Objective performance of the GW approximation and the Bethe-Salpeter Equation for molecules

We have evaluated the quality of the quasiparticle energies obtained within the $GW$ approximation and of the optical excitations with the solution of the Bethe-Salpeter equation (BSE) for molecules. The calculations have been performed with a recently developed code based on Gaussian [1,2] that allowed us to use the exact same techniques as the one employed in traditional quantum chemistry. We demonstrate [3] the extreme sensitivity of the $GW$ and BSE results upon the Kohn-Sham starting point. Most of the starting point dependence in BSE is to be ascribed to the underlying $GW$ band structure. We highlight the problem of the triplet excitations that are equally underestimated in time-dependent density-functional theory and in BSE. [1] F. Bruneval, J. Chem. Phys. \textbf{136}, 194107 (2012). [2] F. Bruneval and M.A.L. Marques, J. Chem. Theory Comput. \textbf{9}, 324 (2013). [3] F. Bruneval, S. M. Hamed and J. B. Neaton, J. Chem. Phys. \textbf{142}, 244101 (2015).