Theoretical study of the efficiencies of graphyne supported Mo single-atom catalyst (SAC) and Mo-Ni dual-atom catalyst (DAC) on hydrogen evolution reaction

In this work, by adding one molybdenum atom or two molybdenum and nickel atoms on the surface graphyne support, single atom catalyst (SAC) and dual atoms catalyst (DAC) were designed. The different spin multiplicities for both catalysts were analyzed by the relative energies, adsorption energies and frontier orbitals. The results showed in both case of SACs and DACs, the catalyst with spin multiplicity = 3 is desired. Then, the efficiency of these two catalysts as high-performance and cost-effective catalysts in the HER process was investigated theoretically. All calculations were performed using M06-2X/def2SV level of theory. In the HER mechanism, it has been found that the DAC has higher favorability than the SAC. Both steps (Volmer reaction and Tafel or Heyrovsky reaction) are more exothermic using DAC, and the difference between SAC and DAC is higher in the second step. The effect of solvent on these steps has been studied using water and methanol as two common solvents. The reactions are less exothermic in the solvent; but they are still highly exothermic and thermodynamically favorable. Moreover, despite the gas phase data, in both solvents, the use of DAC gives less favorable data versus the SAC. The data also showed the little preference of water versus the methanol as solvent.