Electronic and spin–orbit properties of the kagome MOF family M₃(1,2,5,6,9, 10-triphenylenehexathiol)₂ (M  =  Ni, Pt, Cu and Au)

We investigate, through first-principles calculations, the electronic band structure—including the spin–orbit coupling—of single-layer M₃(THT)₂ metal-organic frameworks, where M  =  Ni, Pt, Cu and Au, and THT is the 1,2,5,6,9,10-triphenylenehexathiol molecule. This MOF family contains, in its electronic structure, spin–orbit gaps that could allow their use in quantum spin Hall effect devices. We find that the partial inclusion of exact exchange in the calculations (beyond a semi-local exchange-correlation level) leads to quantitative, and even qualitative, modifications of the electronic structure of Ni₃(THT)₂ and Pt₃(THT)₂ relative to calculations at semi-local exchange-correlation level: upon inclusion of exact exchange, the predicted fundamental band gap of these semiconductor materials increases to more than twice, and the predicted spin–orbit gaps change by as much as 44%. Even the qualitative description of the valence bands of these materials changes upon inclusion of exact exchange. We also find that the magnitudes of the spin–orbit gaps are not monotonic with the atomic number of the metal atom. (letter)