Size-dependent trends in the hydrogen evolution activity and electronic structure of MoS 2 nanotubes.

The thermodynamics of hydrogen evolution on MoS 2 nanotubes is studied for the first time using periodic density functional theory calculations to obtain hydrogen adsorption free energies (Δ G H ads ) on pristine nanotubes and those with S-vacancy defects. Armchair and zigzag MoS 2 nanotubes of different diameters, ranging from 12 to 22 Å, are examined. The H adsorption energy is observed to become more favourable (lower Δ G H ads ) as nanotube diameter decreases, with Δ G H ads 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 Δ G H ads 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 Δ G H ads , 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 Δ G H ads . A linear relation between the position of the Mo d-states and Δ G H ads is found, with d-states closer to the Fermi level leading to strong hydrogen adsorption. Overall this work highlights the relevance of MoS 2 nanotubes as promising hydrogen evolution catalysts and explains trends in their activity using the energies of the electronic states involved in binding hydrogen.