Supplementary Material

Nonlinear least squares fit of periodic RPA ΔEads versus E_cut^χ; Nonlinear least squares fits of periodic RPA EIS and EFS versus k-point mesh density; Periodic DFT-PBE structures along the MEP using the 3×3 surface supercell Fe(110) slab models; Computational details of thermal and vibrational corrections to derive an experiment-based adsorption electronic energy; Periodic DFT-PBE energy profiles along the MEP using 2×2 and 3×3 surface supercell Fe(110) slab models; Emb-RPA energy profiles with spin constraints of 32 unpaired electrons using E_(cluster,GTO)^(emb-DFT) as E_cluster^(emb-DFT); Emb-RPA energy profiles with spin constraints of 30, 34, and 36 unpaired electrons using E_(cluster,PW)^(emb-DFT) or E_(cluster,GTO)^(emb-DFT) as E_cluster^(emb-DFT); Adsorption energies and barriers predicted by emb-RPA with spin constraints of 30, 32, 34, and 36 unpaired electrons