  We present a systematic study of the variables affecting the electronic and
optical properties of two-dimensional(2D) crystals within \textit{ab initio} GW
and GW plus Bethe Salpeter Equation (GW-BSE) calculations. As a prototypical 2D
transition metal dichalcogenide material, we focus our study on monolayer
MoS${}_2$. We find that the reported variations in GW-BSE results in the
literature for monolayer MoS${}_2$ and related systems arise from different
treatments of the long-range Coulomb interaction in supercell calculations and
convergence of k-grid sampling and cutoffs for various quantities such as the
dielectric screening. In particular, the quasi-2D nature of the system gives
rise to fast spatial variations in the screening environment, which are
computationally challenging to resolve. We also show that common numerical
treatments to remove the divergence in the Coulomb interaction can shift the
exciton continuum leading to false convergence with respect to k-point
sampling. Our findings apply to GW-BSE calculations on any low-dimensional
semiconductors.
