First and Second Reductions in an Aprotic Solvent: Comparing Computational and Experimental One-Electron Reduction Potentials for 345 Quinones

Using reference reduction potentials of quinones recently measured relative to the saturated calomel electrode (SCE) in N,N-dimethylformamide (DMF), we benchmark absolute one-electron reduction potentials computed for 345 Q/Q•- and 265 Q•-/Q2- half-reactions using adiabatic electron affinities computed with density functional theory and solvation energies computed with four continuum solvation models: IEF-PCM, C-PCM, COSMO, and SM12. Regression analyses indicate a strong linear correlation between experimental and absolute computed Q/Q•- reduction potentials with Pearson's correlation coefficient (r) between 0.95 and 0.96 and the mean absolute error (MAE) relative to the linear fit between 83.29 and 89.51 mV for different solvation methods when the slope of the regression is constrained to 1. The same analysis for Q•-/Q2- gave a linear regression with r between 0.74 and 0.90 and MAE between 95.87 and 144.53 mV, respectively. The y-intercept values obtained from the linear regressions are in good agreement with the range of absolute reduction potentials reported in the literature for the SCE but reveal several sources of systematic error. The y-intercepts from Q•-/Q2- calculations are lower than those from Q/Q•- by around 320-410 mV for IEF-PCM, C-PCM, and SM12 compared to 210 mV for COSMO. Systematic errors also arise between molecules having different ring sizes (benzoquinones, naphthoquinones, and anthraquinones) and different substituents (titratable vs nontitratable). SCF convergence issues were found to be a source of random error that was slightly reduced by directly optimizing the solute structure in the continuum solvent reaction field. While SM12 MAEs were lower than those of the other solvation models for Q/Q•-, SM12 had larger MAEs for Q•-/Q2- pointing to a larger error when describing multiply charged anions in DMF. Altogether, the results highlight the advantages of, and further need for, testing computational methods using a large experimental data set that is not skewed (e.g., having more titratable than nontitratable substituents on different parent groups or vice versa) to help further distinguish between sources of random and systematic errors in the calculations.

Mechanisms Associated with Superoxide Radical Scavenging Reactions Involving Phenolic Compounds Deduced Based on the Correlation between Oxidation Peak Potentials and Second-Order Rate Constants Determined Using Flow-Injection Spin-Trapping EPR Methods

Flow-injection spin-trapping electron paramagnetic resonance (FI-EPR) methods that involve the use of 5,5-dimethyl-pyrroline-N-oxide (DMPO) as a spin-trapping reagent have been developed for the kinetic study of the O2•- radical scavenging reactions occurring in the presence of various plant-derived and synthetic phenolic antioxidants (Aox), such as flavonoid, pyrogallol, catechol, hydroquinone, resorcinol, and phenol derivatives in aqueous media (pH 7.4 at 25 °C). The systematically estimated second-order rate constants (ks) of these phenolic compounds span a wide range (from 4.5 × 10 to 1.0 × 106 M-1 s-1). The semilogarithm plots presenting the relationship between ks values and oxidation peak potential (Ep) values of phenolic Aox are divided into three groups (A1, A2, and B). The ks-Ep plots of phenolic Aox bearing two or three OH moieties, such as pyrogallol, catechol, and hydroquinone derivatives, belonged to Groups A1 and A2. These molecules are potent O2•- radical scavengers with ks values above 3.8 × 104 (M-1 s-1). The ks-Ep plots of all phenol and resorcinol derivatives, and a few catechol and hydroquinone derivatives containing carboxyl groups adjacent to the OH groups, were categorized into the group poor scavengers (ks < 1.6 × 103 M-1 s-1). The ks values of each group correlated negatively with Ep values, supporting the hypothesis that the O2•- radical scavenging reaction proceeds via one-electron and two-proton processes. The processes were accompanied by the production of hydrogen peroxide at pH 7.4. Furthermore, the correlation between the plots of ks and the OH proton dissociation constant (pKa•) of the intermediate aroxyl radicals (ks-pKa• plots) revealed that the second proton transfer process could potentially be the rate-determining step of the O2•- radical scavenging reaction of phenolic compounds. The ks-Ep plots provide practical information to predict the O2•- radical scavenging activity of plant-derived phenolic compounds based on those molecular structures.

Transition Metal Pyrithione Complexes (Ni, Mn, Fe, and Co) as Electrocatalysts for Proton Reduction of Acetic Acid

A series of mononuclear first-row transition metal pyrithione M(pyr) _n complexes (M = Ni(II), Mn(II), n = 2; M = Co(III), Fe(III), n = 3) have been prepared from the reaction of the corresponding metal salt with the sodium salt of pyrithione. Using cyclic voltammetry, the complexes have been shown to behave as proton reduction electrocatalysts albeit with varying efficiencies in the presence of acetic acid as the proton source in acetonitrile. The nickel complex displays the optimal overall catalytic performance with an overpotential of 0.44 V. An ECEC mechanism is suggested for the nickel-catalyzed system based on the experimental data and supported by density functional theory calculations.

How to Predict the pK a of Any Compound in Any Solvent

Acid-base properties of molecules in nonaqueous solvents are of critical importance for almost all areas of chemistry. Despite this very high relevance, our knowledge is still mostly limited to the pK a of rather few compounds in the most common solvents, and a simple yet truly general computational procedure to predict pK a's of any compound in any solvent is still missing. In this contribution, we describe such a procedure. Our method requires only the experimental pK a of a reference compound in water and a few standard quantum-chemical calculations. This method is tested through computing the proton solvation energy in 39 solvents and by comparing the pK a of 142 simple compounds in 12 solvents. Our computations indicate that the method to compute the proton solvation energy is robust with respect to the detailed computational setup and the construction of the solvation model. The unscaled pK a's computed using an implicit solvation model on the other hand differ significantly from the experimental data. These differences are partly associated with the poor quality of the experimental data and the well-known shortcomings of implicit solvation models. General linear scaling relationships to correct this error are suggested for protic and aprotic media. Using these relationships, the deviations between experiment and computations drop to a level comparable to that observed in water, which highlights the efficiency of our method.

Dithiolato-Bridged Nickel(II) Salicylcysteamine Complexes as Robust Proton Reduction Electrocatalysts: Cyclic Voltammetry and Computational Studies

A series of Schiff-base nickel(II) complexes were prepared from the reaction of nickel(II) acetate with N-salicylcysteamine [HO-C₆H₄-CH═N(CH₂)₂SH] ligands. These complexes were analyzed to be dimeric nickel complexes containing two bridging thiolato ligands. Using cyclic voltammetry, they were found to be efficient homogeneous proton reduction electrocatalysts when acetic acid was used as the proton source in acetonitrile. Catalysis was triggered upon electrochemical reduction of the nickel complex. In particular, rate constants (k_obs) in the range of 10⁴ s^-1 at moderate overpotentials of 0.5-0.6 V were achieved when chloro- or bromo-containing nickel complexes were used. Combined with the experimental data, density functional theory calculations lent support to an ECEC mechanism, with the first electrochemical reduction step contributing significantly to the rate-determining step.

From absolute potentials to a generalized computational standard hydrogen electrode for aqueous and non-aqueous solvents

We describe a simple and efficient procedure to compute a conversion factor for the absolute potential of the standard hydrogen electrode in water to any other solvent. In contrast to earlier methods our procedure only requires the pKa of an arbitrary acid in water and few simple quantum chemical calculations as input. Thus, it is not affected adversely by experimental shortcomings related to measurements in non-aqueous solvents. By combining this conversion factor with the absolute potential in water, the absolute potential in the solvent of interest is obtained. Based on this procedure a new generalized computational standard hydrogen electrode for the computation of electron transfer and proton-coupled electron transfer potentials in non-aqueous solvents and ionic liquids is developed. This enables for the first time the reliable prediction of redox potentials in any solvent. The method is tested through calculation of absolute potentials in 36 solvents. Using the Kamlet-Taft linear solvation energy model we find that the relative absolute potentials consistently increase with decreasing polarisability and decreasing hydrogen bonding ability. For protic solvents good agreement with literature is observed while significant deviations are found for aprotic solvents. The obtained conversion factors are independent of the quantum chemical method, while minor differences are observed between solvation models. This does, however, not affect the global trends.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Method for the accurate prediction of electron transfer potentials using an effective absolute potential

A protocol for the accurate computation of electron transfer (ET) potentials from ab initio and density functional theory (DFT) calculations is described. The method relies on experimental pKa values, which can be measured accurately, to compute a computational setup dependent effective absolute potential. The effective absolute potentials calculated using this protocol display strong variations between the different computational setups and deviate in several cases significantly from the "generally accepted" value of 4.28 V. The most accurate estimate, obtained from CCSD(T)/aug-ccpvqz, indicates an absolute potential of 4.14 V for the normal hydrogen electrode (nhe) in water. Using the effective absolute potential in combination with CCSD(T) and a moderately sized basis, we are able to predict ET potentials accurately for a test set of small organic molecules (σ = 0.13 V). Similarly we find the effective absolute potential method to perform equally good or better for all considered DFT functionals compared to using one of the literature values for the absolute potential. For, M06-2X, which comprises the most accurate DFT method, standard deviation of 0.18 V is obtained. This improved performance is a result of using the most appropriate effective absolute potential for a given method.

A Density Functional Theory-Based Scheme to Compute the Redox Potential of a Transition Metal Complex: Applications to Heme Compound

We estimated the redox potential of a model heme compound by using the combination of our density functionals with a computational scheme, which corrects the solvation energy to the normal solvent model. Among many density functionals, the LC-BOP12 functional gave the smallest mean absolute error of 0.16 V in the test molecular sets. The application of these methods revealed that the redox potential of a model heme can be controlled within 200 mV by changing the protonation state and even within 20 mV by the flipping of the ligand histidine. In addition, the redox potential depends on the inverse of the dielectric constant, which controls the surroundings. The computational results also imply that a system with a low dielectric constant avoids the charged molecule by controlling either the redox potential or the protonation system.

A computational scheme of pKa values based on the three-dimensional reference interaction site model self-consistent field theory coupled with the linear fitting correction scheme

A scheme for quantitatively computing the acid dissociation constant, pKa, of hydrated molecules is proposed. It is based on the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory coupled with the linear fitting correction (LFC) scheme. In LFC/3D-RISM-SCF, pKa values of target molecules are evaluated using the Gibbs energy difference between the protonated and unprotonated states calculated by 3D-RISM-SCF and the parameters fitted by the LFC scheme to the experimental values of training set systems. The pKa values computed by LFC/3D-RISM-SCF show quantitative agreement with the experimental data.

Theoretical estimation of redox potential of biological quinone cofactors

Redox potentials are essential to understand biological cofactor reactivity and to predict their behavior in biological media. Experimental determination of redox potential in biological system is often difficult due to complexity of biological media but computational approaches can be used to estimate them. Nevertheless, the quality of the computational methodology remains a key issue to validate the results. Instead of looking to the best absolute results, we present here the calibration of theoretical redox potential for quinone derivatives in water coupling QM + MM or QM/MM scheme. Our approach allows using low computational cost theoretical level, ideal for long simulations in biological systems, and determination of the uncertainties linked to the calculations. © 2017 Wiley Periodicals, Inc.

Faraday efficiency and mechanism of electrochemical surface reactions: CO2 reduction and H2 formation on Pt(111)

An atomic scale model of the electrical double layer is used to calculate the mechanism and rate of electrochemical reduction of CO₂ as well as H₂ formation at a Pt(111) electrode. The water layer contains solvated protons and the electrode has excess electrons at the surface. Density functional theory within the generalized gradient approximation is used to describe the electronic structure while the mechanism and activation energy of the various elementary reactions is obtained by calculating minimum energy paths using the nudged elastic band method. The applied electrical potential is deduced from the calculated work function. The optimal reaction mechanism for CO₂ reduction to either methane or methanol is found and the estimated rate compared with that of the competing reaction, H₂ formation. When the free energy of only the intermediates and reactants is taken into account, not the activation energy, Pt(111) would seem to be a good electrocatalyst for CO₂ reduction, significantly better than Cu(111). This, however, contradicts experimental findings. Detailed calculations reported here show that the activation energy for CO₂ reduction is high for both Heyrovsky and Tafel mechanisms on Pt(111) in the relevant range of applied potential. The rate-limiting step of the Heyrovsky mechanism, *COOH + H⁺ + e⁻ → *CO + H₂O, is estimated to have an activation energy of 0.95 eV at −0.9 V vs. standard hydrogen electrode. Under the same conditions, the activation energy for H₂ formation is estimated to be only 0.5 eV. This explains why attempts to reduce CO₂ using platinum electrodes have produced only H₂. A comparison is made with analogous results for Cu(111) [J. Hussain et al., Procedia Comput. Sci., 2015, 51, 1865] where a reaction mechanism with low activation energy for CO₂ electroreduction to methane was identified. The difference between the two electrocatalysts is discussed.

A density functional theory protocol for the calculation of redox potentials of copper complexes

The calculated redox potentials of copper complexes agree nicely with their corresponding experimental redox potentials.

Accurate standard hydrogen electrode potential and applications to the redox potentials of vitamin C and NAD/NADH

We computationally evaluated the standard hydrogen electrode (SHE) potential in aqueous phase and the Gibbs energy of a proton from the experimental pKa values of alcohol molecules. From the "golden standard" CCSD(T)/aug-cc-pVTZ level calculation, we estimated the SHE potential as 4.48 V, which is very close to the IUPAC-recommended experimental value of 4.44 V. As applications to the Gaussian-3 (G3) methods, which also reproduce the "golden standard" level calculations, we computed various pKa values and redox potentials for a vitamin series. For vitamin C, we support the experimental result of +0.35 V and predict the pKa value of d-ascorbic acid to be 3.7-3.9. Using a model molecule for nicotinamide adenine dinucleotide (NAD), we reproduced the redox potential and determined the order of the proton/electron addition, based on both the proton affinity and redox potential.

Redox Reaction Mechanisms with Non-triiodide Mediators in Dye-Sensitized Solar Cells by Redox Potential Calculations

We investigate reaction mechanisms of the redox mediators in dye-sensitized solar cells through systematic calculations of redox potentials of possible cobalt complexes and iodides in acetonitrile solution by use of the thermodynamic cycle method with continuum solvent model. The calculated redox potentials were in good agreement with the experimental values, although the experimentalists used different reference electrodes. The maximum open circuit voltage (VOC) of the mediators calculated in this work indicate that the I2(•-)/2I(-) and I2/I2(•-) as well as the net I2/2I(-) redox reactions can dominate at both photoanode and counter-electrode.