Drastic difference in lifetimes of the charge-separated state of the formanilide-anthraquinone dyad versus the ferrocene-formanilide-anthraquinone triad and their photoelectrochemical properties of the composite films with fullerene clusters

A long-lived charge-separated (CS) state, which can be observed even at 900 mus after laser excitation, has been attained in the formanilide-anthraquinone dyad (FA-AQ) in dimethyl sulfoxide, whereas the CS lifetime is shortened significantly to 20 ps in the ferrocene-formanilide-anthraquinone triad (Fc-FA-AQ). Such a drastic decrease in the CS lifetime by the addition of a ferrocene moiety to the FA-AQ dyad is ascribed to a decrease in the driving force of back electron transfer and an increase in the reorganization energy of electron transfer despite the longer charge-separation distance. The FA-AQ dyad and the Fc-FA-AQ triad have been employed as components of photovoltaic cells, where composite molecular nanoclusters of the FA-AQ dyad or the Fc-FA-AQ triad with fullerene (C60) are assembled onto a SnO2 electrode using an electrophoretic method. The composite films of the Fc-FA-AQ triad exhibit 10 times smaller values of an incident photon-to-photocurrent efficiency (IPCE) as compared with those of the FA-AQ dyad in accordance with a drastic decrease of the CS lifetime by addition of a ferrocene moiety to the FA-AQ dyad.     

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 B2g 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(-1) s(-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.     

Marcus电子转移理论的科学性探讨

利用科学原理对Marcus电子转移理论的科学性进行了考察, 结果表明Marcus电子转移理论违背了能量守恒定律.     

Complete basis set, Gaussian, and hybrid density functional theory evaluation of the proton affinities of water and ammonia

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.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Measurement of the free-energy dependence of interfacial charge-transfer rate constants using ZnO/H2O semiconductor/liquid contacts

The dependence of electron-transfer rate constants on the driving force for interfacial charge transfer has been investigated using n-type ZnO electrodes in aqueous solutions. Differential capacitance versus potential and current density versus potential measurements were used to determine the energetics and kinetics, respectively, of the interfacial electron-transfer processes. A series of nonadsorbing, one-electron, outer-sphere redox couples with formal reduction potentials that spanned approximately 900 mV allowed evaluation of both the normal and Marcus inverted regions of interfacial electron-transfer processes. All rate processes were observed to be kinetically first-order in the concentration of surface electrons and first-order in the concentration of dissolved redox acceptors. The band-edge positions of the ZnO were essentially independent of the Nernstian potential of the solution over the range 0.106-1.001 V vs SCE. The rate constant at optimal exoergicity was observed to be approximately 10(-)(16) cm(4) s(-)(1). The rate constant versus driving force dependence at n-type ZnO electrodes exhibited both normal and inverted regions, and the data were well-fit by a parabola generated using classical Marcus theory with a reorganization energy of 0.67 eV. NMR line broadening measurements of the self-exchange rate constants indicated that the redox couples had reorganization energies of 0.64-0.69 eV. The agreement between the reorganization energy of the ions in solution and the reorganization energy for the interfacial electron-transfer processes indicated that the reorganization energy was dominated by the redox species in the electrolyte, as expected from an application of Marcus theory to semiconductor electrodes.     

Scaling for Experimental Inner-Sphere Reorganization Energy of Hydrated Ions via Accurate Potential Function

Reported here are several new calculation methods for the inner-sphere reorganization energy of hydrated metal ions involved in electron transfer processes.It is based on the self-exchange model of reorganization and utilizes the more exact potential functions between central metal ion and the inner-sphere ligands.The parameters involved are determined via the spectroscopic and thermodynamic data.The predictions of the inner-sphere reorganization energies from those models agree well with the photoemission experimental results.     

Theoretical study on charge carrier mobilities of tetrathiafulvalene derivatives

We calculated the hole and electron mobilities of tetrathiafulvalene (TTF) derivative crystals using first-principles calculations and the Marcus theory of electron transfer. The hole and electron reorganization energies were found to decrease with the extension of π-conjugated orbitals. The calculated hole mobilities of TTF, dibenzo-tetrathiafulvalene (DB-TTF), and dinaphtho-tetrathiafulvalene (DN-TTF) agree well with the experimental results. In addition, with the increase of the number of benzene rings attached to the TTF skeleton, the hole mobilities decrease and the electron mobilities increase. The calculated electron mobility of dianthro-tetrathiafulvalene (DA-TTF) based on a virtual crystal structure is much larger than the hole one due to the small electron reorganization energy and large electron coupling. This suggests that the charge transfer properties of the TTF derivatives can be modified when the number of aromatic rings on TTF skeleton increases.     

An inner-sphere reorganization model of hetero-exchange electron transfer reaction of diatomic reactants

An accurate theoretical scheme for obtaining directly the inner-sphere reorganization energies of the hetero-exchange electron transfer reactions from ionization potentials and electron affinities is first reported in this paper. Ionization potentials and electron affinities are alternatively obtained from the Rydberg spectroscopic data via a numerical procedure for some diatomic molecules. The inner-sphere reorganization energy values are calculated for the hetero-exchange electron transfer reactions (AB + CD⁺ → AB⁺ + CD) of diatomic molecules and are compared with those from other approximate methods.     

Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

This work presents a thermodynamic method for treating nonequilibrium solvation. By imposing an extra electric field onto the nonequilibrium solvation system, a virtual constrained equilibrium state is prepared. In this way, the free energy difference between the real nonequilibrium state and the con-strained equilibrium one is simply the potential energy of the nonequilibrium polarization in the extra electronic field, according to thermodynamics. Further, new expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. Analysis shows that the present formulations will give a value of reorganization energy about one half of the traditional Marcus theory in polar solvents, thus the explanation on why the traditional theory tends to overestimate this quantity has been found out. For the purpose of numerical determination of solvent reorganization energy, we have modified Gamess program on the basis of dielectric polarizable continuum model. Applying the procedure to the well-investigated intramolecular electron transfer in biphenyl-androstane-naphthyl and biphenyl-androstane-phenanthryl systems, the numerical results of solvent reorganization energy have been found to be in good agreement with the experimental fittings.     

Effect of energy disorder in interfacial kinetics of dye-sensitized solar cells with organic hole transport material

We describe the kinetic rates for dye regeneration in dye-sensitized solar cells with organic solid hole conductors, taking as a reference the experimental results of Haque et al. (ChemPhysChem 2003, 4, 89). Our model is based on Marcus rates for electron and hole transfer, emphasizing the Gaussian spread of energy levels in the molecular materials involved. We show that the energy disorder implies a broadening of the efficiency of hole transfer with respect to the thermodynamic driving force, as observed experimentally. The model also shows that tunning of the kinetic processes for high efficiency of energy conversion of the solar cell depends critically on the interplay between the reorganization energy and the broadening parameters of the energy distributions.     

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.     

Molecular dynamics investigation of ferrous-ferric electron transfer in a hydrolyzing aqueous solution: calculation of the pH dependence of the diabatic transfer barrier and the potential of mean force

We present a molecular model for ferrous-ferric electron transfer in an aqueous solution that accounts for electronic polarizability and exhibits spontaneous cation hydrolysis. An extended Lagrangian technique is introduced for carrying out calculations of electron-transfer barriers in polarizable systems. The model predicts that the diabatic barrier to electron transfer increases with increasing pH, due to stabilization of the Fe3+ by fluctuations in the number of hydroxide ions in its first coordination sphere, in much the same way as the barrier would increase with increasing dielectric constant in the Marcus theory. We have also calculated the effect of pH on the potential of mean force between two hydrolyzing ions in aqueous solution. As expected, increasing pH reduces the potential of mean force between the ferrous and ferric ions in the model system. The magnitudes of the predicted increase in diabatic transfer barrier and the predicted decrease in the potential of mean force nearly cancel each other at the canonical transfer distance of 0.55 nm. Even though hydrolysis is allowed in our calculations, the distribution of reorganization energies has only one maximum and is Gaussian to an excellent approximation, giving a harmonic free energy surface in the reorganization energy F(DeltaE) with a single minimum. There is thus a surprising amount of overlap in electron-transfer reorganization energies for Fe(2+)-Fe(H2O)6(3+), Fe(2+)-Fe(OH)(H2O)5(2+), and Fe(2+)-Fe(OH)2(H2O)+ couples, indicating that fluctuations in hydrolysis state can be viewed on a continuum with other solvent contributions to the reorganization energy. There appears to be little justification for thinking of the transfer rate as arising from the contributions of different hydrolysis states. Electronic structure calculations indicate that Fe(H2O)6(2+)-Fe(OH)n(H2O)(6-n)(3-n)+ complexes interacting through H3O2- bridges do not have large electronic couplings.     

Adiabatic and non-adiabatic concerted proton-electron transfers. Temperature effects in the oxidation of intramolecularly hydrogen-bonded phenols

The one-electron electrochemical and homogeneous oxidations of two closely similar aminophenols that undergo a concerted proton-electron transfer reaction, in which the phenolic proton is transferred to the nitrogen atom in concert with electron transfer, are taken as examples to test procedures that allow the separate determination of the degree of adiabaticity and the reorganization energy of the reaction. The Marcus (or Marcus-Hush-Levich) formalism is applicable in both cases, but not necessarily in its adiabatic version. Linearization of the activation-driving force laws simplifies the treatment of the kinetic data, notably allowing the use of Arrhenius plots to treat the temperature dependence of the rate constant. A correct estimation of the adiabaticity and reorganization energy requires the determination of the variation of the driving force with temperature. Application of these procedures led to the conclusion that, unlike previous reports, the homogeneous reaction is non-adiabatic, with a transmission coefficient of the order of 0.005, and that the self-exchange reorganization energy is about 1 eV lower than previously estimated. With such systems, the intramolecular reorganization energy, although sizable, is in fact rather modest, being only slightly larger than that for the outer-sphere electron transfer that produced the cation radical. The electrochemical reaction is, in contrast, adiabatic, as revealed by the temperature dependence of its standard rate constant obtained from cyclic voltammetric experiments. This difference in behavior is deemed to derive from the effect of the strong electric field within which the electrochemical reaction takes place, stabilizing a zwitterionic form of the reactant (in which the proton has been transferred from oxygen to nitrogen). Taking this difference in adiabaticity into account, the magnitudes of the reorganization energies of the two reactions appear to be quite compatible with one another, as revealed by an analysis of the solvent and intramolecular contributions in both cases.     

Breakdown of the Born–Oppenheimer–Condon–Marcus approximation in long distance electron transfer

We consider the issue of how the breakdown of the Born–Oppenheimer–Condon–Marcus approximation affects the dependence of the electron-transfer rate k upon distance, as well as the dependences upon the driving force and temperature. For large distances, ca. r>10 Å, it is predicted that: (i) the slope of lnk vs r dependence decreases down to zero; (ii) the bell-shaped Marcus dependence upon the driving force is distorted, with the maximum shifting toward ΔG>0; and (iii) the apparent activation energy increases and the temperature dependence more and more declines from the Arrhenius form. These effects can be experimentally distinguished from similar effects due to other mechanisms, such as thermal activation of the electron transferred and temperature dependence of the reorganization parameters and driving force. Experimental data by Isied et al. [J. Phys. Chem. 97 (1993) 11456] on electron transfer between metal ions across rigid oligoproline bridges are well fitted using the present theory.     

Intermolecular and intracomplex photoinduced electron transfer from planar and nonplanar metalloporphyrins to p-quinones

The rate constants of intermolecular photoinduced electron transfer from triplet excited states of metalloporphyrins to a series of p-benzoquinone derivatives in benzonitrile were determined to examine the effects of the driving force, the metal, and the conformational distortion of the porphyrin ring on the reorganization energies (λ) of electron transfer by laser flash photolysis. The λ values were evaluated from the determined rate constants on the basis of the Marcus theory of electron transfer. The λ values of planar metalloporphyrins, [Al(TPP)(PhCOO)] and [Zn(TPP)] (TPP(2-)=tetraphenylporphyrin dianion), are approximately the same, but they are 0.27 eV smaller than those of the corresponding nonplanar (saddle-distorted) metalloporphyrins [Al(DPP)(PhCOO)] and [Zn(DPP)] (DPP(2-)=dodecaphenylporphyrin dianion) when they are compared for the same driving force of photoinduced electron transfer. The axial ligand PhCOO(-) of [Al(TPP)](+) and [Al(DPP)](+) was replaced by anthraquinone-2-carboxylate (AqCOO(-)) to afford the electron donor-acceptor complexes [Al(TPP)(AqCOO)] and [Al(DPP)(AqCOO)], respectively. The X-ray crystal structure of [Al(TPP)(AqCOO)] revealed strong coordination of AqCOO(-) to the Al(3+) ion of [Al(TPP)](+) and the existence of π-π interactions between AqCOO(-) and the porphyrin ring. In the case of the saddle-distorted [Al(DPP)(AqCOO)], however, the AqCOO(-) moiety is nearly perpendicular to the porphyrin ring. The photodynamics of intracomplex photoinduced electron transfer from the singlet excited state of [Al(TPP)](+) and [Al(DPP)](+) to the AqCOO(-) moiety were also examined in comparison with the intermolecular photoinduced electron-transfer reactions, and the determined rate constants were evaluated in light of the Marcus theory of electron transfer to reveal that the electron transfer is adiabatic in each case.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Theoretical insights into the 1D‐charge transport properties in a series of hexaazatrinaphthylene‐based discotic molecules

Discotic liquid crystal (DLC) materials have attracted considerable attention mainly due to their high charge carrier mobilities in quasi‐one‐dimensional columns. In this article, five hexaazatrinaphthylene‐based DLC molecules were investigated theoretically, and their frontier molecular orbital energy levels, crystal structures, and electron/hole drift mobilities were calculated by combination of density functional theory (DFT) and semiclassical Marcus charge transfer theory. The systems studied in this work include three experimentally reported molecules ( 1 , 2 , and 3 ) and two theoretically designed molecules ( 4 and 5 ). Compared with the 1 – 3 compounds, 4 and 5 have three more extended benzene rings in the π‐conjugated core. The present results show that the orders of the frontier molecular orbital energy levels and electron drift mobilities agree very well with the experiment. For 4 and 5 , the electron/hole reorganization energies are lower than those of compounds 1 – 3 . Furthermore, the calculated electron/hole transfer integral of 5 is the largest among all the five systems, leading to the highest electron and hole mobilities. In addition, the hydrophobicity and solubility were also evaluated by DFT, indicating that compound 5 has good hydrophobicity and good solubility in trichloromethane. As a result, it is expected that compound 5 can be a potential charge transport material in electronic and optoelectronic devices. © 2017 Wiley Periodicals, Inc.