We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.

Many-body perturbation theory in the GW approximation is a useful method for describing electronic properties associated with charged excitations. A hierarchy of GW methods exists, starting from non-self-consistent G 0 W 0 , through partial self-consistency in the eigenvalues (evscGW) and in the Green's function (scGW 0 ), to fully self-consistent GW (scGW). Here, we assess the performance of these methods for benzene, pyridine, and the diazines. The quasiparticle spectra are compared to photoemission spectroscopy (PES) experiments with respect to all measured particle removal energies and the ordering of the frontier orbitals. We find that the accuracy of the calculated spectra does not match the expectations based on their level of selfconsistency. In particular, for certain starting points G 0 W 0 and scGW 0 provide spectra in better agreement with the PES than scGW.

GW calculations with a fully self-consistent Green's function G and screened interaction W -based on the iterative solution of the Dyson equation-provide a consistent framework for the description of groundand excited-state properties of interacting many-body systems. We show that for closed-shell systems selfconsistent GW reaches the same final Green's function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed-shell systems compared to G 0 W 0 based on Hartree-Fock and (semi)local density-functional theory. These improvements also translate to the electron density, as exemplified by an improved description of dipole moments, and permit us to assess the quality of ground-state properties such as bond lengths and vibrational frequencies. Many-body perturbation theory (MBPT) 1 in the GW approximation of the electronic self-energy 2,3 is presently the state-of-the-art method for describing the spectral properties of solids. 4,5 Recently, it has steadily gained popularity for molecules and nanosystems. 6 In addition, MBPT provides a prescription to extract total energies and structural properties from the GW approximation and therefore is a consistent theoretical framework for single-particle spectra and total energies.Due to its numerical cost and algorithmic difficulties, the GW method has only recently been applied self-consistently (i.e., nonperturbatively) to atoms, 7 molecules, 8 and molecular transport. 6 Predominantly, GW calculations are still performed perturbatively (one-shot G 0 W 0 ) on a set of singleparticle orbitals and eigenvalues obtained from a preceding density-functional theory 9 (DFT) or Hartree-Fock (HF) calculation. This procedure introduces a considerable starting-point dependence, 10-12 which can be eliminated by iterating the Dyson equation to self-consistency. [6][7][8]13 The resulting selfconsistent GW (sc-GW ) framework is a conserving approximation in the sense of Baym and Kadanoff 14 (i.e., it satisfies momentum, energy, and particle number conservation laws). sc-GW gives total energies 15 free from the ambiguities of the G 0 W 0 scheme, in which the results depend on the chosen total energy functional. 7 However, as in any self-consistent theory, the question remains if the self-consistent solution of the Dyson equation is unique. This issue is fundamentally different from the initial-state dependence of G 0 W 0 . For HF (Ref. 16) and local-density approximation (LDA)/generalized gradient approximation + U (GGA + U ) (Ref. 17) calculations, it is well known that the self-consistency cycle can reach many local minima instead of the global minimum. Moreover, a previous sc-GW study for the Be atom showed that normconserving pseudopotential calculations do not produce the same final GW Green's function (and the corresponding ionization potential) as all-electron calculations. 18 In this Rapid Communication, we demonstrate certain key aspects of the sc-GW approximation for closed-shell molecules that make...