Spin-state energetics of heme-related models from DFT and coupled cluster calculations

Spin-state energetics of metalloporphyrins and heme groups is elucidated by performing high-level coupled cluster calculations for their simplified mimics. An efficient computational protocol is proposed—based on the mix of extrapolation to complete basis set and explicitly correlated (F12) methodology—which retains the high accuracy of the CCSD(T) method at a cost that makes it applicable also to relatively large models, e.g., FeP and FeP(Cl) (P = porphin). Adequacy of CCSD(T) is supported by analysis of multireference character and comparison with the completely renormalized CR-CC(2,3) method. The high-level coupled cluster results are used for assessment of density functional theory (DFT) methods, for which an accurate description of the spin-state energetics is recognized as a major challenge. Although the DFT results are highly functional-dependent, it is shown that the spin-state energetics of a full heme model and its simplified mimic remain in a good linear correlation. This makes it possible to estimate the spin-state energetics of full heme models based on the accurate CCSD(T) results for their mimics, as illustrated for porphyrin complexes of Fe(II), Mn(II), and Co(II); pentacoordinate heme complexes of Fe(II) and Fe(III); and a ferryl heme model. Comparison with the available experimental data is also presented