Facet- and thickness-dependent band-edge alignment at ZrSe\texorpdfstring{$_3$}{3} surfaces: hybrid-functional calculations with spin-orbit coupling
Transition-metal trichalcogenides MX$_3$ are quasi-one-dimensional van der Waals materials whose layers form through lateral chain binding, giving them an interlayer cleavage plane and in-plane electronic anisotropy. Among them, ZrSe$_3$ is stable under ambient conditions and semiconducting. Exfoliated crystals expose four crystallographic planes, and electrocatalytic measurements on an individual crystal assigned the hydrogen evolution activity to the high-energy (210) facet rather than to the basal plane. Those non-basal surfaces remain uncharacterized, since the available calculations treat either the bulk crystal or the free-standing basal monolayer. Here, we compute the surface energies and the equilibrium morphology of these four surfaces with a dispersion-corrected semilocal functional, and their band-edge alignment with the HSE06 hybrid functional including spin-orbit coupling. The surface energies span nearly an order of magnitude, from \SI{0.097}{\joule\per\meter\squared} for (001) to \SI{0.869}{\joule\per\meter\squared} for (010), and the Wulff shape exposes the four observed planes with area fractions of \SI{17.1}{\percent}, \SI{4.4}{\percent}, \SI{71.4}{\percent}, and \SI{7.0}{\percent}. The ionization potential varies by \SI{0.45}{\electronvolt} between facets and the electron affinity by \SI{0.80}{\electronvolt}, the gap of (210) falls from 1.43 to \SI{0.94}{\electronvolt} between 10 and \SI{23}{\angstrom}, and (010) remains metallic. The facets separate according to whether the cut preserves or distorts the Se-Se dimer, and the distorted dimers concentrate the frontier states. Because the same dimer governs the bulk electronic structure of the MX$_3$ family, the criterion transfers to the related trichalcogenides.