A modified two-sphere model for solvent reorganization energy in electron transfer

In this work, the solvent reorganization energy is formulated within the framework of classical thermodynamics, by adding some external charges to construct a constrained equilibrium state. The derivation clearly shows that the reorganization energy is exactly the polarization cost for the inertial part of the polarization. We perform our derivation just within the framework of the first law of thermodynamics, and the final form of the reorganization energy is completely the same as that we gave in our recent work by defining a nonequilibrium solvation free energy. With the two-sphere model approximation, our solvent reorganization energy is derived as λ(0) = Δq(2)/2[1/r(D) + 1/r(A) - 2/d][(ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s))]. This amends Marcus' model by a factor of (ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s)), which is coupled with the solvent polarity. Making use of the modified expression of solvent reorganization energy, two recently reported electron transfer processes are investigated in representative solvents. The results show that our formula can well reproduce the experimental observations.     

Probing inhomogeneous vibrational reorganization energy barriers of interfacial electron transfer

An atomic force microscopy (AFM) and confocal Raman microscopy study of the interfacial electron transfer of a dye-sensitization system, i.e., alizarin adsorbed upon TiO(2) nanoparticles, has revealed the distribution of the mode-specific vibrational reorganization energies encompassing different local sites ( approximately 250-nm spatial resolution). Our experimental results suggest inhomogeneous vibrational reorganization energy barriers and different Franck-Condon coupling factors of the interfacial electron transfer. The total vibrational reorganization energy was inhomogeneous from site to site; specifically, mode-specific analyses indicated that energy distributions were inhomogeneous for bridging normal modes and less inhomogeneous or homogeneous for nonbridging normal modes, especially for modes far away from the alizarin-TiO(2) coupling hydroxyl modes. The results demonstrate a significant step forward in characterizing site-specific inhomogeneous interfacial charge-transfer dynamics.     

Marcus theory of outer-sphere heterogeneous electron transfer reactions: dependence of the standard electrochemical rate constant on the hydrodynamic radius from high precision measurements of the oxidation of anthracene and its derivatives in nonaqueous solvents using the high-speed channel electrode

The validity of Marcus theory for outer-sphere heterogeneous electron transfer for the electro-oxidation of a range of anthracene derivatives in alkyl cyanide solvents is investigated. The precision measurement of these fast electron transfers (k(0) >or= 1 cm s(-1)) is achieved by use of the high-speed channel electrode and, where necessary, fast-scan cyclic voltammetry. First, the solvent effect on the rate of electron transfer is studied by considering the first oxidation wave of 9,10-diphenylanthracene in the alkyl cyanide solvents: acetonitrile, propionitrile, butyronitrile, and valeronitrile. Second, the variation of k(0) for a series of substituted anthracenes is investigated by analyzing the voltammetric response of the one-electron oxidations of 9-phenylanthracene, 9,10-dichloroanthracene, 9-chloroanthracene, 9,10-dicyanoanthracene, 9-cyanoanthracene, 9-nitroanthracene, 9,10-diphenylanthracene, and anthracene in acetonitrile. It is shown that the rate of electron transfer of a single compound in different alkyl cyanides is determined by the longitudinal dielectric relaxation properties of the solvent, while differences in rate between the substituted anthracenes in acetonitrile can be quantitatively rationalized by considering their relative hydrodynamic radii. This makes possible the accurate prediction of electron-transfer rates for a molecule by interpolation of rate constants known for related molecules.     

Self-assembly and heterogeneous electron transfer properties of metallo-octacarboxyphthalocyanine complexes on gold electrode

Electrochemical properties of redox-active self-assembled molecular films of novel metallo-octacarboxyphthalocyanine (MOCPc, M = Fe, Co and Mn) complexes integrated with cysteamine (Cys) monolayer on gold electrodes via amide bonds were investigated. X-Ray photoelectron spectroscopy confirmed the appearance of the various elements in their expected chemical environment upon immobilization of these species. The heterogeneous electron transfer properties of the Au-Cys-MOCPc molecular films using an outer-sphere ([Fe(CN)(6)](4-)/[Fe(CN)(6)](3-)) redox probe were studied using cyclic voltammetry and electrochemical impedance spectroscopy. The electron transfer rate constant (k(app)) depends markedly on the central metal of the metallophthalocyanine cores (k(app): Co > Mn > Fe). A strong pH dependence of the electron transport of the Au-Cys-MOCPc molecular films was found. The surface pK(a) values of the MOCPc complexes were essentially the same (ca. 7.5). The differences in the electron transports and ionization constants are discussed. The electrodes are sensitive to the electrooxidation of epinephrine in physiological pH conditions, peak potential (E(p)/V vs. Ag|AgCl, saturated KCl) decreasing as FeOCPc (0.20 V) < MnOCPc (0.26 V) < CoOCPc (0.34 V).     

Optical electron transfer processes. The dependence of intervalence line shape and transition energy on chromophore concentration

Optical electron transfer in the mixed-valence cation of biferrocenylacetylene (BF⁺) has been examined in CD₂Cl₂ solvent. The intervalence absorption line shape is relatively narrow at both low and high chromophore concentrations, but broader at intermediate concentrations. The transition energy for metal-to-metal charge transfer increases from ≈4440 cm⁻¹ at infinite dilution to 5995 cm⁻¹ for 3.8 mM BF⁺. Related effects exist due to added electrolyte. Neither the electrolyte nor chromophore concentration effects are expected from a simple reading of electron transfer theories. Nevertheless, both phenomena can be understood and within the context of theory upon careful consideration of the effects of ion-pairing (and tripling) equilibria upon electron-transfer energetics.     

Determination of heterogeneous electron transfer rate constants at microfabricated iridium electrodes

There has been an increasing use of both solid metal and microfabricated iridium electrodes as substrates for various types of electroanalysis. However, investigations to determine heterogeneous electron transfer rate constants on iridium, especially at an electron beam evaporated or dc magnetron sputtered surface, have not previously been performed. This paper compares the results of these microfabricated surfaces using ultramicroelectrode arrays and steady-state currents. Even though the dc magnetron sputtered iridium surface demonstrated a slightly more reversible electrochemical behavior than the electron beam evaporated surface, overall the microfabricated microelectrodes and ring electrode indicated similar reversibility to the polished metallic iridium disk electrode.     

Proton-coupled electron transfer from tyrosine: a strong rate dependence on intramolecular proton transfer distance

Proton-coupled electron transfer (PCET) was examined in a series of biomimetic, covalently linked Ru(II)(bpy)(3)-tyrosine complexes where the phenolic proton was H-bonded to an internal base (a benzimidazyl or pyridyl group). Photooxidation in laser flash/quench experiments generated the Ru(III) species, which triggered long-range electron transfer from the tyrosine group concerted with short-range proton transfer to the base. The results give an experimental demonstration of the strong dependence of the rate constant and kinetic isotope effect for this intramolecular PCET reaction on the effective proton transfer distance, as reflected by the experimentally determined proton donor-acceptor distance.     

Subphthalocyanines: tuneable molecular scaffolds for intramolecular electron and energy transfer processes

A series of four subphthalocyanine-C(60) fullerene dyads have been prepared through axial functionalization of the macrocycle with m-hydroxybenzaldehyde and a subsequent dipolar cycloaddition reaction. The subphthalocyanine moiety has been peripherally functionalized with substituents of different electronic character, namely fluorine or iodine atoms and ether or amino groups, thus reaching a control over its electron-donating properties. This is evidenced in cyclic voltammetry experiments by a progressive shift to lower potentials, by ca. 200 mV, of the first oxidation event of the SubPc unit in the dyads. As a consequence, the energy level of the SubPc(*)(+)-C(60)(*)(-) charge-transfer state may be tuned so as to compete with energy transfer deactivation pathways upon selective excitation of the SubPc component. For instance, excitation of those systems where the level of the radical pair lies high in energy triggers a sequence of exergonic photophysical events that comprise (i) nearly quantitative singlet-singlet energy transfer to the C(60) moiety, (ii) fullerene intersystem crossing, and (iii) triplet-triplet energy transfer back to the SubPc. On the contrary, the stabilization of the SubPc(*)(+)-C(60)(*)(-) radical pair state by increasing the polarity of the medium or by lowering the donor-acceptor redox gap causes charge transfer to dominate. In the case of 1c in benzonitrile, the thus formed radical pair has a lifetime of 0.65 ns and decays via the energetically lower lying triplet excited state. Further stabilization is achieved for dyad 1d, whose charge-transfer state would lie now below both triplets. The radical pair lifetime consequently increases in more than 2 orders of magnitude with respect to 1c and presents a significant stabilization in less polar solvents, revealing a low reorganization energy for this kind of SubPc-C(60) systems.     

Method for the evaluation of the reorganization energy of electron transfer reactions produced under restricted geometry conditions

The kinetics of the electron transfer reactions between S(2)O(8)(2-) and the complexes (Ru(NH(3))(5)L)(2+) (L = pyridine, pyrazine, and 4-cyanopyridine) have been studied in micellar (SDS) solutions. A method for the evaluation of the reorganization energy of these reactions, based on the comparison of their rate constants, is proposed. From the results obtained, we concluded that the observed rate constants go through a minimum for the surfactant concentration in which the reorganization energy goes through a maximum. The method can be applied to any kind of restricted geometry conditions.     

Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.     

Ab initio calculation for inner reorganization energy of gas-phase electron transfer in organic molecule–ion systems

A series of electron transfer (ET) reactions between some organic molecules have been investigated through ab initio calculations. Biphenyl (Bp) and 9,9^′-dimethylfluorene anion radicals are chosen as the donor, whereas several organic molecules with different redox abilities are chosen as the acceptor. The inner reorganization energy and the endothermicity of the ET reactions in those molecule–ion systems have been estimated through the HFSCF and complete active space multiconfiguration SCF calculations. Double-well potentials for the gas-phase ET reactions have been constructed using the linear reaction coordinate, and the results show that the quinone-containing ET reactions are in Marcus' inverted region. It has been found that the inner reorganization energies are different for various donor-acceptor couples, unlike the experimentally fitted ones. The contribution from the inter-ring torsional motion in Bp to the inner reorganization energy has been evaluated from the energy difference of the biphenyl-acceptor and the dimethylfluorine-acceptor systems. Comparisons with the experimentally observed results have been made.     

Continuous medium theory for nonequilibrium solvation: IV. Solvent reorganization energy of electron transfer based on conductor-like screening model

In this work the authors present some evidences of defects in the popular continuous medium theories for nonequilibrium solvation. Particular attention has been paid to the incorrect reversible work approach. After convincing reasoning, the nonequilibrium free energy has been formulated to an expression different from the traditional ones. In a series of recent works by the authors, new formulations and some analytical application models for ultrafast processes were developed. Here, the authors extend the new theory to the cases of discrete bound charge distributions and present the correct form of the nonequilibrium solvation energy in such cases. A numerical solution method is applied to the evaluation of solvent reorganization energy of electron transfer. The test calculation for biphenyl-cyclohexane-naphthalene anion system achieves excellent agreement with the experimental fitting. The central importance presented in this work is the very simple and a consistent form of nonequilibrium free energy for both continuous and discrete charge distributions, based on which the new models can be established.     

Photochemistry of 1,3-cyclopentanediones. Oxetane formation involving both energy transfer and electron transfer processes

Photolysis of 2,2-dimethyl-1,3-cyclopentanedione in acetone resulted in oxetane formation in a two photon process involving energy transfer from triplet excited acetone and electron transfer from singlet excited acetone.