Reorganization Energy Of Electron Transfer Research Articles

The potential impact of the graphene oxide on the cytochrome c − from the insight of electron transfer theory

We have studied the electron transfer (ET) reaction between the cytochrome c (Cyt c) and the graphene oxide (GO). The ET reorganization energy, the ET coupling matrix element and the ET rate constant for Cyt c-GO system have been calculated using QM+MM method based on semi-classical Marcus theory. The total reorganization energy of Cyt c and GO system is about 0.9 eV. Although the conformation of Cyt c and the relative orientation of Cyt c to GO have little influence on the reorganization energy, they make a significant influence on the coupling matrix element, which results in the tremendously different ET rate constants by different orders of magnitudes. Comparing the ET rate constant of Cyt c-Go system with that between Cyt c and Cyt c1, it indicates that there is a competition between GO and Cyt c1 in the ET reaction with Cyt c.

Regulating the electrochemical reduction kinetics by the steric hindrance effect for a robust Zn metal anode

Regulating the Zn2+ solvation structure with steric hindrance can result in larger electron transfer reorganization energy, which helps to moderate the electrochemical kinetics and facilitates compact zinc deposition.

Photooxidation by a long-lived photoexcited state of a triflic acid-bound Mn(IV)-oxo complex with the highest quantum efficiency

The photoexcited state of high-valent metal-oxo complexes binding protons would show the much enhanced oxidizing reactivity, providing a new way to achieve a photochemical oxidation of thermally inert substrates. However, there has been only one example for the long-lived photoexcited state of a MnIV-oxo complex binding scandium ion that is a rare-earth metal element. We report herein the formation of a long-lived photoexcited state of a MnIV-oxo complex binding triflic acid, composed of only earth-abundant elements, which exhibits the highest oxidizing reactivity among the high-valent metal-oxo species, including the excited state, reported so far. Photoexcitation of a triflic acid-bound MnIV-oxo complex (1, [(N4Py)MnIV(O)]2+–(HOTf)2) in a deaerated trifluoroethanol/acetonitrile resulted in the formation of a long-lived photoexcited state with a lifetime of 21 μs, which oxidized toluene to produce benzyl alcohol that was further oxidized to benzaldehyde. The driving force dependence of the rate constant of the photoinduced electron transfer from electron donors to the long-lived 2E excited state of 1 afforded a small reorganization energy of electron transfer (λ = 0.53 eV), since the 2E excited state of 1 may be composed of the ligand-to-metal charge-transfer (LMCT) state and the efficient electron transfer to the excited sate of 1 occurs at the ligand center. The quantum efficiency of 200% was achieved for the photochemical four-electron oxidation of toluene by 1, being the highest among various photooxidation reactions reported so far. The photodynamics were measured by laser-induced transient absorption spectroscopy to clarify the photooxidation mechanism of 1.

The Rate Constant - Reaction Free Energy Dependence for the Electron Transfer Reactions in Solutions. The Way to Interpret the Experimental Data Correctly

The relative influences of the reorganization energies of the classical and quantum modes on the maximum position of the rate constant – reaction free energy curve have been studied. In the framework of the continuum electrostatics, the electron transfer reorganization energies in methyltetrahydrofurane solutions for the system biphenylyl – spacer – acceptor were calculated. For different acceptors the solvent reorganization energy varies from 1.0 to 1.1 eV. When added with the rather small reorganization energies for classical intra-molecular modes we obtain 1.13 - 1.34 eV. With account of possible errors this coincides practically with the experimental estimate of the energy at the maximum of the rate–free energy curve DGmax ? -1.2 eV. Hence, we can conclude that the reorganization of quantum modes does not influence substantially the position of this maximum. To the contrary, in a non-polar solvent isooctane were the solvent reorganization does not play any role the reorganization of the quantum intra-reactants modes becomes determinant. These conclusions agree fully with the results of the general theoretical analysis and should be accounted for in the experimental data interpretation.

Reorganization energy of electron transfer.

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

Aliphatic and Aromatic C–H Bond Oxidation by High-Valent Manganese(IV)-Hydroxo Species

The strong C-H bond activation of hydrocarbons is a difficult reaction in environmental and biological chemistry. Herein, a high-valent manganese(IV)-hydroxo complex, [MnIV(CHDAP-O)(OH)]2+ (2), was synthesized and characterized by various physicochemical measurements, such as ultraviolet-visible (UV-vis), electrospray ionization-mass spectrometry (ESI-MS), electron paramagnetic resonance (EPR), and helium-tagging infrared photodissociation (IRPD) methods. The one-electron reduction potential (Ered) of 2 was determined to be 0.93 V vs SCE by redox titration. 2 is formed via a transient green species assigned to a manganese(IV)-bis(hydroxo) complex, [MnIV(CHDAP)(OH)2]2+ (2'), which performs intramolecular aliphatic C-H bond activation. The kinetic isotope effect (KIE) value of 4.8 in the intramolecular oxidation was observed, which indicates that the C-H bond activation occurs via rate-determining hydrogen atom abstraction. Further, complex 2 can activate the C-H bonds of aromatic compounds, anthracene and its derivatives, under mild conditions. The KIE value of 1.0 was obtained in the oxidation of anthracene. The rate constant (ket) of electron transfer (ET) from N,N'-dimethylaniline derivatives to 2 is fitted by Marcus theory of electron transfer to afford the reorganization energy of ET (λ = 1.59 eV). The driving force dependence of log ket for oxidation of anthracene derivatives by 2 is well evaluated by Marcus theory of electron transfer. Detailed kinetic studies, including the KIE value and Marcus theory of outer-sphere electron transfer, imply that the mechanism of aromatic C-H bond hydroxylation by 2 proceeds via the rate-determining electron-transfer pathway.

Electrochemistry of Protein Electron Transfer

Protein fold and slow relaxation times impose constraints on configurations sampled by the protein. Incomplete sampling leads to the violation of fluctuation-dissipation relations underlying the traditional theories of electron transfer. The effective reorganization energy of electron transfer is strongly reduced thus leading to lower barriers and faster rates (catalytic effect). Electrochemical kinetic measurements support low activation barriers for protein electron transfer. The distance dependence of the rate constant displays a crossover from a plateau at short distances to a long-distance exponential decay. The transition between these two regimes is controlled by the protein dynamics.

Reorganization Energy of Electron Transfer in Ionic Liquids

Bandshape analysis of charge-transfer optical bands in room-temperature ionic liquids (ILs) was performed to extract the reorganization energy of electron transfer. Remarkably, the reorganization energies in ILs are close to those in cyclohexane. This result runs against common wisdom in the field since conducting ILs, which are characterized by an infinite static dielectric constant, and nonpolar cyclohexane fall to the opposite ends of the polarity scale based on their dielectric constants. Theoretical calculations employing structure factors of ILs from molecular dynamics simulations support the low values of the reorganization energy. Standard dielectric arguments do not apply to solvation in ILs, and nonergodic reorganization energies are required for a quantitative analysis.

Frustration Dynamics and Electron-Transfer Reorganization Energies in Wild-Type and Mutant Azurins.

Long-range electron tunneling through metalloproteins is facilitated by evolutionary tuning of donor–acceptor electronic couplings, formal electrochemical potentials, and active-site reorganization energies. Although the minimal frustration of the folding landscape enables this tuning, residual frustration in the vicinity of the metallocofactor can allow conformational fluctuations required for protein function. We show here that the constrained copper site in wild-type azurin is governed by an intricate pattern of minimally frustrated local and distant interactions that together enable rapid electron flow to and from the protein. In contrast, sluggish electron transfer reactions (unfavorable reorganization energies) of active-site azurin variants are attributable to increased frustration near to as well as distant from the copper site, along with an exaggerated oxidation-state dependence of both minimally and highly frustrated interaction patterns.

Molecular Geometry Dependent Electronic Coupling and Reorganization Energy for Electron Transfer between Dye Molecule Adsorbed on TiO2 Electrode and Co Complex in Electrolyte Solutions

Molecular Geometry Dependent Electronic Coupling and Reorganization Energy for Electron Transfer between Dye Molecule Adsorbed on TiO₂ Electrode and Co Complex in Electrolyte Solutions

Heterogeneous electron transfer reorganization energy at the inner Helmholtz plane in a polybromide redox-active ionic liquid.

In ionic liquids (ILs), the electric double layer (EDL) is where heterogeneous electron transfer (ET) occurs. Nevertheless, the relationship between the EDL structure and its kinetics has been rarely studied, especially for ET taking place in the inner Helmholtz plane (IHP). This is largely because of the lack of an appropriate model system for experiments. In this work, we determined the reorganization energy (λ) of Br2 reduction in a redox-active IL 1-ethyl-1-methylpyrrolidinium polybromide (MEPBr2n+1) based on the Marcus–Hush–Chidsey model. Exceptionally fast mass transport of Br2 in MEPBr2n+1 allows voltammograms to be obtained in which the current plateau is regulated by electron-transfer kinetics. This enables investigation of the microscopic environment in the IHP of the IL affecting electrocatalytic reactions through reorganization energy. As a demonstration, TiO2-modified Pt was employed to show pH-dependent reorganization energy, which suggests the switch of major ions at the IHP as a function of surface charges of electrodes.

Kinetics and Energetics of Intramolecular Electron Transfer in Single-Point Labeled TUPS-Cytochrome c Derivatives.

Electron transfer within and between proteins is a fundamental biological phenomenon, in which efficiency depends on several physical parameters. We have engineered a number of horse heart cytochrome c single-point mutants with cysteine substitutions at various positions of the protein surface. To these cysteines, as well as to several native lysine side chains, the photoinduced redox label 8-thiouredopyrene-1,3,6-trisulfonate (TUPS) was covalently attached. The long-lived, low potential triplet excited state of TUPS, generated with high quantum efficiency, serves as an electron donor to the oxidized heme c. The rates of the forward (from the label to the heme) and the reverse (from the reduced heme back to the oxidized label) electron transfer reactions were obtained from multichannel and single wavelength flash photolysis absorption kinetic experiments. The electronic coupling term and the reorganization energy for electron transfer in this system were estimated from temperature-dependent experiments and compared with calculated parameters using the crystal and the solution NMR structure of the protein. These results together with the observation of multiexponential kinetics strongly support earlier conclusions that the flexible arm connecting TUPS to the protein allows several shortcut routes for the electron involving through space jumps between the label and the protein surface.

Effect of water frustration on water oxidation catalysis in the nanoconfined interlayers of layered manganese oxides birnessite and buserite

Reacting out of frustration: unlike buserite, the nanoconfined interlayer of birnessite results in geometric frustration of water molecules, which decreases the Marcus reorganization energy of electron transfer and enhances water oxidation catalysis.

Prediction of Internal Reorganization Energy in Photoinduced Electron Transfer Processes of Molecular Dyads.

A novel theoretical methodology is proposed to estimate the magnitude of internal reorganization energy for electron transfer and charge recombination processes in donor-bridge-acceptor (D-B-A) type molecular dyads. The potential energy surface for each process is plotted for the shortest path by assuming a displaced but slightly distorted harmonic oscillator model. Structural changes occurring upon photoexcitation and ionization were exploited to calculate the activation energies needed for electron transfer reactions with the aid of involved vibrational modes. D-B-A dyads consisting of octathiophene (T8) paired with three (di)imide acceptors (naphthalene diimide (NDI), benzene diimide (BDI), and naphthalimide (NI)) were studied as model systems for theoretical calculations. It has been found that T8NDI and T8BDI possess very low activation energies for both forward electron transfer and charge recombination, and hence the rates for relevant processes should be very rapid. In contrast, the activation energies for such processes for T8NI were found to be relatively large, and free energy estimations predict that the charge recombination mechanism in T8NI falls into the inverted regime of Marcus semiclassical electron transfer theory. All of the calculated properties of the dyads are in very good agreement with the available experimental data, suggesting the suitability of the proposed theoretical approach in revealing the photoinduced electron transfer mechanisms of molecular dyads.

Equilibrium Solvation, Electron-Transfer Reactions, and Stokes-Shift Dynamics in Ionic Liquids.

A microscopic theory of solvent response by room-temperature ionic liquids is formulated based on the dynamic longitudinal susceptibility of liquid's charge density. The susceptibility function combines the structural information in terms of reciprocal-space structure factors with the memory function responsible for solvation dynamics. The charge-density structure factors and corresponding intermediate scattering functions are analyzed here by molecular dynamics simulations. They show the existence of two drastically different time scales of charge-density fluctuations. Faster, stretched-exponential dynamics are consistent with dielectric measurements. It contributes to the Stokes-shift dynamics of coumarin-153 optical dye calculated with the new theory and compared to experimental reports. The second, much slower and exponential, relaxation shows the phenomenology of de Gennes narrowing: the relaxation time passes through a strong maximum at the wave vector representing the first peak of the structure factor. This peak, which is particularly sharp for the charge density, contributes significantly to the equilibrium free energy of solvation, thus invalidating dielectric theories of solvation for ionic liquids. Dynamics of charge density fluctuations at the length scale consistent with the sharp peak require long observation times. Electron-transfer reactions occurring on faster time-scales are not affected by these slow dynamics. Nonergodic reorganization energy of electron transfer, accounting for the observation window established by the reaction time, drops sharply when the reaction rate crosses the main peak in the Stokes-shift loss spectrum. The dependence of the reorganization energy on the reaction rate strongly affects the energy-gap law of electron transfer, with a tendency for a shallow or entirely disappearing inverted region.

Electron transfer in nonpolar media.

The Marcus theory of electron transfer views fluctuating orientations of permanent dipoles as the nuclear mode bringing the donor and acceptor into the tunneling resonance. Electronic polarization of the solvent is excluded as the fast mode adiabatically following the electronic density. This view, valid for solids, does not apply to molecular liquids where molecular translations (density fluctuations) modulate the induction interaction of the donor-acceptor complex with the solvent. This mechanism of promoting radiationless electronic transitions is considered here in the framework of the perturbation liquid-state theory. The reorganization energy of electron transfer in nonpolar solvents is nonzero and reaches the values of 0.1-0.3 eV for typical molecular sizes and solvents used in applications. The reorganization energy scales quadratically with the molecular polarizability of the solvent and decays as the inverse fifth power with the size of the donor and acceptor. The combination of the entropic character of the density fluctuations, driven by re-packing of molecular cores, with the short range of induction solute-solvent interactions leads to the violation of the fluctuation-dissipation theorem for the variance of the donor-acceptor energy gap. An explicit, approximately hyperbolic, dependence of the reorganization energy on temperature is predicted. It leads to a non-Arrhenius kinetic law for the rate constant of electron transfer in nonpolar liquid solvents.

Electron Transfer Reorganization Energies in the Electrode-Electrolyte Double Layer.

The total reorganization energy, λ, for interfacial electron transfer, ET, from a conductive electrode to redox-active molecules at fixed positions within the electric double layer, EDL, has been determined experimentally. Conductive indium-tin-oxide (ITO, In2O3:Sn) mesoporous films were functionalized with 4-[N,N-di(p-tolyl)-amino]benzylphosphonic acid (TPA) and/or [RuII(bpy)2(4,4'-(PO3H2)2-bpy)]2+ (RuP), where bpy is 2,2'-bipyridine. The small inner-sphere reorganizations, λi, for RuIII/IIP and TPA+/0 make them excellent probes of outer-sphere reorganization energy, λo, as λi ≪ λo such that λ = λi + λo ≈ λo. Consecutive layer-by-layer addition of ZrIV-bridged methylenediphosphonic acid enabled positioning at distances from 4 to 27 Å from the ITO. Excited-state injection into the ITO by RuP* generated ITO(e-)|RuIIIP. For ITO cofunctionalized with TPA and RuP, subnanosecond lateral ET yielded ITO(e-)|TPA+. The kinetics for ET from ITO to RuIIIP or TPA+ were quantified spectroscopically as a function of applied potential (Eapp) and hence driving force, -ΔG°. Marcus-Gerischer analysis of this data provided λ. Significantly, λo was near zero at close electrode proximity, λ = 0.11 eV at a distance of ∼4 Å, as manifest by kinetics largely insensitive to Eapp. In agreement with dielectric continuum theory, λ increased to values expected in CH3CN solution when the molecule was positioned at a distance of ∼27 Å (λ = 0.94 eV). The data reveal small intrinsic barriers for electron transfer proximate to conductive interfaces, which is an exploitable behavior in solar energy conversion and other applications that utilize transparent conductive oxides to accept or deliver electrons.

Understanding the Solvent Contribution to Chemical Reaction Barriers.

Absolute rate theories attempt to predict the rate constants of reactions from basic principles and independent data. For the contribution of solvent to a reaction rate constant, this requires connecting absolute rate data to fundamental solvent properties such as dielectric constant and refractive index. We have explored this connection for the unimolecular fragmentation reaction of a pinacol radical cation. The rate constants for fragmentation were measured as a function of temperature in 12 different solvents with dielectric constants from 4.7 to 36.2, and the free energies of activation for bond fragmentation in each solvent determined using transition state theory. Using the solvent effects on electron-transfer reactions as a starting point, Marcus theory was used to model the solvent effect on the reaction activation energies. The solvent contribution to both the activation free energy and the overall reaction energy is best described using the Born model rather than the Pekar solvation model. The solvent reorganization energies for bond fragmentation are substantially larger than solvent reorganization energies for electron transfer, presumably because of the requirement to translate the solvent molecules in the course of bond breaking.

Small Reorganization Energy for Ligand-Centered Electron-Transfer Reduction of Compound I to Compound II in a Heme Model Study

The electron-transfer (ET) processes from electron-donor substrates to oxoiron(IV) porphyrin π-cation-radical species (Cpd I) are key steps in their oxygenation reactions. Here, we have evaluated the rate constants of the outer-sphere ET reduction of Cpd I model complexes of meso-tetramesitylporphyrin (1) and 2,7,12,17-tetramesityl-3,8,13,18-tetramethylporphyrin (2) in light of the Marcus theory of ET to determine the ET reorganization energies (λ). The λ values of the ligand-centered ET reduction of Cpd I model complexes are much smaller than those of the metal-centered ET reduction of various oxoiron(IV) complexes. Moreover, the λ value of 1 is larger than that of 2, resulting from the difference in the nature of the a1u/a2u porphyrin π-cation-radical orbitals.

Determination of Proton-Coupled Electron Transfer Reorganization Energies with Application to Water Oxidation Catalysts.

The reorganization energy, λ, for interfacial electron transfer (ET) and for proton-coupled electron transfer (PCET) between a water oxidation catalyst and a conductive In2O3:Sn (ITO) oxide were extracted from kinetic data by application of Marcus-Gerischer theory. Specifically, light excitation of the water oxidation catalyst [RuII(tpy)(4,4'-(PO3H2)2-bpy)OH2]2+ (RuII-OH2), where tpy is 2,2':6',2″-terpyridine and bpy is 2,2'-bipyridine, anchored to a mesoporous thin film of ITO nanocrystallites resulted in rapid excited-state injection ( kinj > 108 s-1). The subsequent reaction of the injected electron (ITO(e-)) and the oxidized catalyst was quantified spectroscopically on nanosecond and longer time scales. The metallic character of ITO allowed potentiostatic control of the reaction free energy change -Δ Go over a 1 eV range. At pH values below the p Ka = 1.7 of the oxidized catalyst, ET was the primary reaction. Within the pH range 2 ≤ pH ≤ 5, an interfacial PCET reaction (ITO(e-) + RuIII-OH + H+→ RuII-OH2) occurred with smaller rate constants. Plots of the rate constants versus -Δ Go provided a reorganization energy of λPCET = 0.9 eV and λET = 0.5 eV. A second water oxidation catalyst provided similar values and demonstrated generality. The utilization of conductive oxides is shown to be a powerful tool for quantifying PCET reorganization energies at oxide surfaces for the first time.