Biased Spin-State Energetics of Fe(II) Molecular Complexes within Density-Functional Theory and the Linear-Response Hubbard<i>U</i>Correction

Abstract

The spin-state energetics of six Fe(II) molecular complexes are computed using the linear-response Hubbard <i>U</i> approach within DFT. The adiabatic energy differences, Δ<i>E</i>_H-L, between the high-spin (<i>S</i> = 2) and the low-spin (<i>S</i> = 0) states are computed and compared with accurate-coupled cluster-corrected CASPT2 results. We show that DFT+U fails in correctly capturing the ground state for strong-field ligands yielding Δ<i>E</i>_H-L that are almost constant throughout the molecular series. This bias toward high spin together with the metal/ligand charge transfer upon <i>U</i> correction are here quantified and explained using molecular orbital diagrams involving both σ- and π-bonding interactions. With increasing ligand-field strengths this bias also increases owing to the stronger molecular character of the metal/ligand Kohn-Sham orbitals thus resulting in large deviations from the reference larger than 4 eV. Smaller values of <i>U</i> can be employed to mitigate this effect and recover the right energetics.