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

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