Rate Constants For Electron Transfer Reactions Research Articles

Diabatic models with transferrable parameters for generalized chemical reactions

Diabatic models applied to adiabatic electron-transfer theory yield many equations involving just a few parameters that connect ground-state geometries and vibration frequencies to excited-state transition energies and vibration frequencies to the rate constants for electron-transfer reactions, utilizing properties of the conical-intersection seam linking the ground and excited states through the Pseudo Jahn-Teller effect. We review how such simplicity in basic understanding can also be obtained for general chemical reactions. The key feature that must be recognized is that electron-transfer (or hole transfer) processes typically involve one electron (hole) moving between two orbitals, whereas general reactions typically involve two electrons or even four electrons for processes in aromatic molecules. Each additional moving electron leads to new high-energy but interrelated conical-intersection seams that distort the shape of the critical lowest-energy seam. Recognizing this feature shows how conical-intersection descriptors can be transferred between systems, and how general chemical reactions can be compared using the same set of simple parameters. Mathematical relationships are presented depicting how different conical-intersection seams relate to each other, showing that complex problems can be reduced into an effective interaction between the ground-state and a critical excited state to provide the first semi-quantitative implementation of Shaik’s “twin state” concept. Applications are made (i) demonstrating why the chemistry of the first-row elements is qualitatively so different to that of the second and later rows, (ii) deducing the bond-length alternation in hypothetical cyclohexatriene from the observed UV spectroscopy of benzene, (iii) demonstrating that commonly used procedures for modelling surface hopping based on inclusion of only the first-derivative correction to the Born-Oppenheimer approximation are valid in no region of the chemical parameter space, and (iv), demonstrating the types of chemical reactions that may be suitable for exploitation as a chemical qubit in some quantum information processor.

Temperature independence of the primary electron transfer reaction rate constants in photosynthetic bacterial reaction centers

Temperature independence of the primary electron transfer reaction rate constants in photosynthetic bacterial reaction centers

Investigation of the oxidation of hydroquinone at the liquid/liquid interface

The oxidation of hydroquinone (QH 2) was investigated for the first time at liquid/liquid (L/L) interface by scanning electrochemical microscopy (SECM). In this study, electron transfer (ET) from QH 2 in aqueous to ferrocene (Fc) in nitrobenzene (NB) was probed. The apparent heterogeneous rate constants for ET reactions were obtained by fitting the experimental approach curves to the theoretical values. The results showed that the rate constants for oxidation reaction of QH 2 were sensitive to the changes of the driving force, which increased as the driving force increased. In addition, factors that would affect ET of QH 2 were studied. Experimental results indicated ion situation around QH 2 molecule could change the magnitude of the rate constants because the capability of oxidation of QH 2 would be affected by them.

Theoretical studies on the self-exchange electron-transfer reaction between 2,3-dicyano-5,6-dichloro- p-benzoquinone (DDQ) and its radical anion DDQ −[rad

The structure of 2,3-dicyano-5,6-dichloro- p-benzoquinone (DDQ) and its radical anion was optimized by semi-empirical AM1, PM3, ab initio HF/3-21G, 6-31G, 6-31G(d), 6-31+G(d), and density functional B3LYP/6-31G(d), 6-31+G(d) methods. Nelsen’s model was used to calculate the internal reorganization energy λ i. The results of λ i from the AM1, PM3 and B3LYP methods are reasonable, while those from the HF method are too large because of not considering the effect of electron correlation. The linear reaction coordinate R was used to construct the double-well potential surface for the donor and acceptor, and then the transition state was determined at the point of R=0.50. Then Marcus’s two-sphere model was applied to estimate the solvent reorganization energy λ o in different solvents CH 3CN, benzonitrile, acetone, CHCl 3, and CH 2Cl 2. The electron transfer (ET) matrix element V rp was calculated using two-state model. The self-exchange ET reaction rate constants k ET in different solvents were calculated and the results were consistent with the experimental values. The reason why the behavior of self-exchange ET reaction between DDQ and DDQ − does not correlate with Marcus’s theory was discussed as well.

On the theory of electron transfer reactions at semiconductor electrode/liquid interfaces

Electron transfer reaction rate constants at semiconductor/liquid interfaces are calculated using the Fermi Golden Rule and a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the electronic structures of semiconductors with surfaces and are compared. The maximum electron transfer rate constants at Si/viologen2+/+ and InP/Me2Fc+/0 interfaces are computed using the tight-binding type calculations for the solid and the extended-Hückel for the coupling to the redox agent at the interface. These results for the bulk states are compared with the experimentally measured values of Lewis and co-workers, and are in reasonable agreement, without adjusting parameters. In the case of InP/liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Charged Species in the Radiolysis of Supercritical CO2

The pulse radiolysis technique has been employed in studying charge-transfer reactions of anionic C{sub 2}O{sub 4}{sup {minus}}, and cationic C{sub 2}O{sub 4}{sup +} species in supercritical carbon dioxide (scCO{sub 2}) over a range of reduced densities {rho}{sub r} = 0.36--1.5 and at a reduced temperature of T{sub r} = 1.03. The absorption spectrum measured in the visible region with a maximum around 700 nm is assigned to the dimer cation C{sub 2}O{sub 4}{sup +}. The pressure dependence of charge-transfer reactions was examined using dimethylaniline (DMA), benzoquinone (BQ), and oxygen as charge acceptors. The reaction rates of DMA with cations, and BQ with anions are at or near the diffusion-controlled limit. The rates decrease an order of magnitude with increase of pressure. The reaction of C{sub 2}O{sub 4}{sup +} with oxygen is much slower with an almost constant rate over the pressure range examined. The measured rate constants of electron-transfer reactions are analyzed in terms of the diffusion constants of reactants in scCO{sub 2}, and the dependence of measured and theoretical values on the bulk density is discussed.

Chronoamperometry of Surface-Confined Redox Couples for Irreversible Two-Step and Three-Step Consecutive Reaction Mechanisms

Chronoamperometry has been widely employed to determine kinetic rate constants for electron-transfer reactions of surface-confined redox couples. When the mechanism for the transformation is more complicated than a one-electron transfer, deviations can be expected from an exponential decay of the current transient. Theory is presented in this paper for irreversible, two-step and three-step consecutive reaction mechanisms in the form of analytical solutions of the corresponding differential equations. The theory should find application to surface electrode reactions with two-electron "n-values".

Photoinduced Electron Transfer from N,N-Dimethylaniline to Pyrrolidinofullerenes (C60(C3H6N)R): Emphasized Substituent Effects with Solvent Polarity Change

Photoinduced electron-transfer reactions of pyrrolidinofullerenes {C60(C3H6N)R; R = H (1), C6H4NO2-p (2), C6H4CHO-p (3), C6H5 (4), C6H4OMe-p (5), and C6H4NMe2-p (6)} with N,N-dimethylaniline have been systematically studied by means of nanosecond laser photolysis. From the direct observation of the rises of the anion radicals accompanied by the decays of the triplet states of the fullerenes, the rate constants of electron-transfer reactions (kET) via the triplet states were evaluated in polar solvents. Although the kET values are considerably decreased by the substituents as compared with that of pristine C60, the electron is accepted by the C60 moiety. Among the derivatives, the kET values of 2 and 3 with electron-withdrawing groups are larger than those of 4 and 1. In less polar solvent, such a substituent effect becomes prominent with decrease in the kET values, which is in accord with the reactivity−selectivity principle. This behavior can be explained by the Rehm−Weller relation and/or Marcus equation in consideration of the solvent polarity change. Back-electron-transfer rate constants in less polar solvent are larger than those in polar solvent, which is related to the desolvation process and/or loose ion pair formation.

Factors Influencing Redox Thermodynamics and Electron Self-Exchange for the [Fe4S4] Cluster in Chromatium vinosum High Potential Iron Protein: The Role of Core Aromatic Residues in Defining Cluster Redox Chemistry

The roles of aromatic core residues in regulating the reduction potential, the enthalpy and entropy of reduction, and the self-exchange rate constants for electron-transfer reactions for the prosthetic [Fe4S4]3+/2+ cluster of Chromatium vinosum high potential iron protein (HiPIP) have been addressed by a combination of site-directed mutagenesis, high field NMR (EXSY) experiments, and variable temperature spectrochemical redox titration measurements. Minimal changes are observed following nonconservative mutation of residues Tyr19, Phe48, and Phe66. Apparently these hydrophobic residues play only a minor role in defining the electronic properties of the cluster. These data support a model, first defined from results obtained on Tyr19 mutant HiPIP's [Agarwal, A., Li, D., & Cowan, J.A. (1995) Proc. Natl. Acad. Sci. U.S.A. 92, 9440-9444], in which the aromatic core restricts solvent accessibility and thereby stabilizes the oxidized [Fe4S4]3+ cluster.

The multi-configurational adiabatic electron transfer theory and its invariance under transformations of charge density basis functions

The continuum multi-configurational dynamical theory of electron transfer (ET) reactions in a chemical solute immersed in a polar solvent is developed. The solute wave function is represented as a CI expansion. The corresponding decomposition of the solute charge density generates a set of dynamical variables, the discrete medium coordinates. A new expression for the free energy surface in terms of these coordinates is derived. The stochastic equations of motion derived earlier are shown to be invariant under unitary transformations of orbitals used to build the CI expansion provided the latter is complete over the corresponding orbital subspace, and also under general linear transformations of the bases employed in expanding the charge density. The interrelation between the present general treatment and the reduced theory applied previously in terms of the two-level ET model is investigated. Finally, the explicit expression for the screening potential of medium electrons is derived in the electronic Born-Oppenheimer approximation (fast (slow) electronic timescale for solvent (solute)). The theory leads to a self-consistent scheme for practical calculations of rate constants for ET reactions involving complex solutes. Illustrative test calculations for two-level ET systems are presented, and the importance of proper boundary conditions for realistic molecular cavities is demonstrated.

Electron transfer from triplet thymine and thymidine to lipoic acid

Electron transfer from the triplet excited state of thymine or thymidine to the disulphide compound lipoic acid (RSSR) was studied using KrF laser flash photolysis (248 nm, 20 ns). The electron transfer reaction rate constants, measured at 310 nm, were determined to be 1.3×10 10 M −1 s −1 and 6.9×10 9 M −1 s −1 for thymine and thymidine respectively. The transient absorbance at 400 nm in the presence of the quencher is attributed to the anion radical of lipoic acid.

Protein-protein orientation in electron-transfer reactions of the cytochromec/plastocyanin complex with free cytochromec and with free plastocyanin

Cross-linking of horse-heart cytochromec (cyt) and French bean plastocyanin (pc), promoted by a carbodiimide, yields the covalent complex cyt/pc, in which the basic (positively charged) patch around the surface-exposed heme edge in the former protein and the acidic (negatively charged) patch remote from the copper site in the latter protein abut each other and thus largely neutralize each other's charge and shield each other. Four major fractions of the covalent complex cyt/pc separated by cation-exchange chromatography are structurally similar to one another and to the electrostatic (noncovalent) complex cyt/pc; the fractions have different charges because of different numbers and locations ofN-acylurea groups, by-products of the reaction with carbodiimide. The kinetic studies are done with the first chromatographic fraction, whose net charge and dipole moment could be determined most accurately. The rate constants for electron-transfer reactions of the protein complex with each of its constituent proteins separately were determined by laser flash photolysis, with riboflavin semiquinone as the reductant, at pH 7.0 and an ionic strength from 10 to 500 mM. Electrostatic interactions in the two reactions were treated according to van Leeuwen theory, which stresses the importance ofmonopole-dipole and dipole-dipole forces, in addition to the well-known monopole-monopole force. Semiquantitative analysis of dipolar interactions indicated probable orientation of the diprotein complex and the individual protein in both electron-transfer reactions. The cupriplastocyanin moiety in the cyt(III)/pc(II) complex seems to use its hydrophobic patch for reaction with free ferrocytochromec. Free cupriplastocyanin also seems to use its hydrophobic patch for reaction with the ferrocytochromec moiety in the cyt(II)/pc(II). Protein-protein orientation in electron-transfer reactions is governed by both electrostatic and steric factors.

Rate constants for electron-transfer reactions of cuboidal [Mo 4S 4(edta) 2] 4−, 3−, 2− cluster complexes

Green [Mo 4 S 4 (edta) 2 ] 3− is obtained by reduction of the di-μ-sulfido Mo(V) dimer, [Mo 2 O 2 S 2 (edta)] 2− with NaBH 4 . Rate constants for cross reactions were obtained by stopped-flow and in one case conventional spectrophotometry

Thermal and photochemical reactions of d9 metal complexes: the silver(II) macrocycles

Rate constants for electron-transfer reactions of d/sup 9/ metal (Cu(II), Ni(I), and Ag(II)) macrocyclic complexes have been determined by pulse radiolysis. The self-exchange rate constants reveal slow exchanges for d/sup 9/10/ couples (values between 10/sup 3/ and 10/sup -2/ M/sup -1/ s/sup -1/) and fast ones for d/sup 8/9/ couples (values between 10/sup 4/ and 10/sup 9/ M/sup -1/ S/sup -1/). The photochemical oxidation of the macrocyclic ligand in Ag((14)aneN/sub 4/)/sup 2 +/ takes place with larger quantum yields than in the corresponding Cu(II) complex (10/sup -1/ vs 10/sup -3/). No photooxidation of axially coordinated ligands has been detected with Ag(II) complexes. The thermal and photochemical reactivities are discussed in terms of the differences in the electronic levels and nuclear configurations between these d/sup 9/ metal complexes. 37 references, 4 figures, 3 tables.

Photoinduced electron-transfer reactions of poly(pyridine)ruthenium(II) complexes with europium(III/II) cryptates

Rate constants for electron-transfer reactions between poly(pyridine)ruthenium(II) (RuL/sub 3//sup 2 +/) excited states and the europium cryptates (Eu contains 2.2.1)/sup 3 +/ and (Eu contains 2.2.1)/sup 2 +/ have been measured in aqueous solution by luminescence quenching techniques. The rate constants for a few electron-transfer back-reactions between the photogenerated RuL/sub 3//sup 3 +/ and (Eu contains 2.2.1)/sup 2 +/ or RuL/sub 3//sup +/ and (Eu contains 2.2.1)/sup 3 +/ species have also been measured by flash photolysis experiments. The results obtained have been elaborated and discussed on the basis of current electron-transfer theories. Comparison of the results obtained with those previously available for the Eu/sub aq//sup 3 +/ and Eu/sub aq//sup 2 +/ ions shows that cryptation decreases the intrinsic barrier and/or increases the adiabaticity coefficient of the electron-transfer reaction. A plot of the rate constants vs. the free energy changes of the electron-transfer processes shows that the data concerning (Eu contains 2.2.1)/sup 3 +/ reduction do not correlate with those concerning (Eu contains 2.2.1)/sup 2 +/ oxidation. Possible reasons for this asymmetric behavior include (i) different shapes of the potential energy wells for (Eu contains 2.2.1)/sup 3 +/ and (Eu contains 2.2.1)/sup 2 +/, (ii) different work terms formore » the formation of the precursor complex, and (iii) different distances of closest approach of (Eu contains 2.2.1)/sup 3 +/ and (Eu contains 2.2.1)/sup 2 +/ with the hydrophobic RuL/sub 3//sup n+/ reaction partners.« less

Laser photolysis studies on the rate constants of electron transfer reactions of aromatic molecules in solution

Absolute rate constants for electron-transfer reactions of aromatic molecules in solution at room temperature have been studied by the nanosecond laser photolysis method. Holes or electrons of photochemically produced radical cations or anions were tranferred to second aromatic compounds. The decay of the ion radical donor and the rise in the amount of the ion radical acceptor for each donor and acceptor pair were observed at their absorption maxima, and the simulation of this rise and decay gave electron transfer rate constants. The relationship between these rate constants and the reaction free energy change showed that the electron transfer of highly exothermic reactions proceeds with a diffusion-controlled rate cosntant, which suggests that electron transfer occurs through some loose complex in solution.

Frequency factor in the rate constants of electron-transfer reactions

Frequency factor in the rate constants of electron-transfer reactions

On the Electron-transfer Reaction Rate between Different Molecular Species of Aromatic Hydrocarbons as Measured by ESR

Abstract The rate constants of electron-transfer reactions between the anthracene anion radical and pyrene, and those between the former radical and 1,2-benzanthracene, were measured by the ESR method in tetrahydrofuran containing 20 mm of tetra-n-butylammonium perchlorate. In the analysis of the experimental results, correction of the ESR line width was made for the change in the radical concentration caused by the addition of neutral molecules. The rate constants thus obtained were (2.0±0.4)×107m−1sec−1 and (8.1±1.0)×10−7m−1sec−1 respectively at 25°C. Under the same experimental conditions, the rate constants of the electron exchange of anthracene and pyrene with their respective anions were about one-tenth of the rate constants of free anions. This fact led us to the supposition that the anion radicals had been combined with tetra-n-butylammonium ions into stable ion-pairs in our experiment. A semi-empirical method was proposed for the theoretical calculation of the rate constant according to the theory of R. A. Marcus. The agreement of the observed and the calculated rate constants was satisfactory. Further discussion of the dependence of the rate constant on the standard free energy of reaction was made in connection with the so-called “Linear Free Energy Relationship.”