Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

Quantum and non-Markovian effects in the electron transfer reaction dynamics in the Marcus inverted region

Electron transfer reactions in large molecules may often be coupled to both the polar solvent modes and the intramolecular vibrational modes of the molecule. This can give rise to a complex dynamics which may in some systems, like betaine, be controlled more by vibrational rather than by solvent effects. Additionally, a significant contribution from an ultrafast relaxation component in the solvation dynamics may enhance the complexity. To explain the wide range of behavior that has been observed experimentally, Barbara et al. recently proposed that a model of an electron transfer reaction should minimally consist of a low-frequency classical solvent mode (X), a low-frequency vibrational mode (Q), and a high-frequency quantum mode (q) (J. Phys. Chem. 1991, 96, 3728). In the present work, a theoretical study of this model is described. This study generalizes earlier work by including the biphasic solvent response and the dynamics of the low-frequency vibrational mode in the presence of a delocalized, extended reaction zone. A novel Green's function technique has been developed which allowed us to study the non-Markovian dynamics on a multidimensional surface. The contributions from the high-frequency vibrational mode and the ultrafast component in the non-Markovian solvent dynamics are found to be primarily responsible for the dramatic increase in charge transfer rate over the prediction of the classical theories that neglect both these factors. These, along with a large coupling between the reactant and the product states, may combine to render the electron transfer rate both very large and constant over a wide range of solvent relaxation rates. A study on the free energy gap dependence of the electron transfer rate reveals that the rates are sensitive to changes in the quantum frequency particularly when the free energy gap is very large.

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Influence of Solvent on Photoinduced Electron-Transfer Reaction: Time-Resolved Resonance Raman Study

Time-resolved resonance Raman spectroscopy (TR3) has been used to study the effect of solvent polarity on the mechanism and nature of intermediates formed in photoinduced electron-transfer reaction between triplet flouranil ((FL)-F-3) and tetramethylbenzene (TMB). Comparison of the TR3 spectra in polar, nonpolar, and medium polar media suggests that formation of radical anion due to electron-transfer reaction between (FL)-F-3 and TMB is favored in more polar solvents, whereas ketyl radical formation is more favored in less polar media. Compared to ketyl radical, the extent of radical anion formation is negligible in nonpolar solvents. Therefore, it is inferred that in nonpolar media ketyl radical is mainly generated by hydrogen-transfer reaction in the encounter complex between (FL)-F-3 and TMB. In solvents of medium polarity, the ion-pair decay leads to the formation of both ketyl radical and ketyl radical formed from the encounter between triplet state and the donor. Thus, competition between the formation of ketyl radical and ion pair is influenced by the solvent polarity. The nature of the ion pair in different solvent polarity has been investigated from the changes observed in the vibrational frequency of (fluoranil) FL part of the complex.

A direct borohydride fuel cell employing Prussian Blue as mediated electron-transfer hydrogen peroxide reduction catalyst

A direct borohydride-hydrogen peroxide fuel cell employing carbon-supported Prussian Blue (PB) as mediated electron-transfer cathode catalyst is reported. While operating at 30 °C, the direct borohydride-hydrogen peroxide fuel cell employing carbon-supported PB cathode catalyst shows superior performance with the maximum output power density of 68 mW cm−2 at an operating voltage of 1.1 V compared to direct borohydride-hydrogen peroxide fuel cell employing the conventional gold-based cathode with the maximum output power density of 47 mW cm−2 at an operating voltage of 0.7 V. X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Energy Dispersive X-ray Analysis (EDAX) suggest that anchoring of Cetyl-Trimethyl Ammonium Bromide (CTAB) as a surfactant moiety on carbon-supported PB affects the catalyst morphology. Polarization studies on direct borohydride-hydrogen peroxide fuel cell with carbon-supported CTAB-anchored PB cathode exhibit better performance with the maximum output power density of 50 mW cm−2 at an operating voltage of 1 V than the direct borohydride-hydrogen peroxide fuel cell with carbon-supported Prussian Blue without CTAB with the maximum output power density of 29 mW cm−2 at an operating voltage of 1 V.

Time-Resolved Resonance Raman Studies on Proton-Induced Electron-Transfer Reaction from Triplet Excited State of 2-Methoxynaphthalene to Decafluorobenzophenone

In this paper time-resolved resonance Raman (TR3) spectra of intermediates generated by proton induced electron-transfer reaction between triplet 2-methoxynaphthalene ((ROMe)-R-3) and decafluorobenzophenone (DFBP) are presented The TR3 vibrational spectra and structure of 2-methoxynaphthalene cation radical (ROMe+) have been analyzed by density functional theory (DFT) calculation It is observed that the structure of naphthalene ring of ROMe+ deviates from the structure of cation radical of naphthalene

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

A porphyrin bearing tetrahydrothiophene pickets; co-ordination behaviour and electron transfer

A novel ‘picket-fence’ porphyrin, 5,10,15,20-tetrakis[o-(tetrahydro-2-thenoylamino)phenyl]porphyrin (H2L) with ligating tetrahydrothiophene rings disposed perpendicular to the porphyrin plane has been synthesised. Its zinc(II) derivative, [ZnL], binds two silver(I) ions co-operatively with a dissociation constant of 4.8 × 10–8 dm3 mol–1. Time-resolved fluorescence lifetime measurements reveal the presence of intramolecular photoexcited electron transfer in this donor–acceptor system.

Functions Of Cytochrome-C In Regulation Of Electron-Transfer And Protein Folding

Cytochrome c, a "mobile electron carrier" of the mitochondrial respiratory chain, also occurs in detectable amounts in the cytosol, and can receive electrons from cytochromes present in endoplasmic reticulum and plasma membranes as well as from superoxide and ascorbate. The pigment was found to dissociate from mitochondrial membranes in liver and kidney when rats were subjected to heat exposure and starvation, respectively. Treating cytochrome c with hydroxylamine gives a partially deaminated product with altered redox properties; decreased stimulation of respiration by deficient mitochondria, increased reduction by superoxide, and complete loss of reducibility by plasma membranes. Mitochondria isolated from brown adipose tissue of cold-exposed rats are found to be sub-saturated with cytochrome c. The ability of cytochrome c to reactivate reduced ribonuclease is now reinterpreted as a molecular chaperone role for the hemoprotein.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Photoinduced electron transfer in zinc porphyrin-crown ether supramolecule with Eu3+ electron acceptor in crown void

Photoinduced electron transfer (ET) reactions in the zinc porphyrin-crown ether (ZnPCE) supramolecule, in which one crown ether moiety containing Eu3+ as electron acceptor is covalently linked to zinc porphyrin (ZnP), were studied by flash photolysis. In methanol solutions, highly efficient charge separation occurs via intramolecular ET from (ZnP)-Zn-3 to Eu3+ encapsulated in the crown ether void (k(1) = (3 +/- 1) X 10(3) s(-1)) and intramolecular ET from 3ZnP to uncomplexed Eu2+ (k(2) = (2.5 +/- 0.5) X 10(3) s(-1)). Intermolecular ET from Eu2+ escaped from the crown ether void to ZnP.+ (k(tau) = (4.3 +/- 0.7) X 10(8) M(-1) s(-1)) seems to be the main pathway of charge recombination.

Time-resolved fluorescence studies on covalently linked porphyrin�nitroarene complexes. Conformational control of photoinduced electron transfer reactions

Time-resolved fluorescence studies were carried out on a series of free-base and zinc(II) derivatives of meso-tetraphenylporphyrins covalently linked to either 1,3-dinitrobenzene (DNB) or 1,3,5-trinitrobenzene (TNB) acceptor units. These acceptor units were linked at different sites (at the ortho, meta or para positions of one of the phenyl groups of meso-tetraphenylporphyrin) to the donor porphyrins such that the resulting isomeric intramolecular donor-acceptor complexes exhibit different centre-to-centre (ctc) distances and relative orientations. Biexponential fluorescence decay profiles observed for several of these covalently linked complexes were rationalized in terms of the presence of ''closed'' and ''extended'' conformers. Detailed analyses of the fluorescence decay data have provided a comprehensive understanding of the photoinduced electron transfer (PET) reactions occurring in systems containing zinc(II) porphyrin donors. It is observed that although DNB-linked zinc(II) complexes follow the trends predicted for the efficiency of PET with respect to donor-acceptor distance, the TNB-linked zinc(II) porphyrins exhibit a behaviour which is dictated by steric effects. Similarly, although the thermodynamic criteria predict a greater efficiency of charge separation in TNB-linked complexes compared with DNB-linked complexes, the reverse trend observed has been attributed to orientational effects. In the complexes containing free-base porphyrin donors, PET is expected to be less efficient from a thermodynamic viewpoint. In a few of these cases, fluorescence quenching seems to occur by parallel mechanisms other than PET.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics