Inner-sphere Reorganization Research Articles

Effect of the Ligand Nature in Zinc(II) Complexes on the Inner-Sphere Reorganization in the Electron Transfer Reactions

The effect of the ligand surrounding on the character and degree of the inner-sphere reorganization during electroreduction of aqua, aquahydroxy, hydroxy, and Edta complexes of zinc(II) is studied in the framework of a quantum-chemical approach. It is established that the most substantial intramolecular reorganization occurs during the transfer of the first electron onto [Zn(Edta)]2–. The solvent's reorganization energy is estimated.

Inner-sphere reorganization for redox pairs M(NH3)62+/3+ (M=Mn, Fe, and Co): Models and calculations

The inner-shell reorganization and activation models of the electron-transfer reactions of transition-metal hexammine complexes are presented. The inner-shell reorganization and activation energies of several hexammine redox pairs M(NH3)62+/3+ (M=Mn, Fe, and Co) in self-exchange reactions are studied by different formalisms. The extent of the anharmonicities in the vibration between the metal–ion and the ligands in the reorganization process of these complexes is determined. The inner-shell barriers of these redox pairs are dependent on reorganization model used. The contribution of the individual reactants to the inner-shell barrier is sensitive to the model used. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Stepwise hapticity changes in sequential one-electron redox reactions of indenyl-molybdenum complexes: combined electrochemical, ESR, X-ray, and theoretical studies.

Reduction of the dication [(eta5-Ind)(Cp)Mo[P(OMe)3]2]2+ (1(2+)) and oxidation of the neutral complex (eta3-Ind)(Cp)Mo[P(OMe)3]2 (1) proceed through a one-electron intermediate, 1+. The structures of 1(2+) and 1 have been determined by X-ray diffraction studies, which show the slip-fold distortion angle, Omega, of the indenyl ring increasing from 4.1 degrees in 1(2+) to 21.7 degrees in 1. Cyclic voltammetry and bulk electrolysis were employed to define the thermodynamics and heterogeneous charge-transfer kinetics of reactions 1(2+) + e(-) <==> 1+ and 1+ + e(-) <==> 1: DeltaE1/2 = 113 mV in CH3CN and 219 mV in CH2Cl2/0.1 M [NBu4][PF6]; k(s) = 0.4 cm x s(-1) for 1(2+)/1+ couple, 1.0 cm x s(-1) for 1+/1 couple in CH3CN. ESR spectra of 1+ displayed a surprisingly large hyperfine splitting (7.4 x 10(-4) x cm(-1)) from a single 1H nucleus, and spectra of the partially deuterated indenyl analogue confirmed assignment of a(H) to the H2 proton of the indenyl ring. The related eta5 18-electron complexes [(eta5-Ind)(Cp)Mo(dppe)]2+ (2(2+)) (dppe = diphenylphosphinoethane) and (eta5-Ind)(Cp)Mo(CN)2 (3) may also be reduced in two successive one-electron steps; ESR spectra of the radicals 2+ and 3- showed a similarly large a(H2) (8.7 x 10(-4) and 6.4 x 10(-4) x cm(-1), respectively). Molecular orbital calculations (density functional theory, DFT, and extended Hückel, EH) predict metal-indenyl bonding in 1+ that is approximately midway between that of the eta5 and eta3 hapticities (e.g., Omega = 11.4 degrees ). DFT results show that the large value of a(H2) arises from polarization of the indenyl-H2 by both inner-sphere orbitals and the singly occupied molecular orbital (SOMO) of 1+. The measured ks values are consistent with only minor inner-sphere reorganizational energies being necessary for the electron-transfer reactions, showing that a full eta5/eta3 hapticity change may require only small inner-sphere reorganization energies when concomitant with a pair of stepwise one-electron-transfer processes. The indenyl ligand in 1+ is best described as donating approximately four pi-electrons to Mo by combining a traditional eta3 linkage with two "half-strength" Mo-C bonds.

Quantum mechanical investigation of the inner-sphere reorganization energy of cyclooctatetraene/cyclooctatetraene radical anion. Part I

The inner-sphere reorganization energy of the electron self-exchange of the couple cyclooctatetraene/cyclooctatetraene radical anion has been investigated by quantum mechanical calculations. The more stable Jahn Teller distorted B 2 g conformation of the radical anion has been used in this study. Two different theories have been applied in this first part. The harmonic approximation in the classical Marcus scheme has been modified by using projected force constants, which are obtained from the complete force constant matrix and the geometry changes of the molecule during the ET (introduced by Mikkelsen). A different approach (introduced by Nelsen) combines the different energies of the neutral and radical anion with and without relaxation corresponding to the vertical ionization potential and the vertical electron affinity. The electronic energies of the neutral molecule and the radical anion differ dramatically applying three different levels of quantum mechanical calculations (UAM1, UB3LYP, PMP2 with three different basis sets with and without diffuse functions). Nevertheless the Nelsen method gives almost consistent results for the inner-sphere reorganization energies: 120.1 kJ/mol for semiempirical UAM1 method, 159.3 kJ/mol, 156.4 kJ/mol and 158.3 kJ/mol for density functional UB3LYP/6–31G*, UB3LYP/6–31++G* and UB3LYP/AUG–cc–pVDZ calculations and 192.5 kJ/mol for ab-initio PMP2/6–31G* investigations, respectively. These values are in agreement with earlier experimental work supposing the total reorganization energy to be larger than 38 kcal/mol assuming an electron self-exchange rate of 10 4 M −1s −1. The simple harmonic approximation of Marcus relation has not yet been applied for a molecule like cyclooctatetraene with large torsional geometry changes. Using the projected force constants after scaling, considerably different results for the inner-sphere reorganization energy have been calculated: 738.1 kJ/mol for the UB3LYP/6–31G*, 743.3 kJ/mol for UB3LYP/6–31++G* and 759.1 kJ/mol for UB3LYP/AUG–cc–pVDZ level of theory. Comparison with our concentration dependent EPR experiments are controversial to the earlier experimental results, but the latter supports the assumption that the electron self-exchange occurs in a time scale so that the molecules cannot complete their vibrational motions. Therefore the projected Marcus relation is not valid for cyclooctatetraene/cyclooctatetraene radical anion including a large torsional change during the electron transfer.

Theoretical investigation of the reaction mechanism and properties for F+H 2→HF+H reaction

The structures and properties of the electron transfer (ET) system for the F+H 2→HF+H reaction are studied using five methods: UHF, UMP2, UBLYP, UB3LYP and UB3P86 at the 6-311+G ∗∗ basis set level. First, the geometry optimization of the precursor complex showed the attacking mode of the F atom. Through the analysis of the net charge, vibration mode and vibration frequency, the reaction mechanism and the process of ET are discussed. Finally, the rate constant was obtained through the calculation of the electron coupling matrix H if, inner-sphere reorganization energy λ, and activation free energy Δ G #.

Study on the structure and property for the NO2+NO2− electron transfer system

The structures and the properties of the NO2+NO2− electron transfer system are studied with ab initio calculations at the B3LYP/6-311+G∗ basis set level for the three selected structures: three species favor the structure of ‘head to head’. The nitrogen dioxide molecule separation distances computed using the DFT/B3LYP method were found to agree with the second order of Møller–Plesset perturbation theory lever (MP2) results. The 351.1nm (3.532eV) photoelectron spectrum of the nitrite anion (NO2−) is obtained. The electron affinity of NO2 is found to be 2.273±0.005eV, which leads to the heat of formation ΔfH00(NO2−)=−183.4±0.9kJ/mol. It shows there are relatively strong interactions between them. Additionally, the geometry of transition state is also obtained by the linear coordinate method. From the analysis of the charge on the transition state and the isolated state, the reaction kinetics mechanism was derived. The activation energy and the coupling matrix element of the rate constant of the ET reaction are also calculated. According to the reorganization energy of the ET reaction, the values obtained from the George–Griffith–Marcus (GGM) method (the contribution only from diagonal elements of force constant matrix) are larger than those obtained from the Hessian matrix method (including the contribution from both diagonal and off-diagonal elements), which suggests that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.

A Comparison of the Inner-Sphere Reorganization Energies of Cytochromes, Iron−Sulfur Clusters, and Blue Copper Proteins

Inner-sphere reorganization energies have been calculated for a number of models of six-coordinate iron porphyrins (with varying axial ligands), using the density functional B3LYP method. If the axial ligands are uncharged, the reorganization energy is very low, 5-9 kJ/mol. If one of the axial ligands is charged, the reorganization energy is higher, 20-47 kJ/mol, but such sites are normally not used in electron carriers. The former reorganization energies are appreciably smaller than what was found for blue copper proteins (62-90 kJ/mol), the dimeric CuA site in cytochrome c oxidase and nitrous oxide reductase (43 kJ/mol), and six different types of iron-sulfur clusters with one, two, or four iron atoms (40-75 kJ/mol), even if these vacuum energies are typically halved inside the protein (as a result of hydrogen bonds and solvation effects). Therefore, the cytochromes seem to have the inherently lowest inner-sphere reorganization energy of the three commonly used electron carriers. All three types of sites have reduced the reorganization energy by using a delocalized charge and N- and S-donors (rather than O-donors) as metal ligands. Moreover, iron is a more appropriate metal for electron transfer than copper because Fe(II) and Fe(III) prefer the same coordination number and geometry and give bonds weaker than those of copper. The low-spin state of the cytochrome has a ∼20 kJ/mol lower reorganization energy than that of the corresponding high-spin site. Moreover, ring strain in the porphyrin reduce the changes in the Fe-NPor distances by 5 pm and therefore the reorganization energy by 8 kJ/mol. (Less)

Inner-sphere reorganization energy of iron-sulfur clusters studied with theoretical methods.

Models of several types of iron-sulfur clusters (e.g., Fe(4)S(4)(SCH(3))(4)(2-/3-/4-)) have been studied with the density functional B3LYP method and medium-sized basis sets. In a vacuum, the inner-sphere reorganization energies are 40, 76, 40, 62, 43, and 42 kJ/mol for the rubredoxin, [2Fe-2S] ferredoxin, Rieske, [4Fe-4S] ferredoxin, high-potential iron protein, and desulfoferrodoxin models, respectively. The first two types of clusters were also studied in the protein, where the reorganization energy was approximately halved. This change is caused by the numerous NH.S(Cys) hydrogen bonds to the negatively charged iron-sulfur cluster, giving rise to a polar local environment. The reorganization energy of the iron-sulfur clusters is low because the iron ions retain the same geometry and coordination number in both oxidation states. Cysteine ligands give approximately the same reorganization energy as imidazole, but they have the advantage of stabilizing a lower coordination number and giving more covalent bonds and therefore more effective electron-transfer paths.

Theoretical Study of Electron, Proton, and Proton-Coupled Electron Transfer in Iron Bi-imidazoline Complexes

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.

Ab initio calculation of inner-sphere reorganization energies of arenediazonium ion couples.

The geometries of a series of substituted arenediazonium cations (p-NO2, p-CN, p-Cl, p-F, p-H, m-CH3, p-CH3, p-OH, p-OCH3, p-NH2) and the corresponding diazenyl radicals were optimized at the HF/6-31G, MP2/6-31G, B3LYP/6-31G, B3LYP/TZP, B3PW91/TZP, and CASSCF/6-31G levels of theory. Inner-sphere reorganization energies for the single electron-transfer reaction between the species were computed from the optimized geometries according to the NCG method and compared to experimental values determined by Doyle et al. All levels of theory predicted a CNN bond angle of 180 degrees in the cation. A bent neutral diazenyl radical was predicted at all levels of theory excepting B3LYP/TZP and B3PW91/TZP for the p-Cl-substituted compound. Inner-sphere reorganization energies determined at the HF, MP2, and CASSCF levels of theory correlated poorly with both experimental results and calculated geometries. Density functional methods correlated best with the experimental values, with B3LYP/6-31G yielding the most promising results, although the ROHF/6-31G survey also showed some promise. B3LYP/6-31G calculations correctly predicted the order of the inner-sphere reorganization energies for the series, excluding the halogen-substituted compounds, with values ranging from 42.8 kcal x mol(-1) for the p-NO2-substituted species to 55.1 kcal x mol(-1) for NH2. The magnitudes of these energies were lower than the experimental by a factor of 2. For the specific cases examined, the closed-shell cation geometries showed the expected geometry about the CNN bond, with variations in the CN and NN bond lengths correlating with the electron-donating/withdrawing capacity of the substituent. As predicted by Doyle et al., a large geometry change was observed upon reduction. The neutral diazenyl radicals showed a nominal CNN bond angle of 120 degrees and variations in the CN and NN bond lengths also correlated with the electron-donating/withdrawing capacity of the substituent. Changes in theta(CNN) and r(CN) both correlated well with calculated lambda(inner). The key parameters influencing inner-sphere reorganization energy were the CN and NN bond lengths and the CNN bond angle. This influence is explained qualitatively via resonance models produced from NRT analysis and is related to the amount of CN double bond character. Based on these observations, B3LYP/6-31G calculations are clearly the most amenable for calculating inner-sphere reorganization energies for the single electron-transfer reaction between cation/neutral arenediazonium ion couples.

Structure, strain, and reorganization energy of blue copper models in the protein

The copper coordination geometry in the blue copper proteins plastocyanin, nitrite reductase, cucumber basic protein, and azurin has been studied by combined density functional (B3LYP) and molecular mechanical methods. Compared to quantum chemical vacuum calculations, a significant improvement of the geometry is seen (toward the experimental structures) not only for the dihedral angles of the ligands but also for the bond lengths and angles around the copper ion. The flexible Cu–SMet bond is well reproduced in the oxidized structures, whereas it is too long in some of the reduced complexes (too short in vacuum). The change in the geometry compared to the vacuum state costs 33–66 kJ/mol. If the covalent bonds between the ligands and the protein are broken, this energy decreases by ∼25 kJ/mol, which is an estimate of the covalent strain. This is similar to what is found for other proteins, so the blue copper proteins are not more strained than other metalloproteins. The inner-sphere self-exchange reorganization energy of all four proteins are ∼30 kJ/mol. This is 30–50 kJ/mol lower than in vacuum. The decrease is caused by dielectric and electrostatic effects in the protein, especially the hydrogen bond(s) to the cysteine copper ligands and not by covalent strain. (Less)

Voltammetric probes of cytochrome electroreactivity: the effect of the protein matrix on outer-sphere reorganization energy and electronic coupling probed through comparisons with the behavior of porphyrin complexes.

Using surface-modified electrodes composed of omega-hydroxyalkanethiols, an experimentally based value for the inner-sphere reorganization energy of the bis(imidazole)iron porphyrin system has been obtained by examining the solvent dependence of the reorganization energy of bis(N-methylimidazole)meso-tetraphenyl iron porphyrin. The value obtained (0.41 +/- 0.06 eV) is remarkably similar to values we have recently reported for the reorganization energy of cytochrome b(5) (0.43 +/- 0.02 eV) and cytochrome c (0.58 +/- 0.06 eV). This strongly suggests that the protein matrix mimics the behavior of a low dielectric solvent and effectively shields the heme from the solvent. The effect of the orientation of the heme relative to the electrode was also explored by sytematically varying the steric bulk of the axial ligands. On the basis of a good linear correlation between the electronic coupling and the cosine of the angle between the heme plane and the surface of the electrode, it is suggested that a parallel orientation of the heme yields a maximum in the electronic coupling. Relevance to interheme protein electron transfer is discussed.

Quantum chemical modelling of the heterogeneous electron transfer: from qualitative analysis to a polarization curve

State-of-the-art in the field of quantum chemical modelling of the heterogeneous electron transfer processes is reviewed. Novel approaches originating from interplay between quantum chemistry and modern theory of charge transfer are discussed and illustrated by recent results on the calculation of relevant kinetic parameters for various electrochemical systems. Emphasis is made on the modelling of the inner-sphere reorganization and the works of approach, as well as on the consideration of reaction layer as an orientational ensemble of reagents. Recent approaches to the estimation of electronic transmission coefficient are analyzed. A possibility to employ traditional phenomenological theory to the analysis of experimental data is re-examined in the framework of microscopic treatment.

Studies on density functional theory for the electron-transfer reaction mechanism between M-C6H6 and M+-C6H6 complexes in the gas phase

Density functional theory (DFT) is used to theoretically investigate the electron-transfer (ET) reactions between M (Li, Na, Mg)–C6H6 and M+–C6H6 complexes in the gas phase. The geometry optimization of the metal–benzene complexes and the encounter state in the process of ET reaction was performed at the 6-31G basis set level. The metal atoms (or metal ions)–benzene molecule separation distances computed using DFT method were found to agree with second-order Moller–Plesset (MP2) results. The precursor complex has C6 symmetry, the distances between acceptor and donor is about 3.0–3.6 A, which yields a bonding energy of approximately 0.9–1.5 eV. It shows there are relatively strong interactions between them. Additionally, the geometry of transition state is also obtained by the linear coordinate method. From the analysis of the charge on the transition state and the isolated state, the reaction mechanism was derived. Also the activation energy and the coupling matrix element of the rate constant of the ET reaction are calculated. According to the reorganization energy of the ET reaction, the values obtained from George–Griffith–Marcus (GGM) method (the contribution only from diagonal elements of force constant matrix) are larger than those obtained from Hessian matrix method (including the contribution from both diagonal and off-diagonal elements), which suggests that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 186–194, 2000

Outer-sphere electron transfer from carbazoles to halomethanes. Reduction potentials of halomethanes measured by fluorescence quenching experiments

Kinetic studies on the photoinduced electron transfer reduction of a variety of halomethanes in acetonitrile and ethanol at 298 K are reported in terms of the quenching rate constants (kq) with a series of reductants (carbazoles and anthracenes) whose one-electron oxidation potentials (Eox) have been measured again in the present work vs. SCE and independently vs. ferrocene. The Rehm–Weller Gibbs energy relationship is applied to determine the fundamental parameters for the one-electron reduction, i.e., the one-electron reduction potentials (ERX/RX−˙) of the halomethanes and the intrinsic barrier for the electron transfer reduction (ΔGG‡o). The ERX/RX−˙ values obtained were related to the concerted electron transfer–bond breaking reduction potentials (ERX/R˙ + X−) and the standard free enthalpies of dissociation of RX−˙ (ΔGo, dissRX−˙) were estimated in each solvent. Additionally, the one-electron reduction potential (ERX/RX−˙) values estimated in acetonitrile were also related to different thermodynamic parameters such as electron affinity (EA), LUMO–HOMO energy differences (ΔE) and the bond dissociation energy (DRX). Optimized geometry, EA and ΔE for halomethanes were calculated by an ab initio method at the B3LYP level using 3-21G, 6-31+G(d,p) and G-311+G(3df,2pd) basis sets. In all these cases good linear correlations were obtained. The ΔGG‡o values obtained are compared with those calculated using the equation ΔGG‡o = λ/4 with λ = λi + λo where the solvent reorganization energy (λo) and the inner-sphere reorganization energies (λi) associated with the structural change upon the electron-transfer process were calculated, the former by using the Marcus–Hush model and the latter by using semiempirical and ab initio molecular modeling and QSAR properties. Results obtained from the preparative irradiation of carbazoles in the presence of halomethanes, which are consistent with a photoinduced electron transfer mechanism are also discussed.

Multistate continuum theory for multiple charge transfer reactions in solution

In this article we present a multistate continuum theory for multiple charge transfer reactions such as proton-coupled electron transfer and multiple proton transfer reactions. The solute is described with a multistate valence bond model, the solvent is represented as a dielectric continuum, and the transferring protons are treated quantum mechanically. This theory provides adiabatic free energy surfaces that depend on a set of scalar solvent variables corresponding to the individual charge transfer reactions. Thus this theory is a multidimensional analog of standard Marcus theory for single charge transfer reactions. For processes involving significant inner-sphere (i.e., solute) reorganization, the effects of solute intramolecular vibrations can be incorporated into the adiabatic free energy surfaces. The input quantities required for this theory are gas phase valence bond matrix elements fit to standard quantum chemistry calculations and solvent reorganization energy matrix elements calculated with standard continuum electrostatic methods. The goal of this theory is to provide insight into the underlying fundamental physical principles dictating the mechanisms and rates of multiple charge transfer reactions.

Temperature Dependence of the Outer-Sphere Reorganization Energy

The temperature dependence of the intervalence charge transfer transition (IT) has been studied for a mixed-valence dinuclear iron complex. The two “halves” of this complex consist of trisbipyridineiron moieties that are triply linked with saturated alkyl chains. Because the complex is symmetric, the energy of the IT band is a direct measure of the reorganization energy for electron transfer between the two irons. Moreover, for the specific complex under investigation here, the inner-sphere reorganization energy is essentially zero because of an exact cancellation of sigma- and pi-bonding changes upon changing the oxidation state of each iron. As a consequence, the energy of the IT transition is a direct measure of the outer-sphere (solvent) reorganization energy. The energy of the IT band has been investigated over the temperature range −28 °C to 30 °C. The derivative of the outer-sphere reorganization energy with respect to temperature found from this study was −3.2 ± 0.4 cm-1K-1. Theoretical calculations based on the Marcus two spheres in a dielectric continuum model and a molecular based model developed by Matyushov were also carried out for comparison with the experimental results. The continuum model predicts a positive slope for the derivative while the Matyushov model gives a negative slope that differs from that of the experimental data by a factor of ∼2 in magnitude.

Theoretical study of inner-sphere reorganization energy of the electron transfer reactions between M–C6H6 and M+–C6H6 complexes in the gas phase: an ab initio computation

An ab inito computation of reorganization energy for the electron transfer (ET) reactions between metal–benzene and metal ion–benzene complexes is presented. The geometry optimization of the metal–benzene complexes was performed. The metal atoms (or metal ions)– benzene molecule separation distances computed using an ab initio method were found to agree with earlier reported results. Values of reorganization energies using George-Griffith Marcus (GGM) method (the contribution from only diagonal elements of force constant matrix) and Hessian matrix method (including the contribution from both diagonal and off-diagonal elements) were computed. Results of reorganization energy show that the GGM method gives much lower values compared to those obtained using the Hessian method, suggesting that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.

Protein Tuning of Excited-State Charge-Transfer Dynamics in Azurin

Resonance Raman spectra of azurin from Alcaligenes denitrificans have been measured at wavelengths throughout the S(Cys) → Cu charge-transfer absorption band to examine the effects of structure and environment on the excited-state charge-transfer dynamics. Measurement of the depolarization ratios suggest that the Raman scattering is enhanced by a single electronic transition. Self-consistent analysis of the absorption spectrum and the resonance Raman fundamental, overtone, and combination bands yields a total inner-sphere reorganization energy of 0.26 ± 0.02 eV, similar to that for Pseudomonas aeruginosa. The reorganization energy is distributed along similar vibrational modes in the two azurins, although the contribution from each mode is different. To understand these differences, molecular comparisons of the known structures and molecular modeling of the electrostatic field within the protein were performed. The results show that the two proteins have very similar structures, although the copper site itself has a slightly more tetrahedral geometry in A. denitrificans. The resonance Raman spectral differences between these two azurins are interpreted to arise from this copper site structural difference and a greater distribution of charges and/or dipoles near the coordinating histidines in A. denitrificans.

Asymmetry of inner-sphere reorganization energy for heterogeneous electron transfer

The approach to the calculation of the activation energy of electrochemical charge transfer is considered for systems characterized by asymmetry of inner-sphere reorganization (i.e. by the difference in inner-sphere reorganization energies for direct and reverse reactions). Model calculations are carried out and the region of parameters is evaluated for which the effect is pronounced. A quantum-chemical analysis of inner-sphere reorganization is presented for four cobalt and chromium chelate aminocarboxylate complexes and the corresponding contribution to activation energy is discussed in connection with the difference in rate constants.