Dataset for "Band structures and Z2 invariant of 2D transition metal dichalcogenides from fully relativistic Dirac--Kohn--Sham theory using Gaussian-type orbitals"

Two-dimensional (2D) materials exhibit a wide range of remarkable phenomena, many of which owe their existence to the relativistic spin--orbit coupling (SOC). To understand and predict properties of materials containing heavy elements, such as the transition metal dichalcogenides (TMDs), full account of relativistic effects is mandatory in first-principles calculations. We present an all-electron method based on the four-component Dirac Hamiltonian and Gaussian-type orbitals (GTOs) that overcomes complications associated with linear dependencies and ill-conditioned matrices arising when diffuse functions are included in the basis. Until now, there has been no systematic study of the convergence of GTO basis sets for periodic solids neither at the nonrelativistic nor the relativistic level. Here, we provide such a study of relativistic band structures of the 2D TMDs in the hexagonal (2H), tetragonal (1T), and distorted tetragonal (1T') structural phases while focusing on SOC-driven properties (the Rashba splitting and the $\mathbb{Z}_2$ topological invariant). We demonstrate that our approach is valid even if large basis sets with multiple basis functions corresponding to each valence atomic orbital (denoted triple- and quadruple-$\zeta$) are used in the relativistic regime. The method does not require the use of pseudopotentials and provides access to all electronic states within the same framework, paving the way for direct studies of material properties that depend heavily on the electron density near atomic nuclei where relativistic effects and SOC are strongest, such as the parameters of the spin Hamiltonian.