$GW$100: a plane wave perspective for small molecules

In a recent work, van Setten and coworkers have presented a carefully converged $G_0W_0$ study of 100 closed shell molecules [J. Chem. Theory Comput. 11, 5665 (2015)]. For two different codes they found excellent agreement to within few 10 meV if identical Gaussian basis sets were used. We inspect the same set of molecules using the projector augmented wave method and the Vienna ab initio simulation package (VASP). For the ionization potential, the basis set extrapolated plane wave results agree very well with the Gaussian basis sets, often reaching better than 50 meV agreement. In order to achieve this agreement, we correct for finite basis set errors as well as errors introduced by periodically repeated images. For electron affinities below the vacuum level differences between Gaussian basis sets and VASP are slightly larger. We attribute this to larger basis set extrapolation errors for the Gaussian basis sets. For quasi particle (QP) resonances above the vacuum level, differences between VASP and Gaussian basis sets are, however, found to be substantial. This is tentatively explained by insufficient basis set convergence of the Gaussian type orbital calculations as exemplified for selected test cases.