van der Waals bonding and the quasiparticle band structure of SnO from first principles

In this work we have investigated the structural and electronic properties of SnO, which is built up from layers kept together by van der Waals (vdW) forces. The combination of a vdW functional within density functional theory (DFT) and quasiparticle band structure calculations within the $GW$ approximation provides accurate values for the lattice parameters, atomic positions, and the electronic band structure including the fundamental (indirect) and the optical (direct) band gap without the need of experimental or empirical input. A systematic comparison is made between different levels of self-consistency within the $GW$ approach ${$following the scheme of Shishkin et al. [Phys. Rev. B 75, 235102 (2007)]$}$ and the results are compared with DFT and hybrid functional results. Furthermore, the effect of the vdW-corrected functional as a starting point for the $GW$ calculation of the band gap has been investigated. Finally, we studied the effect of the vdW functional on the electron charge density.