Solvation of ferrocene,cobaltocene, and their ions by the data of quantum-chemical calculations

Quantum-chemical calculations of solvation energy for ferrocene and cobaltocene molecules and their ionic forms in water, acetonitrile, methanol, acetone, and dimethylsulfoxide are performed in terms of the density functional method of the B3LYP type, taking into account the effect of solvent and using the Polarized Continuum Model (PCM). It is shown that the optimization of metallocene structure in liquid introduces only slight quantitative changes as compared with the data calculated for the structures optimized in the gas phase. It is shown that earlier observed deviation of experimental redox potentials of cobaltocene system in dimethylsulfoxide from the regularities of continuum electrostatics is caused by a stronger effect of this solvent on the distribution of electron density over the molecule of dissolved substance.     

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.     

The surface potential of solvent and the intraphase pre-existing potential

Using own and literature data, the differences of real solvation energy for ferricenium and ferrocene in six solvents are found. These quantities are confronted with the calculated difference of the dielectric response energies plus nonelectrostatic energies for the redox couple. Such a comparison allows determining the sum of the surface and intraphase potentials. The comparison of these sums with the experimental values of the surface potential differences obtained by the measuring of Volta potentials allowed determining the differences of pre-existing intraphase potentials formed by solvent molecules on the ferrocene molecule. Thus, the intraphase potentials are evaluated for the first time, using an approach not based on the molecular-dynamic modeling. Using some approximations, the surface potentials of the studied solvents are found.     

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.     

Effect of the aqueous–organic solvent structure on the cobalticenium–cobaltocene redox potential: The redox couple as a basis for determination of the single ion transfer energies

The redox potentials of the cobalticenium–cobaltocene couple have been determined voltammetrically in several aqueous–organic mixed solvents. The cosolvents studied were dimethylformamide, acetone, 1,4-dioxane (all three disrupting the 3D network of the water’s hydrogen bonds), propylenecarbonate (at low content structure-making, at higher – structure-breaking), and glycerol that incorporates into the 3D network. Cobalticenium spectra demonstrate the absence of ion pairs and solute–cosolvent complexes. The liquid junction potentials water-mixed solvent in the range of the cosolvent concentrations studied are small. At equal volume fractions of structure-breaking cosolvents the shifts of redox potential relative to water are similar. The potential shifts are more than by order of magnitude higher than those corresponding to the change of the mixed solvent’s dielectric constant. This is explained as due to disruption of the water hydrogen bonded structure, and disappearance therefore of the water anomalous dielectric response. The cobalticenium redox potential in the hypothetic “structureless” water was estimated as being ∼70 mV more positive than in real water. This is the potential that should be compared directly with the data for practically unstructured aprotic solvents.     

Preferential solvation effects in the electrochemistry and charge-transfer spectra of cyanoiron(II) complexes

The energies of the charge-transfer bands and the redox potentials of substituted cyanoiron complexes are strongly influenced by preferential solvation effects in water-acetonitrile mixed solvents, exhibiting a linear dependence with respect to the acceptor number scale. The dependence increases with the number of cyanide ligands in the complexes.     

Absolute electrode potential and thermodynamics of single ions

A new method, relating the electrode potential to the radius of the solvated ion on whose activity the potential depends, has been developed for the determination of absolute electrode potentials and the thermodynamics of single ions in solution. It is successfully applied to the cells: Pt|H₂(g, 1 atm)|HX, solvent |AgX|Ag, and M|MX, solvent|AgX|Ag, in aqueous, partially aqueous, and non-aqueous solvents. The absolute electrode potentials have been computed in aqueous and methanol+water solvents. The single ion activities, activity coefficients, the radii of solvated cations, and their solvation extent have been calculated. The temperature variation of the standard absolute potential has been utilized to evaluate the standard thermodynamic functions for the electrode reactions, and the standard transfer thermodynamic quantities of single ions from water to methanolic solvents. The results are interpreted in terms of ion—solvent interactions as well as the structural features and the acid—base properties of these solvents.     

Experimental and computed absolute redox potentials of polycyclic aromatic hydrocarbons are highly linearly correlated over a wide range of structures and potentials

A more rigorous theoretical treatment of methods previously used to correlate computed energy values with experimental redox potentials, combined with the availability of well-developed computational solvation methods, results in a shift away from computing ionization potentials/electron affinities in favor of computing absolute reduction potentials. Seventy-nine literature redox potentials measured under comparable conditions from 51 alternant and nonalternant polycyclic aromatic hydrocarbons are linearly correlated with their absolute reduction potentials computed by density functional theory (B3LYP/6-31+G(d)) with SMD/IEF-PCM solvation. The resulting correlation is very strong (R(2) = 0.9981, MAD = 0.056 eV). When extrapolated to the x-intercept, the correlation results in an estimate of 5.17 ± 0.01 eV for the absolute potential of the ferrocene-ferrocenium redox couple in acetonitrile at 25 °C, indicating that this simple method can be used reliably for both calculating absolute redox potentials and for predicting relative redox potentials. When oxidation and reduction data are evaluated separately, the overall MAD value is improved by 50% to 0.028 eV, which improves relative potential predictions, but the computed values do not extrapolate to a reasonable estimate of the absolute potential of the ferrocene-ferrocenium ion reference.     

The theoretical basis of mercurimetry in non-aqueous solutions

The methods for thermodynamic calculations of the equilibria in solutions of mercury salts and complexes are presented. The calculations of equilibrium constants in non-aqueous solvents are based on the transfer activity coefficients of mercury ions from water to the non-aqueous solvent. The dismutation and precipitation reaction constants are calculated, and the redox potentials of mercury systems are measured. Examples of analytical use of the thermodynamic functions of mercury salt solvation are given in the text.     

A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.     

Anisotropic inertial term of the solvation energy in binary solutions

An expression based on the Fröhlich theorem is given for the anisotropic inertial solvation potential of solutions. The principle of the additivity of the anisotropic inertial solvation potentials of solution components is put forward and substantiated. A model thermodynamic function of the anisotropic inertial solvation potential of a binary solution is suggested. The effect of formation of 1:1 complexes and bimolecular associates on the anisotropic inertial solvation potential of a binary solution is analyzed. The composition dependences of the anisotropic inertial solvation potentials of binary solutions of nitrobenzene, acetonitrile, nitromethane, and tetrachloromethane in associated and nonassociated polar and nonpolar solvents and in water are determined. The dependences obtained are compared to the corresponding model functions. Changes in the contribution of specific intermolecular interactions to the anisotropic inertial term of the Helmholtz energy of solvation of binary solutions are revealed by this method. Previously unknown anisotropic inertial solvation potentials are obtained for associated and polar nonassociated liquids in relation to their content in hexane. Conclusions on the magnitude and character of changes in the microstructure of solutions are made. The transformation of the anisotropic inertial to isotropic noninertial term of the Helmholtz energy of solvation is noted by the example of a solution with the ethanol volume fraction in hexane of 0.13.     

On the influence of solvents on the rate of ion-transfer reactions

The literature data on the kinetics of cation electrodeposition on mercury in different solvents were analysed. For all cations considered in different solvents there was a linear decrease of the logarithm of the standard charge-transfer rate constant with increasing basicity of solvent and with more negative formal potential of the electrode reaction expressed in the scale of a solvent-independent electrode, as well as a linear dependence of the activation energy on the Gibbs energy of cation transfer. No dependence of the logarithm of the heterogeneous rate constant on the rate of exchange of solvent molecules from the first solvation sphere was observed. For the different electrode systems studied in one solvent, the dependences of the activation energy on (i) the cation solvation energy, (ii) the Gibbs energy of metal amalgamation, and (iii) metal solubility in mercury were analysed.     

One-electron reduction potential for oxygen- and sulfur-centered organic radicals in protic and aprotic solvents

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.     

Real energies of ferricinium cation transfer from water to organo-aqueous solvents

The redox potentials of ferrocene-ferricinium couple are determined for five organo-aqueous systems with respect to a reversible chloride electrode in the same solvent. Combined with the literature data on real (and some chemical) transfer energies of chloride ion, the effective real energies of ferricinium transfer from water into organo-aqueous mixtures are determined. These values do not obey the Born equation. Most probably, this is due to the selective solvation of cation by water and of neutral ferrocene molecule by an organic component.     

Nanoparticle films as electrodes: voltammetric sensitivity to the nanoparticle energy gap

Electron-transfer reactions of redox solutes at electrode/solution interfaces are facilitated when their formal potentials match, or are close to, the energy of an electronic state of the electrode. Metal electrodes have a continuum of electronic levels, and redox reactions occur without restraint over a wide span of electrode potentials. This paper shows that reactions on electrodes composed of films of metal nanoparticles do have constraints when the nanoparticles are sufficiently small and molecule-like so as to exhibit energy gaps, and resist electron transfers with redox solutes at potentials within the energy gap. When solute formal potentials are near the electronic states of the nanoparticles in the film, electron-transfer reactions can occur. The electronic states of the nanoparticle film electrodes are reflected in the formal potentials of the electrochemical reactions of the dissolved nanoparticles at naked metal electrodes. These ideas are demonstrated by voltammetry of aqueous solutions of the redox solutes methyl viologen, ruthenium hexammine, and two ferrocene derivatives at films on electrodes of 1.1 nm core diameter Au nanoparticles coated with protecting monolayers of phenylethanethiolate ligands. The methyl viologen solute is unreactive at the nanoparticle film electrode, having a formal potential lying in the nanoparticle's energy gap. The other solutes exhibit electron transfers, albeit slowed by the electron hopping resistance of the nanoparticle film. The nanoparticles are not linked together, being insoluble in the aqueous medium; a small amount of an organic additive (acetonitrile) facilitates observing the redox solute voltammetry.     

第一性原理方法预测水相核酸碱基及其代谢物的氧化还原电动势

氧化还原电动势是了解核酸中电荷/电子转移过程以及设计具有新型氧化还原活性的碱基类化合物的重要参数. 本文对82个芳香化合物的氧化还原电动势进行理论预测, 通过计算值和实验值的比较发现: 气相采用B3LYP/6-311++G(2df,2p)//B3LYP/6-31+G(d)方法, 液相采用HF-COSMORS/UAHF方法, 对运用HF- CPCM/UAHF方法在水相重新优化的构型计算溶剂化能, 能有效预测芳香化合物水相氧化还原电动势, 该理论方法计算的绝对均方根误差(RMSD)为0.124 V. 运用该理论方法成功预测了属于芳香化合物的核酸碱基及其代谢物的水相氧化还原电动势. 根据预测结果, 讨论了核酸中电荷/电子转移过程以及结构改变对设计具有新型氧化还原活性的核酸碱基类化合物的影响. 本文为设计具有氧化还原活性的新型核酸碱基类化合物提供了一种理论方法.     

The acceptor number — A quantitative empirical parameter for the electrophilic properties of solvents

The electrophilic properties of 34 solvents have been characterized by the Acceptor Number (AN) which has been derived from³¹P-n.m.r. measurements of triethylphosphine oxide dissolved in the respective solvents. Relationships are found between the acceptor numbers and theZ-values,E _T-values andY-values, as well as the free energies of solvation of anions and the redox potentials of the hexacyanoferrate(III)—hexacyanoferrrate(II) system in different solvents. The new parameter provides—together with the donor number—a useful guide in choosing the most appropriate solvent for a given reaction.     

Theoretical insights into pyridinium-based photoelectrocatalytic reduction of CO2

The role of pyridinium cations in electrochemistry has been believed known for decades, and their radical forms have been proposed as key intermediates in modern photoelectrocatalytic CO(2) reduction processes. Using first-principles density functional theory and continuum solvation models, we have calculated acidity constants for pyridinium cations and their corresponding pyridinyl radicals, as well as their electrochemical redox potentials. Contrary to previous assumptions, our results show that these species can be ruled out as active participants in homogeneous electrochemistry. A comparison of calculated acidities and redox potentials indicates that pyridinium cations behave differently than previously thought, and that the electrode surface plays a critical (but still unknown) role in pyridinium reduction. This work substantially alters the mechanistic view of pyridinium-catalyzed photoelectrochemical CO(2) reduction.