Predicting Spin States of Iron Porphyrins with DFT Methods Including Crystal Packing Effects and Thermodynamic Corrections

The accuracy of DFT methods for spin-state energetics is assessed by probing their ability to predict the experimental ground states of selected iron porphyrins in solid state. To this end, six Fe(III) or Fe(II) porphyrin complexes with experimentally assigned spin states and known crystal structures are taken under scrutiny. In each case, periodic and molecular density functional theory (DFT) calculations are employed to quantify how the crystal packing and porphyrin substituents affect their spin-state energetics. The crystal packing effect is resolved into the direct and structural components. The crystal packing and substituent effects are shown to greatly vary from case to case. It is proposed that by knowing the crystal packing and substituent effects, and the Gibbs free energy thermodynamic correction from calculations on a given experimentally characterized system, one can use the knowledge of the experimental ground state in order to derive a quantitative constrain on the electronic energy difference for the corresponding simplified (porphin) model. The constraints derived in such a way are used to assess the accuracy of dispersion-corrected DFT methods for spin-state energetics of [FeP(2-MeIm)2]+, [FeP(2-MeIm)]+, [FeP(THF)2] and FeP models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). Relatively good accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3). By contrast, hybrid functionals with reduced admixtures of exact exchange (B3LYP*-D3, TPSSh-D3), although often recommended in the literature for transition metal systems, are shown here to considerably overstabilize the intermediate spin state, especially in Fe(III) porphyrins. The new approach presented here, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for e.g., mono- and bis-imidazole ligated Fe(III) porphyrins and square-planar Fe(II) porphyrin, which are important models to understand the electronic properties of heme prosthetic groups in metalloproteins.