A Strategy for Finding a Reliable Starting Point for G$_0$W$_0$ Demonstrated for Molecules

Many-body perturbation theory in the G$_0$W$_0$ approximation is an increasingly popular tool for calculating electron removal energies and fundamental gaps for molecules and solids. However, the predictive power of G$_0$W$_0$ for molecules is limited by its sensitivity to the density functional theory (DFT) starting point. In this contribution, the starting point dependence of G$_0$W$_0$ is demonstrated for several small organic molecules. Analysis of the starting point dependence leads to the development of a non-empirical scheme that allows to find a consistent and reliable DFT starting point for G$_0$W$_0$ calculations by adapting the amount of Hartree-Fock-exchange in a hybrid DFT functional. The G$_0$W$_0$ spectra resulting from this {\it consistent starting point (CSP) scheme} reliably predict experimental photoelectron spectra over the full energy range. This is demonstrated for a test set of various typical organic semiconductor molecules.\\[4pt] [1] T. Korzdorfer and Noa Marom, Phys. Rev. B Rapid Communications {\bf 86}, 041110 (2012).