Assessment of Quantum Mechanical Methods for Copper and Iron Complexes by Photoelectron Spectroscopy

Broken-symmetry density functional theory (BS-DFT) calculations are assessed for redox energetics [Cu(SCH₃)₂]^1-/0, [Cu(NCS)₂]^1-/0, [FeCl₄]^1-/0, and [Fe(SCH₃)₄]^1-/0 against vertical detachment energies (VDE) from valence photoelectron spectroscopy (PES), as a prelude to studies of metalloprotein analogs. The M06 and B3LYP hybrid functionals give VDE that agree with the PES VDE for the Fe complexes, but both underestimate it by ∼400 meV for the Cu complexes; other hybrid functionals give VDEs that are an increasing function of the amount of Hartree-Fock (HF) exchange and so cannot show good agreement for both Cu and Fe complexes. Range-separated (RS) functionals appear to give a better distribution of HF exchange since the negative HOMO energy is approximately equal to the VDEs but also give VDEs dependent on the amount of HF exchange, sometimes leading to ground states with incorrect electron configurations; the LRC-ωPBEh functional reduced to 10% HF exchange at short-range give somewhat better values for both, although still ∼150 meV too low for the Cu complexes and ∼50 meV too high for the Fe complexes. Overall, the results indicate that while HF exchange compensates for self-interaction error in DFT calculations of both Cu and Fe complexes, too much may lead to more sensitivity to nondynamical correlation in the spin-polarized Fe complexes.