Reduction of Systematic Uncertainty in DFT Redox Potentials of Transition-Metal Complexes

Abstract

Reliable calculations of redox potentials could provide valuable insight into catalytic mechanisms of electrochemically active transition-metal complexes as well as guidelines for the design of new electrocatalysts. However, the correlation between theoretical and experimental data is often uncertain, since redox properties depend strongly on experimental conditions of electrochemical measurements, including the nature of the solvent, electrolyte, and working electrode. Here, we show that the use of internal references allows for quantitative theoretical predictions of redox potentials with standard deviations σ comparable to typical experimental errors of cyclic voltammetry measurements. Agreement for first-, second-, and third-row transition-metal complexes is demonstrated even at a rather modest level of density functional theory (σ = 64 mV for the UB3LYP/6-311G* level). This is shown for a series of benchmark redox couples, including ([MCp 2 ] 0/+ (Cp = η 5 -cyclopentadienyl), [MCp* 2 ] 0/+ (Cp* = η 5 -1,2,3,4,5pentamethylcyclopentadienyl), [M(bpy) 3 ] 2+/3+ (bpy =2,2′-bipyridine), and [Ir(acac) 3 ] 0/+ (acac = acetylacetonate), with M = Fe, Co, Ni, Ru, Os, or Ir) in various nonaqueous solvents [acetonitrile (MeCN), dimethyl sulfoxide (DMSO), and dichloromethane (DCM)].

Molecular Design Parameters of Anthraquinone Dyes for Guest–Host Liquid-Crystal Applications: Experimental and Computational Studies of Spectroscopy, Structure, and Stability

“…The Journal of Physical Chemistry C Article the potentials were calculated relative to those of a reference compound, rather than as absolute potentials, in order to remove the influence of systematic errors between the experimental conditions used here and those used to determine absolute potentials of reference compounds reported elsewhere. 65 Duroquinone (DQ), shown in Figure 14, was chosen as the reference compound because of its structural similarity to the dyes and its experimentally accessible oxidation and reduction potentials, which we measured to be +2.15 and −1.21 V vs Fc/Fc + , respectively, using spectroelectrochemistry and the same conditions used for the dyes, as reported in the Supporting Information ( Figure S4); these values are comparable to those reported for DQ under different experimental conditions. 66,67 Isodesmic reaction schemes for the reduction and oxidation of a dye with duroquinone as the reference compound are given as reactions 3 and 4 below, from which eqs 5 and 6, respectively, are obtained using the relationship ΔG = −nFE.…”

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

“…Although the B3LYP hybrid (Hartree-Fock-DFT) functional has been found to accurately predict redox potentials for organic compounds, for transition metal complexes, the GGA DFT functional BP86 performed better than the B3LYP one [55][56][57]. Despite these results for transition metals [34], the B3LYP functional has reproduced redox potentials for actinyl complexes in agreement with experimental values in solution. In addition, the M06 and PBE0 functionals were also found to give good agreement with experimental redox potentials [45,58] and recently, the M06L functional was found to give very small mean unsigned error (MUE) error values, e.g., 0.04 eV for actinyl(VI/V) redox potentials predictions in aqueous solution with respect to experimental redox potentials [59].…”

“…To illustrate the effect of ionic-strength on the Fc/Fc + potentials, different electrolyte concentrations were investigated and reported. Depending on the electrolyte concentration, the Fc/Fc + redox potential varies within a range of ~0.1-0.15 eV, and while this is significant as far as computational predictions are concerned, these uncertainties in experimental redox potentials could also introduce systematic errors in computational predictions [34].…”

“…In addition, this study suggests that the reference complex, as usually employed instead the reference electrode potential in this method, should belong to the same period of the periodic table. This often minimizes systematic errors (to a certain degree by error cancellations using species from the same row) and the redox potentials in solution can be predicted within a MUE of 0.06 eV of experimental redox potentials [34].…”

Phenomenology and Thermodynamics of Underpotential Deposition

“…However, in the last decades the increasing computational power and the systematic application of quantum mechanics have allowed not only drawing general trends but also being able to make quantitative predictions for specific systems. This is for example the case of the prediction of electrode potentials from first-principles calculations, in some cases within a few tenths of millivolts of the experimental values [196][197][198]. In this respect, it would be desirable to establish a thermodynamic formulation that makes it possible to make predictions making use of these new possibilities.…”