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

Transition-metal-containing molecules and materials present significant computa- tional challenges, requiring careful benchmarking to determine which quantum chem- ical methods provide the most accurate estimates. In this work, we assess the perfor- mance of the GW approximation and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing ionization potentials (IP) and electron- attachment (EA) energies across a comprehensive benchmark set of open-shell 3d transition-metal systems, including 10 atoms and 44 molecules. As a reference, we use the ∆CCSD(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. The mean absolute errors range from 0.19 to 0.33 eV for EOM-CCSD and from 0.30 to 0.47 eV for G0W0, when using the PBE0 functional as the starting point. EOM-CCSD is, on average, only 0.13 eV more accurate than G0W0@PBE0 relative to ∆CCSD(T). While eigenvalue (evGW) or quasi-particle (qpGW) self-consistent GW calculations reduce the dependence on the starting point, they come with a higher computa- tional cost and offer no significant improvement in the agreement with ∆CCSD(T). Both G0W0 and the CC-based methods yield mean absolute errors relative to exper- iments below 0.6 eV, further underscoring their reliability for this class of systems. However, G0W0 is significantly more computationally efficient than ∆CCSD(T) and EOM-CCSD, making it a compelling alternative for extended open-shell transition- metal systems.