Benchmarking the <i>GW</i> Approximation against Coupled-Cluster Theory for 3 <i>d</i> Transition Metals

Transition-metal-containing molecules and materials present significant computational challenges, requiring careful benchmarking to determine which quantum chemical methods provide the most accurate estimates. In this work, we assess the performance of the <i>GW</i> 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 3<i>d</i> transition-metal systems, including 10 atoms and 44 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 <i>GW</i> (<i>G</i>₀<i>W</i>₀) 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 <i>G</i>₀<i>W</i>₀, when using the PBE0 functional as the starting point. EOM-CCSD is, on average, only 0.13 eV more accurate than <i>G</i>₀<i>W</i>₀@PBE0 relative to ΔCCSD(T). While eigenvalue (ev<i>GW</i>) or quasi-particle (qp<i>GW</i>) self-consistent <i>GW</i> 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). Both <i>G</i>₀<i>W</i>₀ and the CC-based methods yield mean absolute errors relative to experiments below 0.6 eV, further underscoring their reliability for this class of systems. However, <i>G</i>₀<i>W</i>₀ is significantly more computationally efficient than ΔCCSD(T) and EOM-CCSD, making it a compelling alternative for extended open-shell transition-metal systems.