With first-principles calculations, we find a new strategy for developing high-performance catalysts for hydrogen evolution reaction (HER) via controlling the morphology and size of nanopolygons of monolayer transition-metal dichalcogenides (npm-MS, with M = Mo, W, or V). Particularly, through devising a quantitative method to measure HER-active sites per unit mass and using such HER site density to comparatively gauge npm-MS performance, we identify three keys in making npm-MS with optimal HER performance: (a) npm-MS should be triangular with each edge being M-terminated and each edge-M atom passivated by one S atom; (b) each edge of npm-MoS and WS should have 5-6 metal atoms as HER site density drops below/above these sizes optimal both for HER and practical npm growth; and (c) npm-VS is immune to this overly fastidious size dependence. Known experimental data on npm-MoS indeed support the plausibility of practicing these design rules. We expect that raising the nucleation density and controlling the growth time to favor the production of our proposed ultrasmall npm-MS are critical but practical. Research on npm-VS would bear the highest impact because of its size-forgiving HER performance and relatively high abundance and low cost.
By adopting the first-principle methods based on the density functional theory, we studied the structural, electronic, and magnetic properties of defected monolayer WSe
2
with vacancies and the influences of external strain on the defected configurations. Our calculations show that the two W atom vacancies (V
W2
) and one W atom and its nearby three pairs of Se atom vacancies (V
WSe6
) both induce magnetism into monolayer WSe
2
with magnetic moments of 2 and 6 μ
B
, respectively. The magnetic moments are mainly contributed by the atoms around the vacancies. Particularly, monolayer WSe
2
with V
W2
is half-metallic. Additionally, one Se and one W atom vacancies (V
Se
, V
W
), two Se atom vacancies (V
Se-Se
), and one W atom and the nearby three Se atoms on the same layer vacancy (V
WSe3
)-doped monolayer WSe
2
remain as non-magnetic semiconducting. But the impure electronic states attributed from the W d and Se p orbitals around the vacancies locate around the Fermi level and narrow down the energy gaps. Meanwhile, our calculations indicate that the tensile strain of 0~7% not only manipulates the electronic properties of defected monolayer WSe
2
with vacancies by narrowing down their energy gaps, but also controls the magnetic moments of V
W
-, V
W2
-, and V
WSe6
-doped monolayer WSe
2
.
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