  Two-dimensional (2D) materials exhibit a wide range of remarkable phenomena,
many of which owe their existence to the relativistic spin-orbit coupling (SOC)
effects. To understand and predict properties of materials containing heavy
elements, such as the transition-metal dichalcogenides (TMDs), relativistic
effects must be taken into account 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 that arise 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 either at the
nonrelativistic or 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') structures, along with a discussion of
their SOC-driven properties (Rashba splitting and $\mathbb{Z}_2$ topological
invariants). We demonstrate the viability of our approach even when large basis
sets with multiple basis functions involving various valence orbitals (denoted
triple- and quadruple-$\zeta$) are used in the relativistic regime. Our method
does not require the use of pseudopotentials and provides access to all
electronic states within the same framework. Our study paves the way for direct
studies of material properties, such as the parameters in spin Hamiltonians,
that depend heavily on the electron density near atomic nuclei where
relativistic and SOC effects are the strongest.
