Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe³⁺/Fe²⁺ and the reaction of the hydronium ion discharge.     

Solvation of ions in liquid solvents and proteins

Despite their well-known drawbacks, the approaches of continuum electrostatics are widely used at the analysis of the energies of solvation and reorganization. We propose a method to check the applicability of these approaches in the determination of the solvation energy, which is based on measuring the difference of redox potentials ΔE of two consecutive redox reactions, e.g. for the pairs Co(Cp) ₂ ⁺ /Co(Cp)₂/Co(Cp) ₂ ^? (here, Cp is cyclopentadienyl). In this difference, the solvophobic effects and the liquid junction potential between the working and reference electrodes, which is impossible to measure, cancel out. From the difference of ΔE in two different solvents, the sum of the electrostatic components of the cation-and anion-transfer energies is determined. It is shown that, for large low-charged ions in aprotic media, the continuum electrostatics proves to be true in a wide range of dielectric permittivities including those typical for proteins. The Stokes shift of fluorescence spectra for proflavine (PF) showed that the water reorganization energy and, hence, the energy of the static dielectric response are anomalously high. To study this effect on the solvation energy, we determined the redox potentials of the Co(Cp) ₂ ⁺ /Co(Cp)₂ pair in a number of water-organic media. The organic cosolvent breaks the water structure and reduces the reorganization energy. Accordingly, the redox potential turns more positive. This allowed us to determine the energy of transfer of Co(Cp) ₂ ⁺ ions (and, hence, of other ions) nonviolated by the water structure specifics. The experimental energies of the acetate transfer exceed those calculated by an order of magnitude. This demonstrates the incorrectness of the widely used semicontinuum calculations of the pK of ionogenic groups of proteins. A new algorithm, which permits overcoming this discrepancy, is proposed, namely, the short-range interactions are taken into account based on the experimental energies of the transfer to a model DMF solvent, while the transfer energy from this solvent to the protein is calculated electrostatically. The energy of the ion charging in a protein consists of two physically different components, namely, the charging energy in the pre-existing field of protein dipoles and charges and the energy of the dielectric response of the medium. The former energy is determined by the electronic polarization of the protein (its optical dielectric permittivity), while the latter is determined by all kinds of polarization (static permittivity). Taking into account all the aforementioned peculiarities leads to reasonable agreement with the experiment when estimating the pK of certain groups in α-chymotrypsin. These calculations as well as experimental data (both our and taken form the literature (molecular dynamics)) point to the enhanced dielectric permittivity of the outer layers of proteins.     

Experimental and calculation methods of studying the effect of second coordination sphere on standard rate constants of charge transfer for Cr(III)/Cr(II) redox couple in chloride melts

The cyclic voltammetry method was used to determine the standard rate constants of charge transfer (k _s) on a glassy carbon electrode for the Cr(III)/Cr(II) redox couple in the systems of NaCl-KCl-CrCl₃, KCl-CrCl₃, and CsCl-CrCl₃ in the temperature range of 973–1173 K. It was shown that k _s grows at an increase in the temperature and decreases as sodium cations are replaced by potassium and cesium cations in the second coordination sphere of chromium complexes. The calculations carried out using the PC GAMESS/Firefly quantum-chemical software by means of the DFT technique showed that the values of the charge transfer activation energy change monotonously in the series of Na-K-Cs in accordance with the ratio of reorganization energies. In its turn, this leads to monotonous variation of the charge transfer rate constants.     

Theoretical study of homogeneous electron self-exchange in polar aromatic molecules: the role of the reactant structure

The solvent reorganization energies λ₀ of the electron self-exchange reaction between neutral molecules (nitrobenzene, its five para-substituted derivatives and benzonitrile) and the corresponding radical anions are discussed in terms of the Kirkwood approach combined with a semi-empirical calculation of the reactant structure (AM1 and intermediate neglect of differential overlap (INDO) methods). The theoretical values of λ₀ are compared with the experimental reorganization energies λ calculated from the Marcus equation and the homogeneous rate constants k_ex. It is found that the values of λ₀ obtained using the INDO method are approximately equal to the experimental λ, whereas the AM1 method gives poor results for para-substituted nitrobenzenes. The linear correlation of log k_ex with a_N² where a_N is a nitrogen coupling constant, established for para-substituted nitrobenzenes is interpreted. A simple criterion for slow electron transfer of an arbitrary flat polar arene is formulated in terms of the reactant structure and the model of the “specifying group” suggested earlier by some of the authors.     

Response of polyacrylamide—acyclic poly(oxyethylene)-coated ion-selective electrodes to alkali and alkaline earth metal ions in propylene carbonate and its thermodynamic application

The response of ion-selective electrodes with a membrane of polyacrylamide (PAA) coupled to acyclic poly(oxyethylene) neutral carriers to lithium, sodium, potassium, magnesium and barium ions in propylene carbonate (PC) was investigated. Tetraethylene glycol monododecyl ether (POE4) and hexaethylene glycol monododecyl ether (POE6) were used as the acyclic poly(oxyethylene). Both the PAA-POE4 and the PAA-POE6 electrodes showed a more rapid dynamic response in PC than that in acetonitrile. Nernstian responses to lithium, magnesium and barium ions were obtained with the PAA-POE4 electrode. The selectivity coefficients, logk_Ba²⁺,M^x+, for lithium, sodium, potassium and magnesium ions vs. barium ion obtained in PC with the PAA-POE4 electrode were 3.6, 0.23, 0.02 and 1.1, respectively. The PAA-POE4 electrode was applied to obtain the successive formation constants of the barium ion in PC with N, N-dimethylacetamide (DMA). From the successive formation constants obtained in PC-rich solutions, the Gibbs free energies of transfer of the barium ion from PC to DMA and to PC-DMA mixtures were calculated. The electrode was also used to obtain directly the Gibbs free energies of transfer of the barium ion from PC to PC-DMA mixtures. The calculated values of the free energies were in good agreement with the values obtained experimentally, suggesting that the electrode responded to variations in solvation energy for the barium ion.     

An electrochemical method for determination of the standard Gibbs energy of anion transfer between water and n-octanol

The transfer of the ions Cl⁻, Br⁻, I⁻, ClO₄⁻, SCN⁻, NO₃⁻, BF₄⁻, and (C₆H₅)₄B⁻ across the water|n-octanol (W|OC) liquid interface was studied and the standard Gibbs energies of ion transfer were determined. The ion transfer was achieved by oxidation of decamethylferrocene dissolved in a droplet of n-octanol that was attached to a graphite electrode immersed in the aqueous solutions of the respective alkali salts of the anions. The electrode reaction can be described by the equation: dmfc_(OC)+X_(W)⁻⇄dmfc⁺_(OC)+X⁻_(OC)+e⁻, where X⁻ is the transferred anion. Square-wave voltammetry at this three-phase arrangement was utilised to determine the formal potential of the decamethylferrocene/decamethylferrocenium (dmfc/dmfc⁺) couple under the condition of ion transfer across the water|n-octanol interface. For calibration the standard Gibbs energies of ion transfer have been extrapolated to octanol from the series of known data for methanol, ethanol, n-propanol, and n-butanol. All these data are consistent and the experimental dependence of the formal potentials on the standard Gibbs energies is as predicted by theory. The validity of data is further supported by calculations of Gibbs energies of ion transfer using the Born theory. Until now it was not possible to perform electrochemical measurements at the water|n-octanol interface because in the conventional four-electrode cells this interface cannot be polarised. With the new method it is now for the first time possible to determine the Gibbs energies of transfer of ions across the water|n-octanol interface. These values are of very wide use for assessing the lipophilicity of compounds in chemistry, medicine, and pharmacology.     

On the influence of spatial correlations on the rate of chemical reactions in dense systems. II. Numerical results

The explicit expressions for the rate constant k_f and k_b of a dense system obtained in the preceding paper are investigated numerically. The pair correlation functions representing the spatial correlations are calculated from an associate nonreactive hard sphere system by means of the multicomponent Percus—Yevick equation. The rate constants are found to differ in their dependence on density and time up to an order of magnitude from the corresponding dilute gas value. The time behaviour of k_f and k_b was found to depend sensitively on a relation between the total volumes of the reactant and product molecules.     

Theoretical study of the inner‐sphere energy barrier of the transition‐metal complex M(H2O) in electron‐transfer process

Two theoretical models, a reorganization model and an activation model, are presented for accurately determining the energy barrier of the type M(H₂O) of the transition‐metal complexes in the electron‐transfer process. Ab initio calculations are carried out at UMP2/6‐311G level for several redox pairs M(H₂O) (M=V, Cr, Mn, Fe, and Co) to calculate their inner‐sphere reorganization energies and activation energies according to the models presented in this article. The values of theoretical inner‐sphere reorganization energies and activational energies are comparable with the experimental results obtained from the vibration spectroscopic data. The theoretical reorganization energy of the every redox pair is four times as much as its activation energy, which agrees with Marcus' electron‐transfer theory. The fact proved that the theoretical models presented in this article are scientific and available for studying the electron‐transfer process of the transition‐metal complex. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 119–126, 1999     

Pulse polarography: Part V. on the theory for the kinetic currents with an ece mechanism

We have derived an equation for the instantaneous limiting current in pulse polarography with an ECE mechanism. That equation has been derived for the expanding sphere electrode model (and also for the expanding plane electrode model) with the condition (k₁+k₂)>>1, k₁ and k₂ being the rate constants of the chemical reaction. We show that by an adequate choice of the time of application of the potential and time of the drop growth prior to potential application, it is possible — if the equilibrium constant for chemical reaction is known — to widen the interval of values for k₁ and k₂ that may be determined using this technique. At the same time, we also show that if the electrode sphericity is not taken into account, the values obtained for k₁ and k₂ are always lower than the real ones.     

Dispersion self-free energies and interaction free energies of finite-sized ions in salt solutions

The role for many-body dipolar (dispersion) potentials in ion-solvent and ion-solvent-interface interactions is explored. Such many-body potentials, accessible in principle from measured dielectric data, are necessary in accounting for Hofmeister specific ion effects. Dispersion self-energy is the quantum electrodynamic analogue of the Born electrostatic self-energy of an ion. We here describe calculations of dispersion self-free energies of four different anions (OH-, Cl-, Br-, and I-) that take finite ion size into account. Three different examples of self-free energy calculations are presented. These are the self-free energy of transfer of an ion to bulk solution, which influences solubility; the dispersion potential acting between one ion and an air-water interface (important for surface tension calculations); and the dispersion potential acting between two ions (relevant to activity coefficient calculations). To illustrate the importance of dispersion self-free energies, we compare the Born and dispersion contributions to the free energy of ion transfer from water to air (oil). We have also calculated the change in interfacial tension with added salt for air (oil)-water interfaces. A new model is used that includes dispersion potentials acting on the ions near the interface, image potentials, and ions of finite size that are allowed to spill over the solution-air interface. It is shown that interfacial free energies require a knowledge of solvent profiles at the interface.     

Solvent isotope effects upon the kinetics of some simple electrode reactions

The effects of replacing H₂O with D₂O solvent upon the electrochemical kinetics of simple transition-metal redox couples containing aquo, ammine or ethylenediamine ligands have been investigated at mercury electrodes as a means of exploring the possible contribution of ligand-aqueous solvent interactions to the activation barrier to outer-sphere electron transfer. The general interpretation of solvent isotope effects upon electrode kinetics is discussed; it is concluded that double-layer corrected isotopic rate ratios (k^H/k^D)^E determined at a constant electrode potential vs. an aqueous reference electrode, as well as those determined at the respective standard potentials in H₂O and D₂O (k_S^H/k_S^D), have particular significance since the solvent liquid-junction potential can be arranged to be essentially zero. For aquo redox couples, values of (k_S^H/k_S^D) were observed that are substantially greater than unity and appear to be at least partly due to a greater solvent-reorganization barrier in D₂O arising from ligand-solvent hydrogen bonding. For ammine and ethylenediamine complexes values of (k^H/k^D)^E substantially greater than, and smaller than, unity were observed upon the separate deuteration of the ligands and the surrounding solvent respectively. Comparison of isotope rate ratios for corresponding electrochemical and homogeneous outer-sphere reactions involving cationic ammine and aquo complexes yields values of (k^H/k^D) for the former processes that are typically markedly larger than those predicted by the Marcus model from the homogeneous rate ratios. These discrepancies appear to arise from differences in the solvent environments in the transition states for electrochemical and homogeneous reactions.     

Studies on membrane concentration potentials across heavy metal soap discs

The electrostatic effect of specifically adsorbed electroinactive ions upon electrode processes involving adsorbed reactants with a time of adsorption greater than the characteristic time of surface-diffusion jumps is considered. The validity of the most general form of the Frumkin correction term for double-layer effects, with ψ₁ equal to the local potential ₃ at the position occupied by the reactant in the transition state, is first examined on the basis of current molecular theories of electrode kinetics. Subsequently, approximate expressions of ₃ are derived for the case in which adsorbed reactant and adsorbed supporting ion are charged both of equal and of opposite sign. In both cases the logarithm Φ of the rate constant for the electrode reaction at constant applied potential, as corrected for diffuse-layer effects only, is expected to vary linearly with the charge density q_i due to the adsorbed supporting ion. |ΔΦ/Δq_i| is, however, much greater in the case of electrostatic attraction between reactant and adsorbed supporting ion than in the case of electrostatic repulsion. The influence of reactant adsorption with partial charge transfer upon the magnitude of ΔΦ/Δq_i is considered.     

Theoretical study of lithium-fluoride and lithium-chloride ion pairs in aqueous solution. An SCF-CNDO/2 approach including continuum solvent effects

SCF-CNDO/2 calculations, including solvent effects via an extended version of the Generalized Born Formula (GBF), have been performed for LiX(H₂O) species (n = 1,2; X = F, Cl). Several minima in the free energy surface, representing intimate and solvent-separated ion pair structures, have been analyzed. Qualitative results show a preferential stabilization of the intimate forms with respect to the solvent-separated ones. The results are discussed on the basis of a convenient partition of the total solute-solvent free energy. The interaction of the ionic species with the bulk solvent neglected in previous studies appears to be responsible for the preferential stability of the intimate forms.     

Characteristic and non-characteristic X-ray emission from SF6 and SO2 molecules by electron impact

Cross sections for K-shell ionization of sulphur in collisions of electrons with kinetic energies of 3.5–14.0 keV with SF₆ and SO₂ gases have been measured. In addition, the impact energy dependence of the bremsstrahlung radiation emitted at different photon energies was investigated. The experimental results are compared with theoretical calculations in plane wave Born approximation and with the available semi-empirical models.     

Nucleophilic addition of methanol and methanethiol to acetylene in the superbasic system KOH-DMSO: a quantum chemical model

Cluster-continuum models (KOH·nDMSO, n = 1, 5) were used to model the superbasic system “alkali metal hydroxide-dimethyl sulfoxide” within the framework of MP2/6-311++G**/ and B3LYP/6-31G* methods. The KOH molecule surrounded by five DMSO molecules exists as “solvate-loosened” ion pair with elongated K-O distance. It is proposed to consider the “solvate-loosened” ion pair of potassium cation with hydroxide anion in the surroundings of five solvent molecules as the catalytic coordination sphere of the superbasic system KOH-DMSO. Methanol and methanethiol molecules can be incorporated with ease into the first coordination sphere of potassium cation to form methoxide and methanethiolate ions. The possibility of nucleophilic attack of methoxide and methanethiolate ions on acetylene molecule in the first coordination sphere of potassium cation was studied. The model reaction system C₂H₂-CH₃OK-H₂O with one DMSO molecule included explicitly to maintain the “solvate-loosened” [CH₃O]^?...K⁺ ion pair and additional inclusion of solvent effects within the framework of the IEFPCM continuum model is the most preferable for serial calculations.     

Proton-coupled electron transfer in a model for tyrosine oxidation in photosystem II

Theoretical calculations of a model for tyrosine oxidation in photosystem II are presented. In this model system, an electron is transferred to ruthenium from tyrosine, which is concurrently deprotonated. This investigation is motivated by experimental measurements of the dependence of the rates on pH and temperature (Sj?din et al. J. Am. Chem. Soc. 2000, 122, 3932). The mechanism is proton-coupled electron transfer (PCET) at pH < 10 when the tyrosine is initially protonated and is single electron transfer (ET) for pH > 10 when the tyrosine is initially deprotonated. The PCET rate increases monotonically with pH, whereas the single ET rate is independent of pH and is 2 orders of magnitude faster than the PCET rate. The calculations reproduce these experimentally observed trends. The pH dependence for the PCET reaction arises from the decrease in the reaction free energies with pH. The calculations indicate that the larger rate for single ET arises from a combination of factors, including the smaller solvent reorganization energy for ET and the averaging of the coupling for PCET over the reactant and product hydrogen vibrational wave functions (i.e., a vibrational overlap factor in the PCET rate expression). The temperature dependence of the rates, the solvent reorganization energies, and the deuterium kinetic isotope effects determined from the calculations are also consistent with the experimental results.     

Photoelectron emission spectroscopy of inorganic cations in aqueous solution

Threshold energies (6.1 <E_t ? 8.6 eV) are determined for photoelectron emission by 16 inorganic cations in aqueous solution E_t values are correlated with gas-phase ionization potentials, solvation and reorganization free energies, standard reduction potentials and ligand field stabilization energies (five transition metals). Dielectric saturation is shown to drastically lower threshold energies.     

The kinetics of nucleophilic substitution processes in the alkyl halides. Part B—analysis of experimental data

Nucleophilic substitution reactions in the alkyl halides, RX + Y^? → RY + X^?, proceeding in polar media are considered on the basis of the theory presented in Part A. It is shown that the solvent reorganization energy is the main part of the activation energy for this processes. According to calculations performed, the values of the solvent reorganization energy equal ～2.5–3 eV for H₂O and ～ 1.8–2.3 eV for acetone. From experimental data on the kinetic isotope effect, an estimate for the splitting of nonadiabatic terms and for the slope of the potential curve v′ of the intermolecular interaction between halide ion and methyl halide near transition configuration is made. Further, the parameter v′ is used for calculating the activation entropy of substitution reactions in the methyl halides. Theoretical activation energies and activation entropies agree with experimental values. In the framework of theory presented an interpretation of change of E_a and the preexponential factor with the type of alkyl halide is given.