Benchmark Many-Body <i>GW</i> and Bethe–Salpeter Calculations for Small Transition Metal Molecules

We study the electronic and optical properties of 39 small molecules containing transition metal atoms and 7 others related to quantum-dots for photovoltaics. We explore in particular the merits of the many-body <i>GW</i> formalism, as compared to the ΔSCF approach within density functional theory, in the description of the ionization energy and electronic affinity. Mean average errors of 0.2–0.3 eV with respect to experiment are found when using the PBE0 functional for ΔSCF and as a starting point for <i>GW</i>. The effect of partial self-consistency at the <i>GW</i> level is explored. Further, for optical excitations, the Bethe–Salpeter formalism is found to offer similar accuracy as time-dependent DFT-based methods with the hybrid PBE0 functional, with mean average discrepancies of about 0.3 and 0.2 eV, respectively, as compared to available experimental data. Our calculations validate the accuracy of the parameter-free <i>GW</i> and Bethe–Salpeter formalisms for this class of systems, opening the way to the study of large clusters containing transition metal atoms of interest for photovoltaic applications