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

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin–state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six Fe(III) or Fe(II) complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin–state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way—in the form of single or double inequalities—are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin–state splittings of [Fe(III)(P)(2-MeIm)2]+, [Fe(III)(P)(2-MeIm)]+, [Fe(II)(P)(THF)2] and [Fe(II)(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in Fe(III) porphyrins. The present approach, 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 metalloporphyrins, which are important models to understand the electronic properties of heme proteins.