Crystal field, ligand field, and interorbital effects in two-dimensional transition metal dichalcogenides across the periodic table

Two-dimensional (2D) transition metal dichalcogenides (TMDs) exist in two polymorphs, referred to as 1T and 1H, depending on the coordination sphere of the transition metal atom. The broken octahedral and trigonal prismatic symmetries lead to different crystal and ligand field splittings of the d electron states, resulting in distinct electronic properties. In this work, we quantify the crystal and ligand field parameters of 2D TMDs using a Wannier-function approach. We adopt the methodology proposed by Scaramucci et al (2015 J. Phys.: Condens. Matter 27 175503) that allows to separate various contributions to the ligand field by choosing different manifolds in the construction of the Wannier functions. We discuss the relevance of the crystal and ligand fields in determining the relative stability of the two polymorphs as a function of the filling of the d-shell. Based on the calculated parameters, we conclude that the ligand field, while leading to a small stabilizing factor for the 1H polymorph in the d1 and d2 TMDs, plays mostly an indirect role and that hybridization between different d orbitals is the dominant feature. We investigate trends across the periodic table and interpret the variations of the calculated crystal and ligand fields in terms of the change of charge-transfer energy, which allows developing simple chemical intuition