Size-dependent trends in the hydrogen evolution activity and electronic structure of MoS₂ nanotubes

The thermodynamics of hydrogen evolution on MoS₂ nanotubes is studied for the first time using periodic density functional theory calculations to obtain hydrogen adsorption free energies (ΔG _H ) on pristine nanotubes and those with S-vacancy defects. Armchair and zigzag MoS₂ nanotubes of different diameters, ranging from 12 to 22 Å, are examined. The H adsorption energy is observed to become more favourable (lower ΔG _H ) as nanotube diameter decreases, with ΔG _H values ranging from 1.82 to 1.39 eV on the pristine nanotubes, and from 0.03 to -0.30 eV at the nanotube S-vacancy defect sites. An ideal thermoneutral ΔG _H value of nearly 0 eV is observed at the S-vacancy site on nanotubes around 20 to 22 Å in diameter. For the pristine nanotubes, density of states calculations reveal that electron transfer from S to Mo occurs during H adsorption, and the energy gap between these two states yields a highly reliable linear correlation with ΔG _H , where a smaller gap leads to a more favourable hydrogen adsorption. For the S-vacancy defect site the H adsorption resembles that on a pure metallic surface, meaning that a traditional d-band centre model can be applied to explain the trends in ΔG _H . A linear relation between the position of the Mo d-states and ΔG _H is found, with d-states closer to the Fermi level leading to strong hydrogen adsorption. Overall this work highlights the relevance of MoS₂ nanotubes as promising hydrogen evolution catalysts and explains trends in their activity using the energies of the electronic states involved in binding hydrogen.