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

Abstract

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.

Prediction of the reduction potential in transition‐metal containing complexes: How expensive? For what accuracy?

“…However, these computational protocols (SMD or PCM‐B3LYP/BS1) still had three exceptions, ferri/ferrocyanide couple ( 25 , Fe(CN) 6 3‐/4‐ ) and two 1,1'‐disubstituted ferrocenes: ( 36 , 1,1'‐bis( N , N ‐dimethylamino)ferrocene and 43 , 1,1'‐dibromo‐ferrocene). Baik, Hughes, and Friesner also encountered the same exception of ferricyanide/ferrocyanide couple . The absolute deviations between experimental and computed potentials from their previous study were 1.138 V at B3LYP/6‐31G** level of computation, and 0.787 V for B3LYP/cc‐pVTZ(‐f).…”

“…Density functional theory (DFT) has proven to be a reliable, convenient, and advantageous tool for computing reduction potentials . Although many studies have utilized DFT, the absolute deviations between the experimental data and computed values are still quite large for some transition metal‐containing complexes (including both inorganic and organometallic complexes) compared with simple organic molecules.…”

Computational Redox Potential Predictions: Applications to Inorganic and Organic Aqueous Complexes, and Complexes Adsorbed to Mineral Surfaces

“…While for experimentalists, the nature of the redox process of metal-bound ligands is often difficult to define, be it either metal-based or ligand-based, the source and sink of the electron density can be more easily and quantifiably tracked using calculations. Spin cross over and ligand non-innocence in redox potential predictions are discussed by Hughes et al [81].…”

“…The higher this energy difference between the energy levels of orbital is (the former d orbitals now have so-called t 2g or e g symmetry), the most likely is a low-spin (LS) configuration of the transition metal. In contrast, for degenerate orbitals or small amounts of crystal-field splitting, Hund's rule calls for a high-spin (HS) configuration [81].…”

“…The hybrid DFT B3LYP method with the solvation effects included using the PB continuum solvation model predicted the reduction potentials of 95 octahedral 3d TM complexes coordinating with different ligands [81]. Systematic improvement of the calculated reduction potentials were obtained by introducing a correction term, in which the B3LYP-predicted redox potentials were corrected by applying an empirical correction, the so-called D-block Localized Orbital Correction (DBLOC).…”