap via raising the minimum salary standard may require an increased or a decreased quota provision. The efficiencies of the lottery and auction schemes are very close in terms of the expected social cost, which justifies the use of the lottery scheme in practice.

Electrocatalytic hydrogen evolution reaction (HER) is a critical process in a sustainable energy conversion system. Many metal complexes as small-molecule catalysts for electrochemical H2 evolution have been reported over recent decades, which have made a great contribution to a detailed understanding of their catalytic mechanisms. In most reported mechanistic pathways, metal hydride species are always considered as key intermediates during H2 formation, with the metal centre at the active site docking both electrons and protons. These metal-centred HER routes need to employ metal ions with open coordination sites, which can accommodate multiple redox states to involve two-electron hydride transfer for H2 production. By comparison, an alternative approach, specifically focusing on redox-active ligand-centred electrocatalytic HER, has garnered increasing attention over the last six years. This review highlights recent progress in metal and metal-free ligand-centred homogeneous electrocatalytic HER since 2012 and discusses it according to two categories: organic ligand-centred and inorganic ligand-centred HER. In addition, some existing issues and suggestions for future directions in this catalytic area have been provided.

A discrete 78-nucleus silver–sulfur nanocluster with a sulfate-centered multishell structure was isolated and characterized. Its crystal structure revealed 18 and 60 Ag atoms in the inner and outer shell, respectively. The inner shell of 18-nuclearity Ag atoms is a very rare convex polyhedron featuring an elongated triangular orthobicupola. The incorporation of a sulfate anion and multishell arrangement in the nanocluster led to a dramatic decrease in the band gap (Eg = 1.40 eV). Our study showed that simple anions can also induce the formation of high-nuclearity silver clusters with excellent optical properties.

The synthesis of Group 11 metal chalcogenide supertetrahedral clusters (SCs) still remains a great challenge mainly due to the high tendency of metal aggregation through metallophilicity and global charge balance. Demonstrated herein are the preparation, crystallographic characterization, and optical properties of two stable silver-sulfur SCs through ligand-control; one as a discrete zero-dimensional (0D) V3,4-type cluster and the other as a one-dimensional (1D) zigzag chain extended by alternating V3,2-type clusters. The notation Vn,m (where n is the number of metal layers, and m is the number of vacant corners) is used to describe a new series of vacant-corner SCs, which can be derived from the regular Tn clusters. The existence of vacant-corner-type SCs may be ascribed to the low valence and tri-coordinated environment of silver ions. These are the first representatives of structurally determined silver-sulfur tetrahedral clusters thus far. This work enriches the coinage-metal chalcogenide tetrahedral cluster portfolio, discovers vacant-corner SCs present in silver-sulfur hybrid tetrahedral clusters, and provides effective means for further development of Group 11 coinage-metal chalcogenide SCs.

Inspired by the metal active sites of [NiFeSe]-hydrogenases, a dppf-supported nickel(II) selenolate complex (dppf=1,1'-bis(diphenylphosphino)ferrocene) shows high catalytic activity for electrochemical proton reduction with a remarkable enzyme-like H2 evolution turnover frequency (TOF) of 7838 s-1 under an Ar atmosphere, which markedly surpasses the activity of a dppf-supported nickel(II) thiolate analogue with a low TOF of 600 s-1 . A combined study of electrochemical experiments and DFT calculations shed light on the catalytic process, suggesting that selenium atom as a bio-inspired proton relay plays a key role in proton exchange and enhancing catalytic activity of H2 production. For the first time, this type of Ni selenolate-containing electrocatalyst displays a high degree of O2 and H2 tolerance. Our results should encourage the development of the design of highly efficient oxygen-tolerant Ni selenolate molecular catalysts.