Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.     

Computation of pKa values of substituted aniline radical cations in dimethylsulfoxide solution

A newly developed computation strategy was used to calculate the absolute pKa values of 18 substituted aniline radical cations in dimethylsulfoxide (DMSO) solution with the error origin elucidated and deviation minimized. The B3LYP/6-311++G(2df,2p) method was applied and was found to be capable of reproducing the gas-phase proton-transfer free energies of substituted anilines with a precision of 0.83 kcal/mol. The IEF-PCM solvation model with gas-phase optimized structures was adopted in calculating the pKa values of the substituted neutral anilines in DMSO, regenerating the experimental results within a standard deviation of 0.4 pKa unit. When the IEF-PCM solvation model was applied to calculate the standard redox potentials of anilide anions, it showed that the computed values agreed well with experiment, but the redox potentials of substituted anilines were systematically overestimated by 0.304 eV. The cause of this deviation was found to be related to the inaccuracy of the calculated solvation free energies of aniline radical cations. By adjusting the size of the cavity in the IEF-PCM method, we derived a reliable procedure that can reproduce the experimental pKa values of aniline radical cations within 1.2 pKa units to those from experiment.     

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

Accurate computationally derived reduction potentials are important for catalyst design. In this contribution, relatively inexpensive density functional theory methods are evaluated for computing reduction potentials of a wide variety of organic, inorganic, and organometallic complexes. Astonishingly, SCRF single points on B3LYP optimized geometries with a reasonably small basis set/ECP combination works quite well‐‐B3LYP with the BS1 [modified‐LANL2DZ basis set/ECP (effective core potential) for metals, LANL2DZ(d,p) basis set/LANL2DZ ECP for heavy nonmetals (Si, P, S, Cl, and Br), and 6‐31G(d') for other elements (H, C, N, O, and F)] and implicit PCM solvation models, SMD (solvation model based on density) or IEFPCM (integral equation formalism polarizable continuum model with Bondi atomic radii and α = 1.1 reaction field correction factor). The IEFPCM‐Bondi‐B3LYP/BS1 methodology was found to be one of the least expensive and most accurate protocols, among six different density functionals tested (BP86, PBEPBE, B3LYP, B3P86, PBE0, and M06) with thirteen different basis sets (Pople split‐valence basis sets, correlation consistent basis sets, or Los Alamos National Laboratory ECP/basis sets) and four solvation models (SMD, IEFPCM, IPCM, and CPCM). The MAD (mean absolute deviation) values of SCRF‐B3LYP/BS1 of 49 studied species were 0.263 V for SMD and 0.233 V for IEFPCM‐Bondi; and the linear correlations had respectable R ² values (R ² = 0.94 for SMD and R ² = 0.93 for IEFPCM‐Bondi). These methodologies demonstrate relatively reliable, convenient, and time‐saving functional/basis set/solvation model combinations in computing the reduction potentials of transition metal complexes with moderate accuracy. © 2017 Wiley Periodicals, Inc.     

Theoretical study of ionization and one‐electron oxidation potentials of N‐heterocyclic compounds

A number of density functionals was utilized to predict gas‐phase adiabatic ionization potentials (IPs) for nitrogen‐rich heterocyclic compounds. Various solvation models were applied to the calculation of difference in free energies of solvation of oxidized and reduced forms of heterocyclic compounds in acetonitrile (AN) for correct reproduction of their standard oxidation potentials. We developed generally applicable protocols that could successfully predict the gas‐phase adiabatic ionization potentials of nitrogen‐rich heterocyclic compounds and their standard oxidation potentials in AN. This approach is supported by a MPW1K/6‐31+G(d) level of theory which uses SMD(UA0) approximation for estimation of solvation energy of neutral molecules and PCM(UA0) model for ionized ones. The mean absolute derivation (MAD) and root mean square error (RMSE) of the current theoretical models for IP are equal to 0.22 V and 0.26, respectively, and for oxidation potentials MAD = 0.13 V and RMSE = 0.17. © 2013 Wiley Periodicals, Inc.     

Calculation of electron affinities of polycyclic aromatic hydrocarbons and solvation energies of their radical anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.     

Theoretical study on redox potentials of organic radicals in different solvents

The BMK density functional theory method has been used to examine the redox potentials of organic radicals in different solvents (DMF, N,N-dimethylformamide; DMSO, dimethyl sulfoxide; MeCN, acetonitrile). The polarizable continuum solvation model (PCM) was used to describe the solvation-free energies. The one-electron electrochemical standard potentials (E ⁰) of ca. 100 organic radicals in three solvents were calculated using a single, unified theoretical method whose reliability has been tested against almost all the available experimental data. It was found that the mean absolute deviation (MAD) between the theory and experiment was about 0.08 V. With the newly developed theoretical method in hand, more redox potentials of organic radicals in these three solvents were predicted by this single, unified method. The results showed that the redox potentials of organic radicals in different organic solvents including DMF and DMSO had good correlations with their redox potentials in MeCN.     

Analysis of structural factors related to spectroscopic data and redox potentials of CuT1 models through DFT tools

Six complexes, mimics of T1 Cu active site, were studied under the density functional theory framework and their redox potentials were theoretically estimated with an average error of 0.095 V. Among different functionals, the hybrid functional PBE0 gave the best results to reproduce geometric parameters and to estimate redox potentials. The use of computational methods allowed the identification of relevant structural factors to rationalize spectroscopic and redox potential measurements. The inclusion of explicit molecules of solvent (tetrahydrofurane) showed that only those complexes with net positive charge exhibit coordination with the solvent. The consideration of such interaction permits the correct estimation of redox potentials. When the equilibrium between possible coordination isomers of T1 Cu models is taken into account, a reinterpretation of spectroscopic data (EPR and UV‐vis) is possible. These equilibria are governed mainly by entropic contributions and the solvation energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Quantum-chemical predictions of absolute standard redox potentials of diverse organic molecules and free radicals in acetonitrile

A calibrated B3LYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) method was found to be able to predict the gas-phase adiabatic ionization potentials of 160 structurally unrelated organic molecules with a precision of 0.14 eV. A PCM solvation model was benchmarked that could predict the pK(a)'s of 15 organic acids in acetonitrile with a precision of 1.0 pK(a) unit. Combining the above two methods, we developed a generally applicable protocol that could successfully predict the standard redox potentials of 270 structurally unrelated organic molecules in acetonitrile. The standard deviation of the predictions was 0.17 V. The study demonstrated that computational electrochemistry could become a powerful tool for the organic chemical community. It also confirmed that the continuum solvation theory could correctly predict the solvation energies of organic radicals. Finally, with the help of the newly developed protocol we were able to establish a scale of standard redox potentials for diverse types of organic free radicals for the first time. Knowledge about these redox potentials should be of great value for understanding the numerous electron-transfer reactions in organic and bioorganic chemistry.     

Theoretical prediction of pKa values of seleninic, selenenic, sulfinic, and carboxylic acids by quantum-chemical methods

Aqueous acid dissociation constants of substituted areneseleninic, areneselenenic, arenesulfinic, and benzoic acids are calculated by ab initio (MP2) and DFT (B3LYP) methods in combination with bulk solvation models (IEFPCM, CRSrad) from appropriate thermodynamic cycles. Mean absolute deviations (MAD) between experimental and calculated pK(a) values are quite large for basis sets without diffuse functions; however, trends are reasonably well described. Best agreement with experiment as described by MAD as well as correlation coefficient and slope of the correlation equation pK(a) = a*ΔG(calc)/RT ln(10) + b is obtained with the CPCM solvation model using the defaults optimized within COSMO-RS (CRSrad; MAD = 1.54, R(2) = 0.94, a = 0.83). Sulfenic (selenenic) acid tautomers are significantly more stable than the corresponding sulfoxide (selenoxide) forms.     

Accurate calculation of absolute one-electron redox potentials of some para-quinone derivatives in acetonitrile

Standard ab initio molecular orbital theory and density functional theory calculations have been used to calculate absolute one-electron reduction potentials of several para-quinones in acetonitrile. The high-level composite method of G3(MP2)-RAD is used for the gas-phase calculations and a continuum model of solvation, CPCM, has been employed to calculate solvation energies. To compare the theoretical reduction potentials with experiment, the reduction potentials relative to a standard calomel electrode (SCE) have also been calculated and compared to experimental values. The average error of the calculated reduction potentials using the proposed method is 0.07 V without any additional approximation. An ONIOM method in which the core is studied at G3(MP2)-RAD and the substituent effect of the rest of the molecule is studied at R(O)MP2/6-311+G(3df,2p) provides an accurate low-cost alternative to G3(MP2)-RAD for larger molecules.     

Application of Density Functional Theory for evaluation of standard two-electron reduction potentials in some quinone derivatives

In this research, two-electron reduction potentials are calculated for a set of eight quinones using Density Functional Theory (DFT) at B1B95/6-31G^** and B1B95/6-311++G^** levels in aqueous solution. Two different mechanisms, direct and indirect, which have been presented before, are employed for these calculations. DPCM and CPCM models of solvation are carried out to include solution phase contribution. The results show that CPCM is properly matched with DFT method at the B1B95 level in both direct and indirect mechanisms. It is found that direct mechanism gives more accurate two-electron reduction potentials in comparison to indirect mechanism. Mean Absolute Deviation (MAD) obtained through indirect mechanism and CPCM model of solvation are about 0.041 and 0.022 V for 6-31G^** and 6-311++G^**, respectively. The MAD values of direct mechanism are about 0.024 and 0.018 V for 6-31G^** and 6-311++G^** basis sets, respectively. The calculated MAD for both direct and indirect mechanisms is comparable with MAD previously reported at MP3 level for this set of molecules.     

Redox potentials of trifluoromethyl-containing compounds

Trifluoromethylation reactions are important transformations in the research and development of drugs, agrochemicals and functional materials. An oxidation/reduction process of trifluoromethyl-containing compounds is thought to be involved in many recently tested catalytic trifluoromethylation reactions. To provide helpful physical chemical data for mechanistic studies on trifluoromethylation reactions, the redox potentials of a variety of trifluoromethyl-containing compounds and trifluoromethylated radicals were studied by quantum-chemical methods. First, wB97X-D was found to be a reliable method in predicting the ionization potentials, electron affinities, bond dissociation enthalpies and redox potentials of trifluoromethyl-containing compounds. One-electron absolute redox potentials of 79 trifluoromethyl substrates and 107 trifluoromethylated radicals in acetonitrile were then calculated with this method. The theoretical results were found to be helpful for interpreting experimental observations such as the relative reaction efficiency of different trifluoromethylation reagents. Finally, the bond dissociation free energies (BDFE) of various compounds were found to have a good linear relationship with the related bond dissociation enthalpies (BDE). Based on this observation, a convenient method was proposed to predict one-electron redox potentials of neutral molecules.     

Electronic structure contributions to electron-transfer reactivity in iron-sulfur active sites: 2. Reduction potentials

This study utilizes photoelectron spectroscopy (PES) combined with theoretical methods to determine the electronic structure contributions to the large reduction potential difference between [FeCl(4)](2)(-)(,1)(-) and [Fe(SR)(4)](2)(-)(,1)(-) (DeltaE(0) approximately 1 V). Valence PES data confirm that this effect results from electronic structure differences because there is a similarly large shift in the onset of valence ionization between the two reduced species (DeltaI(vert) = 1.4 +/- 0.3 eV). Specific electronic contributions to DeltaI(vert) have been investigated and defined. Ligand field effects, which are often considered to be of great importance, contribute very little to DeltaI(vert) (DeltaE(LF) < -0.05 eV). By contrast, electronic relaxation, a factor that is often neglected in the analysis of chemical reactivity, strongly affects the valence ionization energies of both species. The larger electronic relaxation in the tetrathiolate allows it to more effectively stabilize the oxidized state and lowers its I(vert) relative to that of the chloride (DeltaE(rlx) = 0.2 eV). The largest contribution to the difference in redox potentials is the much lower effective charge () of the tetrathiolate in the reduced state, which results in a large difference in the energy of the Fe 3d manifold between the two redox couples (DeltaE(Fe)( )(3d) = 1.2 eV). This difference derives from the significantly higher covalency of the iron-thiolate bond, which decreases and significantly lowers its redox potential.     

Absolute standard hydrogen electrode potential measured by reduction of aqueous nanodrops in the gas phase

In solution, half-cell potentials are measured relative to those of other half cells, thereby establishing a ladder of thermochemical values that are referenced to the standard hydrogen electrode (SHE), which is arbitrarily assigned a value of exactly 0 V. Although there has been considerable interest in, and efforts toward, establishing an absolute electrochemical half-cell potential in solution, there is no general consensus regarding the best approach to obtain this value. Here, ion-electron recombination energies resulting from electron capture by gas-phase nanodrops containing individual [M(NH3)6]3+, M = Ru, Co, Os, Cr, and Ir, and Cu2+ ions are obtained from the number of water molecules that are lost from the reduced precursors. These experimental data combined with nanodrop solvation energies estimated from Born theory and solution-phase entropies estimated from limited experimental data provide absolute reduction energies for these redox couples in bulk aqueous solution. A key advantage of this approach is that solvent effects well past two solvent shells, that are difficult to model accurately, are included in these experimental measurements. By evaluating these data relative to known solution-phase reduction potentials, an absolute value for the SHE of 4.2 +/- 0.4 V versus a free electron is obtained. Although not achieved here, the uncertainty of this method could potentially be reduced to below 0.1 V, making this an attractive method for establishing an absolute electrochemical scale that bridges solution and gas-phase redox chemistry.     

Uranyl-Bound Tetra-Dentate Non-Innocent Ligands: Prediction of Structure and Redox Behaviour Using Density Functional Theory

Computational methods have been applied to understand the reduction potentials of [UO₂-salmnt-L] complexes (L=pyridine, DMSO, DMF and TPPO), and their redox behavior is compared with previous experiments in dichloromethane solution. Since the experimental results were inconclusive regarding the influence of the uranyl-bound tetra-dentate ‘salmnt’ ligand, here we will show that salmnt acts as a redox-active ligand and exhibits non-innocent behavior to interfere with the otherwise expected one-electron metal (U) reduction. We have employed two approaches to determine the uranyl (VI/V) reduction potentials, using a direct study of one-electron reduction processes and an estimation of the overall reduction using isodesmic reactions. Hybrid density functional theory (DFT) methods were combined with the Conductor-like Polarizable Continuum Model (CPCM) to account for solvation effects. The computationally predicted one-electron reduction potentials for the range of [UO₂-salmnt-L] complexes are in excellent agreement with shoulder peaks (∼1.4 eV) observed in the cyclic voltammetry experiments and clearly correlate with ligand reduction. Highly conjugated pi-bonds stabilize the ligand based delocalized orbital relative to the localized U f-orbitals, and as a consequence, the ligand traps the incoming electron. A second reduction step results in metal U(VI) to U(V) reduction, in good agreement with the experimentally assigned uranyl (VI/V) reduction potentials.     

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.     

Quantum-chemical predictions of redox potentials of organic anions in dimethyl sulfoxide and reevaluation of bond dissociation enthalpies measured by the electrochemical methods

A first-principle theoretical protocol was developed that could predict the absolute pK(a) values of over 250 structurally unrelated compounds in DMSO with a precision of 1.4 pK(a) units. On this basis we developed the first theoretical protocol that could predict the standard redox potentials of over 250 structurally unrelated organic anions in DMSO with a precision of 0.11 V. Using the two new protocols we systematically reevaluated the bond dissociation enthalpies (BDEs) measured previously by the electrochemical methods. It was confirmed that for most compounds the empirical equation (BDE = 1.37 pK(HA) + 23.1E(o) + constant) was valid. The constant in this equation was determined to be 74.0 kcal/mol, compared to 73.3 kcal/mol previously reported. Nevertheless, for a few compounds the empirical equation could not be used because the solvation energy changed dramatically during the bond cleavage, which resulted from the extraordinary change of dipole moment during the reaction. In addition, we found 40 compounds (mostly oximes and amides) for which the experimental values were questionable by over 5 kcal/mol. Further analyses revealed that all these questionable BDEs could be explained by one of the three following reasons: (1) the experimental pK(a) value is questionable; (2) the experimental redox potential is questionable; (3) the solvent effect cannot be neglected. Thus, by developing practical theoretical methods and utilizing them to solve realistic problems, we hope to demonstrate that ab initio theoretical methods can now be developed to make not only reliable, but also useful, predictions for solution-phase organic chemistry.     

Solvation potentials for flexible chain molecules in solution: on the validity of a pairwise decomposition

The effects of a solvent on the conformation of a flexible n-site solute molecule can be described formally in terms of an n-body solvation potential. Given the practical difficulty in computing such multibody potentials, it is common to carry out a pairwise decomposition in which the n-body potential is approximated by a sum of two-body potentials. Here we investigate the validity of this two-site approximation for short interaction-site chain-in-solvent systems. Using exact expressions for the conformation of an isolated chain, we construct a mapping between the full chain-in-solvent system and its solvation potential representation. We present results for both hard-sphere and square-well systems with n=5 that show that the two-site approximation is sufficient to completely capture the effects of an explicit solvent on chain conformation for a wide range of conditions (which include varying the solvent diameter in the hard-sphere system and varying the chain-solvent coupling in the square-well system). In all cases, a set of two-site potentials (one for each distinct site-site pair) is required. We also show that these two-site solvation potentials can be used to accurately compute a multisite intramolecular correlation function.     

The 6,6‐Dicyanopentafulvene Core: A Template for the Design of Electron‐Acceptor Compounds

The electron‐accepting ability of 6,6‐dicyanopentafulvenes (DCFs) can be varied extensively through substitution on the five‐membered ring. The reduction potentials for a set of 2,3,4,5‐tetraphenyl‐substituted DCFs, with varying substituents at the para‐position of the phenyl rings, strongly correlate with their Hammett σ_p‐parameters. By combining cyclic voltammetry with DFT calculations ((U)B3LYP/6‐311+G(d)), using the conductor‐like polarizable continuum model (CPCM) for implicit solvation, the absolute reduction potentials of a set of twenty DCFs were reproduced with a mean absolute deviation of 0.10 eV and a maximum deviation of 0.19 eV. Our experimentally investigated DCFs have reduction potentials within 3.67–4.41 eV, however, the computations reveal that DCFs with experimental reduction potentials as high as 5.3 eV could be achieved, higher than that of F₄‐TCNQ (5.02 eV). Thus, the DCF core is a template that allows variation in the reduction potentials by about 1.6 eV.