One-dimensional description of multidimensional electron transfer reactions in condensed phase

We derive a one-dimensional energy diffusion equation for describing the dynamics of multidimensional electron transfer reactions in condensed phase, which is conceptually simpler and computationally more economic than the conventional approaches. We also obtain an analytical expression for the rate of electron transfer reactions for a general one-dimensional effective potential as well as an energy dependent diffusitivity. As an illustrative example, we consider application to electron transfer in a contact ion pair system modeled through harmonic potentials consisting of two slow classical modes and a high frequency vibrational mode for which the numerical results calculated using the proposed one-dimensional approach are shown to be in good agreement with experimental results. The energy diffusion equation and the rate expression for electron transfer obtained from the present theory, therefore, open up the possibility of describing the dynamics of electron transfer in complex systems, through a simpler approach.     

Low temperature extension of the generalized Zusman phase space equations for electron transfer

In a previous paper [J. Chem. Phys. 119, 11864 (2003)], we derived a set of two coupled equations which describe electron transfer in the presence of dissipation at high temperature. Employing the low temperature extension of the Fokker-Planck operator, suggested by Haake and Reibold [Phys. Rev. A 32, 2462 (1985)] and Ankerhold [Europhys. Lett. 61, 301 (2003)], we show that one may extend the generalized Zusman equations in a similar manner to low temperature. Numerical simulation shows that addition of the temperature-dependent term which couples the coordinate and momentum causes an increase in the electron transfer rate as compared to the rate obtained from the previous high temperature equations. The increase in the rate comes from the increase in the equilibrium variances of the coordinate and momentum. The low temperature quantum theory allows for higher energy portions of phase space to contribute to the electron transfer rate where the rate is higher thus enhancing the overall rate.     

Femtosecond intermolecular electron transfer in condensed systems

We have investigated the ultrafast intermolecular electron transfer (ET) from an electron-donating solvent (aniline (AN) or N, N-dimethylaniline (DMA)) to an excited dye molecule (oxazines (Nile blue and oxazine 1) or coumarins). A non-exponential time dependence was observed in AN and can be explained by solvent reorientation and nuclear motion of the reactants. However, in DMA, a single exponential process was observed for Nile blue (160 fs) and oxazine 1 (280 fs), which can be explained by assuming that the rate of ET is limited mainly by ultrafast nuclear motion. A clear substituent effect on intermolecular ET was observed for the 7-aminocoumarins. When the alkyl chain on the 7-amino group is extended and a hexagonal ring with the benzene moiety is formed, the rate of ET is reduced by three orders of magnitude. This effect can be explained by a change in the free energy difference of the reaction and by the vibrational motion of the amino group.     

Kinetics of energy transfer in the condensed phase

The decay kinetics of the donor state is studied; this decay is determined by the resonance energy transfer to the surrounding donor molecules of the medium. A new element is the consideration of the strong interaction of the donor with the acceptor over short distances, thanks to which the onset of decomposition assumes an exponential character. It was shown that this circumstance does not affect the fluorescence quenching, but it can exert a considerable effect on phenomena related to radiation shielding.     

Comparison of photoinduced electron transfer reactions of aromatic carbonyl vs. cyano compounds with electron donors in condensed phase:the importance

Photoinduced electron transfer reactions in acetonitrile with bensopheneone, anthraquinone, 9-cyanoanthracene and 9,10-dicyanoanthracene as electron acceptors, and with 1,4-diasabicyclo[2,2,2]octane and N,N-dimethylaniline as electron donors have been studied with ns-laser flash photolysis and fluorescence quenching measurements. For these systems the resulting free ion yield depends on the spin state of the geminate ion pair: its separation is very efficient if formed in a triplet state (carbonyl compounds/donors), while it is very inefficient if formed in a singlet state (cyanoanthracenes/donors). In the triplet systems, geminate back electron transfer is limited by the rate of spin flip.     

Nonperturbative quantum simulation of time-resolved nonlinear spectra: Methodology and application to electron transfer reactions in the condensed phase

A quantum dynamical method is presented to accurately simulate time-resolved nonlinear spectra for complex molecular systems. The method combines the nonpertubative approach to describe nonlinear optical signals with the multilayer multiconfiguration time-dependent Hartree theory to calculate the laser-induced polarization for the overall field–matter system. A specific nonlinear optical signal is obtained by Fourier decomposition of the overall polarization. The performance of the method is demonstrated by applications to photoinduced ultrafast electron transfer reactions in mixed-valence compounds and at dye–semiconductor interfaces.     

Cross sections for low-energy electron scattering from adenine in the condensed phase

Measurements of the vibrational and electronic excitation of a sub-monolayer up to a monolayer film of adenine were performed with a high resolution electron energy-loss (HREEL) spectrometer. The integral cross sections (over the half-space angle) for excitation of the normal vibrational modes of the ground electronic state and electronically excited states are calculated from the measured reflectivity EEL spectra. Most cross sections for vibrational excitation are of the order of 10(-17) cm(2), the largest being the out-of-plane wagging of the amino-group and the six-member ring deformations. A wide resonance feature appears in the incident energy dependence of the vibrational cross sections at 3-5 eV, while a weak shoulder is present in this dependence for combined ring deformations and bending of hydrogen atoms. For the five excited electronic states, at 4.7, 5.0, 5.5, 6.1 and 6.6 eV, the cross sections are of the order of 10(-18) cm(2), except in the case of the state at the energy of 6.1 eV, for which it is two to three times higher.     

The role of long range tunneling in electron transfer processes in condensed media

Experimental evidence is given for the importance of long range tunneling in electron transfer reactions in condensed media: the unusually weak effect of electrostatic repulsion on the rate of some electron transfer and spin exchange processes; electron transfer between distant (up to ≈ 30 A) species in solids at a rate considerably exceeding that of thermal diffusion; the unusual concentration dependence of radiation yields in the presence of scavengers, etc. The concept of long range tunneling is shown to permit quantitative explanation and correlation of experimental data on electron transfer in quite different fields.The factors determining the efficiency of tunneling, as well as some peculiar features of tunneling kinetics are considered.The role of long range tunneling in various chemical processes involving electron transfer in condensed media are discussed (ion reactions in solutions, photochemistry, radiation chemistry, reactions with polymers, some biochemical reactions).     

Bond and site selectivity in dissociative electron attachment to gas phase and condensed phase ethanol and trifluoroethanol

The formation of negative ions following electron impact to ethanol (CH(3)CH(2)OH) and trifluoroethanol (CF(3)CH(2)OH) is studied in the gas phase by means of a crossed electron-molecular beam experiment and in the condensed phase via Electron Stimulated Desorption (ESD) of fragment ions from the corresponding molecular films under UHV conditions. Gas phase ethanol exhibits two pronounced resonances, located at 5.5 eV and 8.2 eV, associated with a remarkable selectivity in the decomposition of the precursor ion. While the low energy resonance exclusively decomposes into O(-), that at higher energy generates OH(-) and a comparatively small signal of [CH(3)CH(2)O](-) due to the loss of a neutral hydrogen. CF(3)CH(2)OH shows a completely different behaviour, as now an intense feature at 1.7 eV appears associated with the loss of a neutral hydrogen atom exclusively occurring at the O site. The H(-) formation from the gas phase compounds is below the detection limit of the present experiment, while in ESD from 3 MonoLayer (ML) films of CH(3)CH(2)OH and CF(3)CH(2)OH the most intense fragment is H(-), appearing from a broad resonant feature between 7 and 12 eV. With CF(3)CH(2)OH, by using the isotopically-labelled analogues CF(3)CD(2)OH and CF(3)CH(2)OD it can be shown that this feature consists of two resonances, one located at 8 eV leading to H(-)/D(-) loss from the O site and a second resonance located at 10 eV leading to the loss of H(-)/D(-) from the CH(2) site.     

Solution phase electron transfer versus bridge mediated electron transfer across carboxylic acid terminated thiols

Self-assembled monolayers (SAMs) of thiols with carboxylic acid terminal groups were formed on gold substrates. The electron transfer characteristics of redox species on the above SAM-modified electrodes were studied in acid and neutral media with the help of voltammetry under two different conditions: (1) solution phase electron transfer and (2) bridge mediated electron transfer. Two redox systems, viz., [Fe(CN)₆]^4-/3− and Ru[(NH₃)₆]^2+/3+ were chosen for the solution phase study. Investigations of bridge mediated electron transfer were carried out by functionalising the SAM with redox moieties and then studying their redox behaviour. For this study, ferrocene carboxylic acid and 1,4-diamino anthraquinone were used and they were linked to carboxylic acid terminated thiols by covalent linkage. The voltammetric results with mercaptoundecanoic acid SAM demonstrate the difference in behaviour between solution phase and bridge mediated electron transfer processes.     

Low temperature phase changes in the urea-trioxane inclusion compound

Three reversible phase transitions have been detected in the urea trioxane inclusion compound between room temperature and −160°C. They involve a doubling of the hexagonal unit cell near −33°C and small distortions of the host lattice at lower temperature. Nitrogen pure quadrupole resonance experiments show that the nitrogen atoms are distributed between two different crystallographic sites. The nature of the phase changes is discussed.     

Benzyl ether from phase transfer catalyzed strongly alkaline hydrolysis of benzyl chloride

The overall rate equation for the production of benzyl ether by phase transfer catalyzed strongly alkaline hydrolysis of benzyl chloride in the pseudo-steady state was derived. The effects of the concentrations and the sizes of the alkyl substituents of the catalysts, the concentration of hydroxide ions in the aqueous phase, the volume-fraction of the organic phase, the reaction temperature and the stirring speed on the production rate of benzyl ether can be explained with the derived rate equation. Under the conditions of 0.842 mol benzyl chloride, 50% aq. NaOH (2.5 mol NaOH), 42.2 mmol Bz(C₂H₅)₃NCl, 70 °C and 500 rpm, the reactions proceeded to nearly 100% benzyl ether within 2 h. The cocatalyst, NaI, is effective for improving the reaction rate, suitable amounts being ~ 5% of the substrate, benzyl chloride. The decomposition rate of the practical catalyst, Bz(C₂H₅)₃NCl, in 30% aq. NaOH at 70 °C is only about 3% per day. The conditions for producing benzyl ether by phase transfer catalyzed hydrolysis of benzyl chloride can be obtained from the rate equation and the experimental data.     

Positive muons in condensed phase ammonia

The chemical behavior of positive muons in condensed phase ammonia has been investigated in order to elucidate the phase and temperature effects on the chemical and physical behavior of the muon and muonium formation in a simple binary compound. Diamagnetic muon yield (P_D) was constant at 0.67±0.01 in both solid and liquid above 125 K. Muonium formation in solids were observed above 100 K with slow muonium spin relaxation. In liquids, the muonium yield and its spin relaxation rate showed temperature dependence. Addition of metallic sodium increased P_D in liquids.     

Radical-olefin addition reactions in condensed phase

A study has been made of the rate constant for the reaction The states of the product have quasilevels E_n — i_n, which, depending on the heat of reaction, may be in resonance with the state of the reactants after surmounting the activation barrier. Because of this, there is no monotonic variation of the propagation rate constant, even as a function of the heat of reaction; the behavior of the rate constant has a resonance character. The results obtained in this investigation are in good agreement with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 1, pp. 25–32, January–February, 1990.     

Stationary points in the temperature dependence of electron transfer rates

The temperature dependence of the rate of electron transfer is analyzed in the framework of a molecular theory presented recently, characterized by decoupling the total solvent reorganization energy into two contributions featuring reorganizations of permanent dipoles as well as solvent density. The inclusion of the temperature dependence of liquid density reorganization can give rise to a maximum in the Arrhenius coordinates for electron transfer in the inverted region and for exothermic reactions with small activation barriers as well.     

Vibrational relaxation in the condensed phase

A modified Landau-Teller equation for vibrational relaxation in the condensed phase is proposed. This equation differs from previous approaches by accounting for the fluctuations of the energies of the vibrational levels that result from the interactions with the surroundings (bath). In the conventional approach the effects of the bath are only included in the coupling between the relaxing and accepting vibrational modes. It is shown that the additional inclusion of the fluctuations of the energy levels can lead to a dramatic change of the vibrational relaxation rate.     

Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.     

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.     

Electron transfer in condensed media with mobile defects

A study has been made of electron transfer in a condensed polar medium containing two types of dynamically changing intrinsic parameters — static polarization and mobile defects, interacting locally with electronic states of the reactants. An expression has been obtained for the rate constant of a homogeneous, nonadiabatic, charge transfer reaction with allowance for large-scale and local fluctuations of the intrinsic parameters of the medium. It is shown that, along with fluctuations of the static polarization, Brownian motion of defects close to the reactants may lead to a significant variance of the electronic levels of the donor and acceptor.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 4, pp. 406–413, July–August, 1990.     

The model of level broadening in condensed phase

We study a model of non-Markovian kinetics for a harmonic oscillator embedded in a harmonic heat bath. We present a new scheme for approximately solving the quantum relaxation equation for the density matrix to find a distribution of level populations. It is found to be an extended Lorentzian with the width depending on the energy. A more convenient non-Markovian distribution called square root Fourier distribution that was implemented in the preceding paper [M. V. Basilevsky et al., J. Chem. Phys. 125, 194513 (2006)] is closely related to this extended Lorentzian model. Both distributions decay exponentially far away from their centers and reproduce well standard Lorentzian widths in the vicinity of the central region. A conventional Lorentzian model with such widths results when the Redfield approximation is applied in the frame of the present procedure.