Development of Accurate DFT Methods for Computing Redox Potentials of Transition Metal Complexes: Results for Model Complexes and Application to Cytochrome P450

Single-electron reduction half potentials of 95 octahedral fourth-row transition metal complexes binding a diverse set of ligands have been calculated at the unrestricted pseudospectral B3LYP/LACV3P level of theory in a continuum solvent. Through systematic comparison of experimental and calculated potentials, it is determined that B3LYP strongly overbinds the d-manifold when the metal coordinates strongly interacting ligands and strongly underbinds the d-manifold when the metal coordinates weakly interacting ligands. These error patterns give rise to an extension of the localized orbital correction (LOC) scheme previously developed for organic molecules and which was recently extended to the spin-splitting properties of organometallic complexes. Mean unsigned errors in B3LYP redox potentials are reduced from 0.40 +/- 0.20 V (0.88 V max error) to 0.12 +/- 0.09 V (0.34 V max error) using a simple seven-parameter model. Although the focus of this article is on redox properties of transition metal complexes, we have found that applying our previous spin-splitting LOC model to an independent test set of oxidized and reduced complexes that are also spin-crossover complexes correctly reverses the ordering of spin states obtained with B3LYP. Interesting connections are made between redox and spin-splitting parameters with regard to the spectrochemical series and in their combined predictive power for properly closing the thermodynamic cycle of d-electron transitions in a transition metal complex. Results obtained from our large and diverse databases of spin-splitting and redox properties suggest that, while the error introduced by single reference B3LYP for simple multireference systems, like mononuclear transition metal complexes, remains significant, at around 2-5 kcal/mol, the dominant error, at around 10-20 kcal/mol, is in B3LYP's prediction of metal-ligand binding. Application of the LOC scheme to the rate-determining hydrogen atom transfer step in substrate hydroxylation by cytochrome P450 shows that this approach is able to correct the B3LYP barriers in comparison to recent kinetics experiments.