  We present a comprehensive first-principles study of the electronic structure
of 51 semiconducting monolayer transition metal dichalcogenides and -oxides in
the 2H and 1T hexagonal phases. The quasiparticle (QP) band structures with
spin-orbit coupling are calculated in the $G_0W_0$ approximation and comparison
is made with different density functional theory (DFT) descriptions. Pitfalls
related to the convergence of $GW$ calculations for 2D materials are discussed
together with possible solutions. The monolayer band edge positions relative to
vacuum are used to estimate the band alignment at various heterostructure
interfaces. The sensitivity of the band structures to the in-plane lattice
constant is analysed and rationalized in terms of the electronic structure.
Finally, the $q$-dependent dielectric functions and effective electron/hole
masses are obtained from the QP band structure and used as input to a 2D
hydrogenic model to estimate exciton binding energies. Throughout the paper we
focus on trends and correlations in the electronic structure rather than
detailed analysis of specific materials. All the computed data is available in
an open database.
