Engineering catalytic sites at the atomic level provides an opportunity to understand the catalyst’s active sites, which is vital to the development of improved catalysts. Here we show a reliable and tunable polyoxometalate template-based synthetic strategy to atomically engineer metal doping sites onto metallic 1T-MoS 2 , using Anderson-type polyoxometalates as precursors. Benefiting from engineering nickel and oxygen atoms, the optimized electrocatalyst shows great enhancement in the hydrogen evolution reaction with a positive onset potential of ~ 0 V and a low overpotential of −46 mV in alkaline electrolyte, comparable to platinum-based catalysts. First-principles calculations reveal co-doping nickel and oxygen into 1T-MoS 2 assists the process of water dissociation and hydrogen generation from their intermediate states. This research will expand on the ability to improve the activities of various catalysts by precisely engineering atomic activation sites to achieve significant electronic modulations and improve atomic utilization efficiencies.

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Platinum (Pt) is the most active and stable HER catalyst, but its high cost and low abundance hinder its widespread applications. [3][4][5][6] Recently, tremendous efforts have been devoted to the search for noble-metal-free catalysts to replace Pt-based catalysts in the generation of H 2 with a high current density at a low overpotential. [7][8][9][10] In particularly, molybdenum carbides and molybdenum phosphides have been demonstrated as active and robust HER catalysts due to their high conductivities, high catalytic activities, and excellent stabilities. [11][12][13][14][15] The high-performance catalytic activities of these materials may be related to the function of their heteroatoms, such as phosphorus, which possesses lone-pair electrons in 3p orbitals and vacant 3d orbitals and can thus accommodate the surface charge as well as induce local charge density. [16] Nitrides of transition metals have also been shown to have excellent catalytic activities in the HER. [17][18][19][20][21] Taking all the above works together, we predicted that nitrogen (N)-doped molybdenum carbide and phosphide hybrids, N@MoPCx, might be promising electrocatalysts for efficient hydrogen evolution. However, it remains a challenge to obtain a targeted N-doped molybdenum carbide and phosphide hybrid with a uniform distribution and desirable porosity that also exhibits high electrocatalytic activity, which requires (i) preventing the aggregation of nanoparticles; (ii) obtaining a desirable porosity; and (iii) achieving uniform carburization, phosphorization, and heteroatoms doping. To avoid the aggregation of nanoparticles and increase their electrical conductivities, substrates such as carbon cloth, carbon nanotubes, and graphene have been introduced into metal-based catalysts for use in multiple catalytic reactions. [22][23][24] However, the introduction of substrates creates additional cost and still cannot completely prevent aggregation.Polyoxometalates (POMs) are a special class of well-defined molecular metal oxide clusters with a wide range of applications in medicine, catalysis, materials sciences, etc. [25][26][27][28][29][30] It is well known that organoimido derivatives of POMs can be prepared by introducing exogenous N-containing ligands to replace the oxo groups in the POM clusters. [31][32][33][34][35] The controllable preparation of multifunctionalized derivatives of hexamolybdate has been achieved by the powerful N,N′-dicyclohexylcarbodiimide (DCC)-dehydrating protocol by Ruhlmann and our group. [36,37] P-containing organoimido derivatives of POMs could be The efficient evolution of hydrogen through electrocatalysis is considered a promising approach to the production of clean hydrogen fuel. Platinum (Pt)-based materials are regarded as the most active hydrogen evolution reaction (HER) catalysts. However, the low abundance and high cost of Pt hinders the large-scale application of these catalysts. Active, inexpensive, and earth-abundant electrocatalysts to replace Pt-based materials would be highly beneficial to the ...

1T-MoS 2 and single-atom modified analogues represent a highly promising class of low-cost catalysts for hydrogen evolution reaction (HER). However, the role of single atoms, either as active species or promoters, remains vague despite its essentiality toward more efficient HER. In this work, we report the unambiguous identification of Ni single atom as key active sites in the basal plane of 1T-MoS 2 (Ni@1T-MoS 2) that result in efficient HER performance. The intermediate structure of this Ni active site under catalytic conditions was captured by in situ X-ray absorption spectroscopy, where a reversible metallic Ni species (Ni 0) is observed in alkaline conditions whereas Ni remains in its local structure under acidic conditions. These insights provide crucial mechanistic understanding of Ni@1T-MoS 2 HER electrocatalysts and suggest that the understanding gained from such in situ studies is necessary toward the development of highly efficient single-atom decorated 1T-MoS 2 electrocatalysts.

Abstract-This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.Index Terms-Power control, coordinated beamforming, maxmin duality, effective network, large system analysis, multicell network, nonlinear Perron-Frobenius theory, random matrix theory.

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains with boundary. We also make precise conjectures about the relationship of this theory to scaling limits of random planar maps with boundary conformally embedded onto the disk.

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2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.