Anomalous reorganization free energies in optical electron transfer in solution

Autoionization bands are observed in the photoelectron emission spectroscopy of aqueous solutions of cyanometalate complexes (Mn, Fe, W, Mo), anions (NO₃, CIO⁻₄ and cations (Ag⁺ TI⁺. Reorganization free energies for autoionization bands are anomalously low in absolute value (by≈1 eV) in comparison with direct transitions to the continuum. Interpretation is based on potential energy profiles and model calculations for the reorganization free energy.     

Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.     

Correlation between thermal electron transfer in solution and photoelectron emission

The activation free energy for electron transfer in solution or at electrodes is correlated to the corresponding Franck—Condon determined reorganization free energy R_m for photoelectron emission. Excellent to fair agreement is obtained between the activation free energies predicted from R_m and experimental values. Data are given for V²⁺, Cr²⁺, Mn²⁺, Fe²⁺, Co²⁺, and Fe(CN)^4?₆ in aqueous solution.     

Dielectric dispersion of oriented polymers

Summary Expressions have been derived for the tensor of the complex dielectric permitivity of an oriented polymer containing polar groups in the main chain. The relevant intramolecular and intermolecular interactions have been assumed to be independent of the degree of orientation; the anisotropy of dielectric permitivity is expected to be given only by the orientation of local equilibrium positions of the dipoles. For the low-temperature dispersion of a polymer oriented by cold-drawing, both the spectra of relaxation times and the magnitudes of the components of the dielelectric permitivity tensor have been calculated. Relation between the calculated values and the dipole-dipole interaction parameters, diffusion coefficients and average dipole-chain angle are given.

---

Zusammenfassung Es wurden Ausdrücke für den komplexen Tensor der Dielektrizitätskonstantante an orientierten Polymeren, die polare Gruppen in der Hauptkette enthalten, abgeleitet. Die maßgebenden intra- und intermolekularen Wechselwirkungen wurden als unabhängig vom Orientierungsgrad angenommen; die Anisotropie der Dielektrizitätskonstante dürfte nur durch die Orientierung lokaler Gleichgewichtspositionen der Dipole gegeben sein. Für die Tieftemperaturdispersion eines kalt verstreckten Polymeren wurden das Spektrum der Relaxationszeiten und die Relaxationsstärken des Tensors berechnet. Beziehungen zwischen berechneten Werten und den Dipol-Dipol-Wechselwirkungsparametern, Diffusionskoeffizienten und den mittleren Winkel zwischen Dipol und Kette sind angegeben.

---

---

With 5 figures     

Determination of the electron transfer parameters of a covalently linked porphyrin-quinone with mesogenic substituents - optical spectroscopic studies in solution

The photoinduced electron transfer (PET) of a covalently linked porphyrin-quinone with mesogenic substituents was studied using visible and near-IR (NIR) spectroscopy. Mesogenic substituents were introduced at the porphyrin moiety in order to mimic the anisotropic membrane properties of the native reaction centre of photosynthesis. Photophysical characterization of this system in homogeneous solution is a prerequisite for a better understanding of the effects occurring in anisotropic medium. For this reason, we studied the fluorescence and phosphorescence quenching and lifetime of the charge-separated state. Time-resolved fluorescence measurements indicated an effective singlet PET. The complete set of PET parameters was calculated using Marcus theory of non-adiabatic electron transfer (ET). Steady state measurement of singlet oxygen luminescence, which allows indirect access to phosphorescence quenching, indicated that no triplet PET was involved in the decay processes. Using transient absorption spectroscopy, the lifetime of the charge-separated state was found to be 1.9 ns.     

Solvent motion controls the rate of intramolecular electron transfer in solution

The fluorescence decay times (τ-_F) for conversion (by intramolecular electron transfer) of the S_1,np state into the S_1,ct state of 6-(4-methylphenyl) amino-2-naphthalenesulfon-N,N-dimethylamide (TNSDMA) correlate well with the constant-charge dielectric relaxation times [τ₁^v = (ε₀₀/ε_s) τ₁] in linear alcohols. Solvent motion thus controls certain intramolecular electron transfers.     

Cation-independent electron transfer between ferricyanide and ferrocyanide ions in aqueous solution

Electron transfer between Fe(CN)(6)(3-) and Fe(CN)(6)(4-) in homogeneous aqueous solution with K(+) as the counterion normally proceeds almost exclusively by a K(+)-catalyzed pathway, but this can be suppressed, and the direct Fe(CN)(6)(3)(-)-Fe(CN)(6)(4-) electron transfer path exposed, by complexing the K(+) with crypt-2.2.2 or 18-crown-6. Fe((13)CN)(6)(4-)-NMR line broadening measurements using either crypt-2.2.2 or (with extrapolation to zero uncomplexed [K(+)]) 18-crown-6 gave consistent values for the rate constant and activation volume (k(0) = (2.4 +/- 0.1) x 10(2) L mol(-1) s(-1) and Delta V(0) = -11.3 +/- 0.3 cm(3) mol(-1), respectively, at 25 degrees C and ionic strength I = 0.2 mol L(-1)) for the uncatalyzed electron transfer path. These values conform well to predictions based on Marcus theory. When [K(+)] was controlled with 18-crown-6, the observed rate constant k(ex) was a linear function of uncomplexed [K(+)], giving k(K) = (4.3 +/- 0.1) x 10(4) L(2) mol(-2) s(-1) at 25 degrees C and I = 0.26 mol L(-1) for the K(+)-catalyzed pathway. When no complexing agent was present, k(ex) was roughly proportional to [K(+)](total), but the corresponding rate constant k(K)' (=k(ex)/[K(+)](total)) was about 60% larger than k(K), evidently because ion pairing by hydrated K(+) lowered the anion-anion repulsions. Ionic strength as such had only a small effect on k(0), k(K), and k(K)'. The rate constants commonly cited in the literature for the Fe(CN)(6)(3-/4-) self-exchange reaction are in fact k(K)'[K(+)](total) values for typical experimental [K(+)](total) levels.     

Resolving electron transfer kinetics at the nanocrystal/solution interface

The kinetics of electron transfer between individual gold nanocrystals and a solution redox species is quantified. The observed rate is dependent on the extent of electronic coupling between nanocrystals in the monolayer indicating the effect of Coulomb blockade on electrochemical kinetics.     

Electron transfer reaction with amide—one electron oxidant system in solution

The kinetics of reduction of Mn(III) by acetamide, formamide (F), N-methylformamide (NMF), and N,N-dimethylformamide (DMF) have been measured spectrophotometrically at 50°C in aqueous acid perchlorate media. Four moles of Mn(III) are consumed for formamides and two moles of Mn(III) are consumed per mole of acetamide, leading in each case to the formation of the respective amines. All rates were first order in each reactant and were independent of [Mn²⁺] and [NaClO₄]. The reciprocals of observed rate constants are inversely dependent on acidity. A free radical mechanism consistent with these results has been proposed for the reactions. Activation energies and entropies are calculated for each reaction.     

Quantum simulation of solution phase intramolecular electron transfer rates in betaine-30

Mixed quantum-classical atomistic simulations have been carried out to investigate the mechanistic details of excited state intramolecular electron transfer in a betaine-30 molecule in acetonitrile. The key electronic degrees of freedom of the solute molecule are treated quantum mechanically using the semiempirical Pariser-Parr-Pople Hamiltonian, including the solvent influence on electronic structure. The intramolecular vibrational modes are also treated explicitly at a quantum level, with the remaining elements treated classically using empirical potentials. The electron-transfer rate, corresponding to S1 --> S0 relaxation, is evaluated via time-dependent perturbation theory with the explicit inclusion of the dynamics of solvation and intramolecular conformation. The calculations reveal that, while solvation dynamics is critical to the rate, the intramolecular torsional dynamics also plays an important role. The importance of the use of multiple high-frequency quantum modes is also discussed.     

Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.     

Kinetics and mechanism of bimolecular electron transfer reaction in quinone-amine systems in micellar solution

Photoinduced electron transfer (ET) reactions between anthraquinone derivatives and aromatic amines have been investigated in sodium dodecyl sulphate (SDS) micellar solutions. Significant static quenching of the quinone fluorescence due to high amine concentration in the micellar phase has been observed in steady-state measurements. The bimolecular rate constants for the dynamic quenching in the present systems k(q) (TR), as estimated from the time-resolved measurements, have been correlated with the free energy changes DeltaG(0) for the ET reactions. Interestingly it is seen that the k(q) (TR) vs DeltaG(0) plot displays an inversion behavior with maximum k(q) (TR) at around 0.7 eV, a trend similar to that predicted in Marcus ET theory. Like the present results, Marcus inversion in the k(q) (TR) values was also observed earlier in coumarin-amine systems in SDS and TX-100 micellar solutions, with maximum k(q) (TR) at around the same exergonicity. These results thus suggest that Marcus inversion in bimolecular ET reaction is a general phenomenon in micellar media. Present observations have been rationalized on the basis of the two-dimensional ET (2DET) theory, which seems to be more suitable for micellar ET reactions than the conventional ET theory. For the quinone-amine systems, it is interestingly seen that k(q) (TR) vs DeltaG(0) plot is somewhat wider in comparison to that of the coumarin-amine systems, even though the maxima in the k(q) (TR) vs DeltaG(0) plots appear at almost similar exergonicity for both the acceptor-donor systems. These observations have been rationalized on the basis of the differences in the reaction windows along the solvation axis, as envisaged within the framework of the 2DET theory, and arise due to the differences in the locations of the quinones and coumarin dyes in the micellar phase.     

Monolayer-based selective optical recognition and quantification of FeCl3 via electron transfer

Reagentless optical recognition and parts-per-million (ppm) quantification of FeCl3 in CH3CN was demonstrated using a redox-active Os(II)-chromophore-based monolayer on glass. The Fe3+-induced oxidation of the monolayer is fully reversible and can be monitored optically with a conventional UV/vis spectrophotometer (260-800 nm). The system can be reset with water within <1 min. Selectivity of the sensor toward FeCl3 is not affected by the presence of representative alkali metals, alkaline earth metals, and other transition-metal salts. Sensing of Fe3+ and concurrent generation of Fe2+ can be also observed with the naked eye by adding 2,2'-bipyridyl (bipy) to the solution to generate [Fe(bipy)3]2+. Validation of the analytical performance characteristics of the sensor was performed including reversibility, reproducibility, stability, and the detection range (0.5-162 ppm of FeCl3 in CH3CN, 100-1000 ppm in water). The monolayer is sensitive and specifically responsive to its target ion. In addition, a blind test was conducted to probe the reproducibility and reproducibility variances of the system. The reaction of the monolayer with a CH3CN solution containing 5 ppm of FeCl3 follows pseudo first-order kinetics in the monolayer with DeltaG298K = 21.6 +/- 0.1 kcal/mol, DeltaH = 10.2 +/- 1.5 kcal/mol, DeltaS = -38.3 +/- 4.9 eu.     

Dielectric dispersion in water + 2-hydroxypyridine solid mixtures

The complex electric permittivity was measured in water + 2-hydroxypyridine (2HP) solid mixtures as a function of concentration, temperature and frequency. Just after freezing of diluted mixtures, (mole fraction of 2HP < 0.2) pronounced dielectric dispersion in the MHz region was observed. The dispersion disappears on cooling between -30 and -40 degrees C in a first-order phase transition. The dispersion was explained in terms of the movement of a guest molecule (2HP) in a clathratelike structure of ice.     

Exact solution of a model of condensed-phase electron transfer with non-Condon effects

Non-Condon effects are important in the analysis of electron transfer in many systems coupled to a condensed-phase environment. We detail a novel condensed-phase electron transfer Hamiltonian that extends the spin-boson model to account for non-Condon effects. We show that the relevant reduced system density matrix dynamics can be calculated exactly for a particular class of bath Hamiltonians and system-bath couplings. An explicit formula for the long-time behavior of these systems is derived. We show that they exhibit non-Boltzmann long-time behavior that is independent of temperature, and depends on the system Hamiltonian and the initial system density matrix.     

Ground vs. excited state electron transfer: adsorbed monolayers and trimers in solution

Transient emission spectroscopy has been used to probe the rate of photoinduced electron transfer between metal centres within a novel trimeric complex [[Os(bpy)2(bpe)2][Os(bpy)2Cl]2]4+, where bpy is 2,2'-bipyridyl and bpe is trans-1,2-bis-(4-pyridyl)ethylene. Transient emission experiments on the trimer, and on [Os(bpy)2 (bpe)2]2+ in which the [Os(bpy)2 Cl]+ quenching moieties are absent, reveal that the rate of photoinduced electron transfer (PET) across the bpe bridge is 1.3 +/- 0.1 x 10(8) s(-1). Investigations into the driving forces for oxidation and reduction of the electronically excited state within the trimer indicate that quenching of the [Os(bpy)2 (bpe)2]2+ centre within the trimer involves electron transfer from the [bpe Os(bpy)2 Cl]+ centres to the electronically excited state with a driving force of -0.3 eV. Monolayers of the complex, [Os(bpy)2 bpe pyridine]2+, have been formed by spontaneous adsorption onto platinum microelectrodes and used to probe the dynamics of electron transfer across the trans-1,2-bis-(4-pyridyl)ethylene bridge in the ground state. These monolayers are stable and exhibit well defined voltammetric responses for the Os2+/3+ redox reaction. Cyclic voltammograms recorded at high scan rates can be accurately modelled according to a non-adiabatic electron transfer model based on the Marcus theory using a standard heterogeneous electron transfer rate constant, k(o), of 3.1 +/- 0.2 x 10(4) s(-1) and a reorganization energy of 0.4 +/- 0.1 eV. This rate constant is a factor of approximately two orders of magnitude smaller than that found for photoinduced electron transfer across the same bpe bridge for identical driving forces. This significant difference is interpreted in terms of both the nature of the orbitals involved in electrochemically and optically driven electron transfer, as well as the strength of electronic coupling between two molecular components as opposed to a molecular component and a metal electrode.