Self-exchange Electron Transfer Reactions Research Articles

Reorganization Energies, Entropies, and Free Energy Surfaces for Electron Transfer.

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

Reconciliation of Differences in Apparent Diffusion Coefficients Measured for Self-Exchange Electron Transfer between Molecules Anchored to Mesoporous Titanium Dioxide Thin Films.

Redox-active sites present at large concentrations as part of a solid support or dissolved as molecules in fluid solutions undergo reversible self-exchange electron-transfer reactions. These processes can be monitored using a variety of techniques. Chronoamperometry and cyclic voltammetry are common techniques used to interrogate this behavior for molecules bound to mesoporous thin films of wide-bandgap semiconductors and insulators. In order to use these techniques to obtain accurate values for apparent diffusion coefficients, which are proxies for rate constants for self-exchange electron transfer, it is imperative to take into consideration nonidealities in redox titrations, parasitic currents, and ohmic resistances. Using spectroelectrochemical measurements taken concurrently with measurements of chronoamperometry data, we show that the spectroscopic data is not confounded from effects of parasitic currents or electroinactive dyes. However, we show that the thickness of the thin film over the region that is optically probed by the measurements must be known. When each of these considerations is included in data analyses, calculated apparent diffusion coefficients are, within error, independent of the method used to obtain the data. These considerations help reconcile variations in apparent diffusion coefficients measured using different techniques that have been reported over the past several decades and allow correct analyses to be performed in the future, independent of the method used to obtain the data.

The Role of Structure Making/Breaking Ions in Solvation Shell and Redox Reaction Entropy of Outer Sphere Electron Transfer Reactions

Marcus theory1 of electron transfer is the dominant theory to describe the rate constant of electron transfer reactions both in chemistry and biology during last several decades. The general treatment on the solvation free energy of reactants is largely based on Born model2 that the solvent is assumed as a dielectric continuum and each reactant is treated as a sphere where the first solvation layer is dielectrically saturated. However, these assumptions could shield the fact of non-covalent interactions within the solvation shell of reactants, including reactant nuclei-solvent, reactant nuclei-inert ion, inert ion-solvent interactions and hydrogen bonding of solvent molecules. The entropy change of an electron transfer reactions, , is the difference of standard molar entropy between the reduced and oxidized forms of a redox couple. The reaction entropy of outer sphere self-exchange can be qualitatively described by Born model even though the Born prediction differs from the experimental data of some redox couples, according to previous studies3. It was shown that the reaction entropy of a given redox couple increases with decreasing in solvent acceptor number. This dependence of upon the solvent nature could be associated with the degree of “internal order” of solvent molecules. Besides solvent-solvent molecule interaction, the “internal order” of solvent could be disrupted by dissolved charged species, including the reactant nuclei of redox couples and inert ions either from the counter-ion of redox couples or from the supporting electrolyte. Depending on its effects on water structure and vice versa, ions are usually categorized in either “structure maker” or “structure breaker”4, which could affect surrounding hydrogen bonds and water molecular arrangement around itself5. In addition to solvent-solvent and ion-solvent interactions, the coulombic interaction between the redox couples and the ions with opposite sign of charge to those of redox couples has been suggested6. It could form an ionic atmosphere and, thereby affects to the reaction entropy of redox couples. In aqueous electrolyte, a simple description of this coulombic interaction by an electrostatic energy necessary for forming an ionic atmosphere by surrounding the species with the counter ions seems not to be prudent due to the fact of ternary interactions of redox nuclei, counter ions and solvent molecules. However, the non-covalent interactions have not, to the best of our knowledge, previously been considered in terms of the entropy change of outer sphere self-exchange electron transfer reactions, and it is the impact of structure making/breaking ions on the structure of the solvation shell of the reactant nuclei that constitutes the focus of this work. Here, we studied reaction entropy of two outer sphere reactions: [Fe(H2O)6]2+/3+ and [Fe(CN)6]3-/4- upon the nature and the concentration of anions and cations, respectively. For both positively and negatively charged redox couples, it was shown that structure maker ions enhance the “order” in vicinity of redox nuclei while structure breaker ions promote “disorder”. We suggest also molecular level models for redox nuclei solvation by taking into account reactant nuclei-solvent, reactant nuclei-inert ion, inert ion-solvent interactions and hydrogen bonding of solvent molecules. References (1) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (2) Born, M. Z. Für Phys. 1920, 1 (1), 45–48. (3) Hupp, J. T.; Weaver, M. J. Inorg. Chem. 1984, 23 (22), 3639–3644. (4) Marcus, Y. Chem. Rev. 2009, 109 (3), 1346–1370. (5) Miller, D. J.; Lisy, J. M. J. Am. Chem. Soc. 2008, 130 (46), 15381–15392. (6) Yamato, Y.; Katayama, Y.; Miura, T. J. Electrochem. Soc. 2013, 160 (6), H309–H314.

Torsional angle dependence and switching of inner sphere reorganisation energies for electron and hole transfer processes involving phenyl substituted diketopyrrolopyrroles; a density functional study

Determination of inner sphere reorganisation energies is important in the development of organic charge mediating materials and electron transfer reactions. In this study, hole and electron inner sphere reorganisation energies, λh and λe respectively, have been computed for the first time for a series of structurally related diketopyrrolopyrrole (DPP) molecular motifs. Inner sphere reorganisation energies for self-exchange electron transfer reactions are calculated as being lower than those associated hole transfer processes in model planar phenyl and thiophenyl substituted DPP systems. It is found that λe < λh for all planar ring/DPP core structures examined. The effect on λh/e of non-planarity between phenyl substituents and DPP core is explored in detail. The relative ordering of λh and λe is dependent upon the torsional angle of phenyl rings and reverses at twist angles of greater than 60° such that λe > λh.

Numerical solution of solvent reorganization energy and its application in electron transfer reaction

According to our recent studies on the nonequilibrium solvation, the solvent reorganization energy λ s is found to be the cost of maintaining the residual polarization, which equilibrates with the constraining extra electric fi eld. In this work, a matrix form of λ s has been formulated based our new analytical expression of the solvent reorganization energy. By means of the integral equation formulation- polarizable continuum model ( IEF - PCM ), a new numerical algorithm for λ s has been implemented as a subroutine coupled with the Q- Chem package. Then, we have performed a comparison of numerical results with analytical solution obtained by two-sphere model for λ s in selfexchange electron transfer (ET) reaction of He–He+ system. The numerical results and analytical solution coincide as the distance between the donor and the acceptor. In order to compare with our pervious numerical algorithm with dielectric polarizable continuum model, self-exchange ET reactions between tetracyanoethylene, tetrathiafulvalene , and their corresponding ionic radicals in acetonitrile have been studied. Overall, the solvent reorganization energy calculated by IEF - PCM is more reasonable since IEF - PCM gives a better self-energy of surface element.

Mechanism of Cobalt Self-Exchange Electron Transfer

A heptanuclear cobalt cluster was synthesized in two different oxidation states, Co(II)7 and a mixed valence Co(III)Co(II)6, as a soluble model of a cobalt-phosphate/borate (Co-OEC) water splitting catalyst. Crystallographic characterization indicates similar cluster cores, distinguished primarily at the central Co atom. An anion associates to the cluster cores via hydrogen bonding. Using an isotope exchange method, an anomalously slow self-exchange electron transfer rate constant (k(obs) = 1.53 × 10(-3) M(-1) s(-1) at 40 °C and 38 mM [OTf] in MeCN), as compared to that predicted from semiclassical Marcus theory, supports a charge transfer process that is accelerated by dissociation of the anion from the oxidized cluster. This mechanism sheds light on the inverse dependence of anions in the self-repair mechanism of Co-OECs. Moreover, because H2O cannot directly bridge cobalt centers, owing to the encapsulation of the central Co within the cluster core, the observed results address a long-standing controversy surrounding the Co(2+/3+) self-exchange electron transfer reaction of the hexaaqua complex.

Theoretical Calculation of Reorganization Energy for Electron Self-Exchange Reaction by Constrained Density Functional Theory and Constrained Equilibrium Thermodynamics

Within the framework of constrained density functional theory (CDFT), the diabatic or charge localized states of electron transfer (ET) have been constructed. Based on the diabatic states, inner reorganization energy λin has been directly calculated. For solvent reorganization energy λs, a novel and reasonable nonequilibrium solvation model is established by introducing a constrained equilibrium manipulation, and a new expression of λs has been formulated. It is found that λs is actually the cost of maintaining the residual polarization, which equilibrates with the extra electric field. On the basis of diabatic states constructed by CDFT, a numerical algorithm using the new formulations with the dielectric polarizable continuum model (D-PCM) has been implemented. As typical test cases, self-exchange ET reactions between tetracyanoethylene (TCNE) and tetrathiafulvalene (TTF) and their corresponding ionic radicals in acetonitrile are investigated. The calculated reorganization energies λ are 7293 cm(-1) for TCNE/TCNE(-) and 5939 cm(-1) for TTF/TTF(+) reactions, agreeing well with available experimental results of 7250 cm(-1) and 5810 cm(-1), respectively.

Quantum Chemical Calculations of Reorganization Energy for Self-Exchange Electron and Hole Transfers of Aromatic Diamines as Electron-donor Molecules

ABSTRACTReorganization energy is one of the important factors to decide the rate of electron transfer according to the Marcus theory. Small reorganization energy is highly desirable in design of optoelectronic and electronic devices like as organic light emitting diode. For this reason, reorganization energy of aromatic diamine derivatives, N,N′-diphenyl-N,N′-bis(3-methylphenyl)- (1,1′-biphenyl)-4,4′-diamine (TPD) and 4,4′-diphenyl-N,N,N′,N′-tetraphenylbenzidine (DTPB) have been studied theoretically by self-exchange electron transfer theory. By executing the Gaussian 03 calculation we can easily figure out the optimization point which needed for calculation of the inner reorganization energy (λ) of self-exchange electron transfer reaction. Also ionization potential and electron affinities of these molecules can be calculated at the density functional theory level with basis set 6-31G** and 6-31G* using Gaussian 03 software on the basis of ab initio method. It gives possibility to develop a semi-empirical model for the observed absorption and photoluminescence spectrum.

Medium Effects on the Nucleation and Growth Mechanisms during the Redox Switching Dynamics of Conducting Polymers: Case of Poly(3,4-ethylenedioxythiophene)

The redox switching dynamics of poly(3,4-ethylenedioxythiophene) (PEDOT) in an acetonitrile solution and a room temperature ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EmiTFSI), are investigated by means of potential step experiments. Redox switching can be viewed as a phase transition in which the nucleation and growth processes occur. We have developed a phenomenological model allowing the determination of the kinetic parameters. Two limiting cases are shown as follows: (i) a progressive and (ii) an instantaneous nucleation. In all cases, the growth process is described in terms of a self-exchange electron transfer reaction. We show that the mechanisms depend upon the medium. In acetonitrile, progressive nucleation and growth occur during oxidation (p-doping), whereas nucleation is instantaneous in the reduction of the PEDOT film. On the other hand, instantaneous nucleation and growth mechanisms are observed for both oxidation and reduction in EmiTFSI. The difference in the mechanisms results from the ionic exchange process associated with electron transfer and the initial structure of the film (open or compact). The influence of the applied potential on the dynamics is analyzed for both media.

Molecular factor analysis in self-exchange electron transfer reactions in solution

We present a systematic method to access molecular factors and rate constants for self-exchange electron transfer reactions in solution using partial least squares and a number of chosen descriptors. In this work it is shown that the log response for the set of reactions considered can be mostly described in terms of the Intersecting State Model (ISM) when the nonadiabaticity of transfers involving electrons in σ*-orbitals is considered.

Nonequilibrium solvation energy by means of constrained equilibrium thermodynamics and its application to self-exchange electron transfer reactions

This work presents a self-consistent thermodynamic approach to nonequilibrium solvation energy. By imposing an extra electric field onto the nonequilibrium solvation system, a constrained equilibrium state is prepared. New expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. The numerical algorithm combining the new formulation with the dielectric polarizable continuum model has been implemented. As an application, self-exchange electron transfer (ET) reactions between tetramethylhydrazine, tetraethylhydrazine, and tetrapropylhydrazine and their corresponding radical cations have been investigated. The inner and solvent reorganization energies are calculated by the "four-point" method and the new method for nonequilibrium solvation, respectively. Besides, we also calculated the electronic coupling matrix. The rate constants for the three self-exchange ET reactions correlate well with experimental results. We have shown that the inner reorganization energies of these self-exchange ET are not very sensitive to compound size while the compound size has some effect on the solvent reorganization energy in acetonitrile. The new method for nonequilibrium solvation energy based on continuum model provides a reasonable result for the solvent reorganization energy.

Three-Coordinate Copper(I) Amido and Aminyl Radical Complexes

A three-coordinate Cu-NR(2) system (R = p-tolyl) supported by the anionic bis(phosphino)borate ligand [Ph(2)B(CH(2)P(t)Bu(2))(2)](-) has been isolated and structurally characterized in both its anionic Cu(I) and neutral (formally) Cu(II) oxidation states. A large rate constant for the self-exchange electron-transfer reaction (k(S) >or= 10(7) M(-1) s(-1)) makes this system a functional model for the type-1 active sites in blue copper proteins. Multiedge X-ray absorption spectroscopy, multifrequency electron paramagnetic resonance, and density functional theory analyses collectively indicate that the oxidized form is best regarded as a Cu(I)-aminyl radical complex rather than a Cu(II)-amido species, with about 70% localization of the unpaired electron on the NR(2) unit. Hydrogen-atom transfer and C-C coupling reactions are presented as examples of chemical reactivity manifested by this unusual electronic structure.

Homogeneous versus Heterogeneous Self-Exchange Electron Transfer Reactions of Metal Complexes: Insights from Pressure Effects

Homogeneous versus Heterogeneous Self-Exchange Electron Transfer Reactions of Metal Complexes: Insights from Pressure Effects

Aspects of Aqueous Iron and Manganese (II/III) Self-Exchange Electron Transfer Reactions

Ab initio methods were applied to the calculation of the reorganization energy λ and the electronic coupling matrix element VAB for the outer-sphere Fe(OH2)6II/III and Mn(OH2)6II/III self-exchange electron transfer (ET) reactions. For the Fe case, we find an appreciable effect on VAB depending on whether the minority spin electron occupies the dxy orbital or a mixture of dxz/dyz orbitals in the FeII ion. While these two possible nearly isoenergetic electron accepting states alter the magnitude and distance dependence of VAB, they do not affect the internal reorganization energy λI to any significant level. The magnitude and distance dependence of VAB are found to be strongly dependent on encounter orientation, as expected. VAB values for corner-to-corner encounter orientations are substantially larger at any given ET distance considered than those for face-to-face encounter orientations. Values of the decay parameter β are in good agreement with well-accepted values. The adiabaticity criterion is tied to orientation and distance dependence of VAB.

Fast self-exchange electron transfer and delocalization of unpaired electron between zinc porphyrin radical cations and zinc porphyrins

Self-exchange electron transfer rates between π-radical cations of zinc porphyrins and the neutral metalloporphyrins have been determined from the line-width broadening in the ESR spectra in different solvents at various temperatures. Fine tuning of the substituent on the porphyrin ring and the proper choice of the solvent have enabled us to observe negative activation enthalpies for the self-exchange electron transfer reactions. The observation of negative activation enthalpies indicates that the self-exchange electron transfer occurs via the charge-transfer π-complexes formed between zinc porphyrin radical cations and the neutral zinc porphyrins. The complete delocalization of the unpaired electron over two porphyrin moieties is observed in the radical cation of a zinc porphyrin dimer, 5,5'-bis(10,20-bis(3,5-di-tert-butylphenyl)porphyrinatozinc(II)). This is regarded as the extreme limit of the rapid self-exchange electron transfer between zinc porphyrin radical cation and the neutral form.

Internal Reorganization Energy Contributed by Torsional Motion in Electron Transfer Reaction between Biphenyl and Biphenyl Anion Radical

AbstractConcerning the theoretical estimation of internal reorganization energy contributed by the tortional motion between biphenyl and biphenyl anion radical, direct calculation of self‐exchange electron transfer reaction was investigated. With the introduction of a proper average bond length and angle parameters (bond Bp), a multiple step relaxation Nelson method was developed to deal with the torsional reorganization energy. Based on the above model, an estimation of pure torsional reorganization energy λt.p with an approximation of λt.1 was achieved. The results of 0.140 and 0.125 eV of torsional reorganization energy for a cross‐reaction at the levels of 4‐31G and HP/DZP, respectively, are in good agreement with the value of 0.13 eV obtained by Miller et al. from the rate measurements. This implies the efficiency and validity of our method to estimate the reorganization energy contributed by pure torsional motion of Bp.

AM1 andab initio studies on the internal reorganization energy of self-exchange electron transfer reactions of several quinone derivatives

The semiempirical AM1 method, ab initio (HF/3-21G, 6-31G, 6-31G(d), 6-31+G(d)) and DFT (B3LYP/6-31G(d), 6-31+G(d)) methods were used to optimize the geometry of DDQ and its anion radical ⋯ ⋯ Nelsen’s model was used to calculate the internal reorganization energy λi of self-exchange electron transfer (ET) reactions. The calculated λi results of DDQ/DDQ⊸ by AM1 and B3LYP/ 6-31G(d), 6-31+G(d) methods are close to each other and consistent with the reported values; while those from Hartree-Fock methods are too large because of not considering the effect of electron correlation. The structure and ET behavior of MQ0/MQ 0 ⊸ couple were studied by AM1 and DFT (B3LYP/6-31G(d), 6-31+ G(d, p)) methods, and those of MQ0/MQ n ⊸ (n = 1–7) were studied by AM1 method for the first time. The results indicate that the values of the heat of formation of MQn increases with the increasing of the length of the isoamylene substituent chains. It also shows that the length of substituent has little effect on the bond lengths, bond angles of ring A, ring B and the dihedral angles of ring B, but it has considerable effect on the dihedral angles between the plane of ring A and oxygen atoms. The calculated λi results of MQ0/MQ 0 ⊸ and MQn/MQ n ⊸ (n = 1–7) indicate that not only the changes of high frequency vibrations, corresponding to the changes of bond lengths and bond angles, contribute to λi of MQn/MQ n ⊸ (n = 1–7), but also do those of the low frequency vibrations, corresponding to the changes of dihedral angles of MQn and MQ n ⊸ . The contribution from the change of low frequency vibrations between the plane of ring A and oxygen atoms to the λi values of MQn/MQ n ⊸ (n = 1–7) is greater than 1.60 kJ/mol; din addition, the contribution from the changes of the low frequency vibrations of the isoamylene substituent to the λi values of MQ4/MQ 4 ⊸ and MQ6/MQ 6 ⊸ is about 2 kJ/mol.

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.

Theoretical study of self-exchange electron-transfer reactions for the M(H2O) (M = V, Cr, Mn, and Fe) systems

Theoretical study of self-exchange electron-transfer reactions for the M(H2O) (M = V, Cr, Mn, and Fe) systems

Direct evaluation of the electron transfer integral for self-exchange reactions in solution

This paper presents several new theoretical schemes for experimentally determining the electronic coupling matrix element of the self-exchange electron transfer reactions between hydrated redox ion pairs in solution by using the experimental electron transfer rate data. The activation energies are determined by using a new hydration potential function model proposed here in which the potential energy surfaces are obtained by fitting the relevant thermodynamic data with an analytical function. The results have shown that the accurate and approximate schemes in the limit of weak electronic coupling are very valid in determining the electron transfer coupling matrix element of the self-exchange reactions in solution. Although inclusion of the Newton approximation may slightly decrease the values of the coupling matrix element, they are still in good agreement with those from the accurate method and the other theoretical methods. The implication that the value of the coupling matrix element is small for this system (<100 cm −1) is that the electron transfer reactions between the hydrated ion pairs in solution are nonadiabatic in nature.