Benchmarking the GW Approximation Against Coupled- Cluster Theory for 3d Transition Metals

Transition-metal-containing molecules and materials present significant computational challenges, requiring careful benchmarking to determine which quantum chemical reference data offers the most accurate approximations. We assess the performance of the GW approximation and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing electron-attachment (EA) energies and ionization potentials (IP) for a benchmark set of open-shell 3d transition-metal atoms and molecules. As a reference, we use the ΔCCSD(T) (coupled-cluster singles and doubles plus perturbative triples) approach. Our results show that the single-shot GW (G0W0) approximation achieves an accuracy comparable to that of higher-level wave function methods. For transition-metal atoms, mean absolute errors range from 0.05 to 0.23 eV for EOM-CCSD and from 0.18 to 0.26 eV for G0W0, when using the PBE0 functional as the starting point. In the molecular benchmark set, these errors increase to 0.25–0.41 eV for EOM-CCSD and 0.37–0.60 eV for G0W0@PBE0. While eigenvalue (evGW) or quasi-particle (qpGW) self-consistent GW calculations reduce the dependence on the starting point, they come with a higher computational cost and offer no significant improvement in the agreement with ΔCCSD(T). Our findings indicate that, for our benchmark set of transition-metal atoms and molecules, EOM-CCSD is, on average, only 0.14 eV more accurate than G0W0@PBE0 relative to ΔCCSD(T). However, G0W0 is significantly more computationally efficient than ΔCCSD(T) and EOM-CCSD, making it a compelling alternative for extended open-shell transition-metal systems.