Improved density matrices for accurate molecular ionization potentials

The ionization potential and the other quasiparticle energies of electrons in molecules or solids are often evaluated within the GW approximation. Though this approximation can be considered as a fantastic tradeoff between accuracy and simplicity, there exist ionization potentials of simple molecules that are unacceptably wrong. We derive here a working approximation to the density matrix that we name the GW density matrix. This relatively light approximation improves several physical properties and, in particular, it yields excellent electronic dipoles for the examined molecules. As a direct consequence, the ionization potentials are affected through the change in the electrostatic potential and in the exchange operator. Benchmarking on a set of 34 molecules, we demonstrate that most of the error in the GW ionization potentials is indeed eliminated thanks to this simple addition. This contribution is not a vertex correction, but nevertheless it is crucial when going beyond the standard GW. (authors)