Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazoline complexes.

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.     

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect, as discussed by the mode-coupling theory. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.     

Cyanation: providing a three-in-one advantage for the design of n-type organic field-effect transistors

The theoretical work presented here demonstrates that, when substitution takes place at appropriate positions, cyanation could be a useful tool for reducing the internal reorganization energy of molecules. A molecular-orbital-based explanation is given for this fundamentally important phenomenon. Some of the cyanated pentacene derivatives (nCN-PENT-n) not only have internal reorganization energies for electron transfer (lambda(-)) smaller than that of pentacene, but the lambda(-) values are even of the same magnitude as the internal reorganization energy for hole transfer (lambda(+)) of pentacene, a small value that few organic compounds have surpassed. In addition, cyanation raises the electron affinity of the parent compound and may afford good electronic couplings between neighboring molecules, because of its ability in promoting pi-stacking. For the design of high performance n-Type Organic field-effect transistors, high electron affinities, large intermolecular electronic couplings, and small reorganization energies are necessary. Cyanation may help in all three aspects. Two cyanated trialkylsilylethynyl pentacene derivatives with known pi-stacking structures are predicted to provide reasonably small internal reorganization energies, large electronic couplings, and high electron affinities. They have the potential to outperform N-fluoroalkylated dicyanoperylene-3,4:9,10-bis(dicarboximides) (PDI-FCN(2)) in terms of electron mobility.     

Buffer-assisted proton-coupled electron transfer in a model rhenium-tyrosine complex

The mechanism for tyrosyl radical generation in the [Re(P-Y)(phen)(CO)3]PF6 complex is investigated with a multistate continuum theory for proton-coupled electron transfer (PCET) reactions. Both water and the phosphate buffer are considered as potential proton acceptors. The calculations indicate that the model in which the proton acceptor is the phosphate buffer species HPO(4)2- can successfully reproduce the experimentally observed pH dependence of the overall rate and H/D kinetic isotope effect, whereas the model in which the proton acceptor is water is not physically reasonable for this system. The phosphate buffer species HPO4(2-) is favored over water as the proton acceptor in part because the proton donor-acceptor distance is approximately 0.2 A smaller for the phosphate acceptor due to its negative charge. The physical quantities impacting the overall rate constant, including the reorganization energies, reaction free energies, activation free energies, and vibronic couplings for the various pairs of reactant/product vibronic states, are analyzed for both hydrogen and deuterium transfer. The dominant contribution to the rate arises from nonadiabatic transitions between the ground reactant vibronic state and the third product vibronic state for hydrogen transfer and the fourth product vibronic state for deuterium transfer. These contributions dominate over contributions from lower product states because of the larger vibronic coupling, which arises from the greater overlap between the reactant and product vibrational wave functions. These calculations provide insight into the fundamental mechanism of tyrosyl radical generation, which plays an important role in a wide range of biologically important processes.     

Protein-water electrostatics and principles of bioenergetics

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.     

Water (in water) as an intrinsically efficient proton acceptor in concerted proton electron transfers

The oxidation of PhOH in water by photochemically generated Ru(III)(bpy)(3) is taken as prototypal example disclosing the special character of water, in the solvent water, as proton acceptor in concerted proton-electron transfer reactions. The variation of the rate constant with temperature and driving force, as well as the variation of the H/D kinetic isotope effect with temperature, allowed the determination of the reaction mechanism characterized by three intrinsic parameters, the reorganization energy, a pre-exponential factor measuring the vibronic coupling of electronic states at equilibrium distance, and a distance-sensitivity parameter. Analysis of these characteristics and comparison with a standard base, hydrogen phosphate, revealed that electron transfer is concerted with a Grotthus-type proton translocation, leading to a charge delocalized over a cluster involving several water molecules. A mechanism is thus uncovered that may help in understanding how protons could be transported along water chains over large distances in concert with electron transfer in biological systems.     

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.     

Model system-bath Hamiltonian and nonadiabatic rate constants for proton-coupled electron transfer at electrode-solution interfaces

An extension of the Anderson-Newns-Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds.     

Proton transfer of excited 7-azaindole in reverse-micellar methanol nanopools: even faster than in bulk methanol

The methanol-catalyzed double-proton transfer of photoexcited 7-azaindole in the free cores of solvation-restricted reverse micelles takes place on the time scale of 90 ps, even shorter than in bulk methanol. This anomalous rate increase with a large kinetic isotope effect of 5 experimentally proves the widely discussed two-step model for the overall reaction of solvent-mediated proton transfer. On the other hand, the molecules in the bound layers and in the headgroup layers relax in 900 and 6000 ps, respectively, without going through proton transfer. The tautomerization and the relaxation of excited 7-azaindole can be exploited to probe the nanopools of methanol reverse micelles.     

Electrochemical approach to concerted proton and electron transfers. Reduction of the water-superoxide ion complex

Concerted proton and electron transfers (CPET) currently attract considerable theoretical and experimental attention, notably in view of their likely involvement in many enzymatic reactions. Electrochemistry, through techniques such as cyclic voltammetry, can provide a quite effective access to CPET in terms of diagnosis and quantitative kinetic characterization. The relationships expressing the rate constant of an electrochemical CPET are given. Besides the CPET standard potential, it depends on two main factors. One is the reorganization energy, which appears as the sum of an intramolecular contribution and two solvent reorganization energies corresponding to proton and electron transfers, respectively. The other is the pre-exponential factor that mainly depends on proton tunneling through the activation barrier. Procedures for estimating these various factors as well as the H/D kinetic isotope effect are described. Application of the theory is illustrated by the experimental results obtained for the cyclic voltammetric reduction of the water-superoxide ion complex in dimethylformamide and acetonitrile.     

The energy and isotope dependence of electronic relaxation in dilute vapors of fluorene and β-naphthylamine

The excitation energy and isotope dependence of fluorescence lifetimes and quantum yields in dilute vapors of fluorene and β-naphthylamine are discussed in relation to the manner in which different channels of radiationless transitions are affected by the vibrational energy content of the molecule. Evidence is presented which shows that vibrational relaxation is slow compared with electronic relaxation for molecules with low excess energies and that the rate of S₁ → S₀ internal conversion is greater in the deuterated compound than in the corresponding protonated species for very large excess energies.     

H-bond relays in proton-coupled electron transfers. Oxidation of a phenol concerted with proton transport to a distal base through an OH relay

Four molecules comprising a phenol moiety and a distal pyridine base connected by an intermediary H-bonding and an H-bonded alcohol group have been synthesized and their electrochemistry has been investigated by means of cyclic voltammetry. The molecules differ by the substituent at the alcohol functional carbon and by methyl groups on the pyridine. The reaction follows a concerted proton-electron transfer pathway as confirmed by the observation of a significant H/D kinetic isotope effect in all four cases. The standard rate constants characterizing each of the four compounds are analyzed in terms of reorganization energy and pre-exponential factor. Intramolecular and solvent reorganization energies appear as practically constant in the series, in which a previously investigated aminophenol is included, whereas significantly different pre-exponential factors are observed. That the latter, which is a measure of the efficiency of proton tunneling concerted with electron transfer, be substantially smaller with the H-bond relay molecules than with the aminophenol is related to the fact that two protons are moved in the first case instead of one in the second. Within the H-bond relay molecules, the pre-exponential factor varies with the substituent present at the alcohol functional carbon in the order CF(3) > H > CH(3), presumably as the result of a fine tuning of the balance between the H-bond accepting and H-bond donating properties of the central OH group. The kinetic H/D kinetic isotope effect increases accordingly in the same order.     

Structural dynamics and energy flow in Rydberg-excited clusters of N,N-dimethylisopropylamine

In molecular beams, the tertiary amine N,N-dimethylisopropyl amine can form molecular clusters that are evident in photoelectron and mass spectra obtained upon resonant multiphoton ionization via the 3p and 3s Rydberg states. By delaying the ionization pulse from the excitation pulse we follow, in time, the ultrafast energy relaxation dynamics of the 3p to 3s internal conversion and the ensuing cluster evaporation, proton transfer, and structural dynamics. While evaporation of the cluster occurs in the 3s Rydberg state, proton transfer dominates on the ion surface. The mass-spectrum shows protonated species that arise from a proton transfer from the alpha-carbon of the neutral parent molecule to the N-atom of its ionized partner in the dimer. DFT calculations support the proton transfer mechanism between tightly bonded cluster components. The photoelectron spectrum shows broad peaks, ascribed to molecular clusters, which have an instantaneous shift of about 0.5 eV toward lower binding energies. That shift is attributed to the charge redistribution associated with the induced dipoles in surrounding cluster molecules. A time-dependent shift that decreases the Rydberg electron binding energy by a further 0.4 eV arises from the structural reorganization of the cluster solvent molecules as they react to the sudden creation of a charge.     

Effect of group electronegativity on electron transfer in bis(hydrazine) radical cations

The radical cation of 4,10-ditert-butyl-5,9-diisopropyl-4,5,9,10-tetraazatetracyclo[6.2.2.2]-tetradecane (sBI4T(+)), as well as its substituted bis(hydrazine) radical cations, is chosen for the investigation of the electronegativity dependence of its intramolecular electron transfer. To do so, two parameters, reorganization energy and electronic coupling, are calculated with several ab initio approaches. It is found that the electronic couplings decrease with the increase of the group electronegativity while the reorganization energies do not show an explicit dependency. Furthermore, Marcus formula is employed to reveal those effect on the electron transfer rates. The predicted rates of electron transfer generally decrease with increasing group electronegativity, although not monotonically.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

Slow geminate‐charge‐pair recombination dynamics at polymer: Fullerene heterojunctions in efficient organic solar cells

We explore charge recombination dynamics at electron donor‐acceptor heterojunctions, formed between a semiconductor polymer (PCDTBT) and a fullerene derivative (PC₇₀BM), by means of combined time‐resolved photoluminescence and transient absorption spectroscopies. Following prompt exciton dissociation across the heterojunction, a subset of bound electron‐hole pairs recombines with a temperature‐independent rate distribution spanning submicrosecond timescales to produce luminescent charge‐transfer excitons (CTX). At 14 K, this slow mechanism is the dominant geminate charge recombination pathway, whereas we also observe CTX emission on subnanosecond timescales at 293 K. We thus find that at these temperatures, a fraction of the initial charge‐pair population is trapped deeply such that they only recombine slowly over a broad distribution of timescales by quantum tunneling. We identify geminate polaron pairs (GPP) as a reservoir of long‐lived localized states that repopulate the CTX up to microsecond timescales. The observation of such distributed geminate‐charge recombination highlights the importance of the molecular nature of specific donor–acceptor electronic interactions in defining the relaxation pathways of trapped GPP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Concerted proton-electron transfer in the oxidation of hydrogen-bonded phenols

Three phenols with pendant, hydrogen-bonded bases (HOAr-B) have been oxidized in MeCN with various one-electron oxidants. The bases are a primary amine (-CPh(2)NH(2)), an imidazole, and a pyridine. The product of chemical and quasi-reversible electrochemical oxidations in each case is the phenoxyl radical in which the phenolic proton has transferred to the base, (*)OAr-BH(+), a proton-coupled electron transfer (PCET) process. The redox potentials for these oxidations are lower than for other phenols, predominately from the driving force for proton movement. One-electron oxidation of the phenols occurs by a concerted proton-electron transfer (CPET) mechanism, based on thermochemical arguments, isotope effects, and DeltaDeltaG(++)/DeltaDeltaG degrees . The data rule out stepwise paths involving initial electron transfer to form the phenol radical cations [(*)(+)HOAr-B] or initial proton transfer to give the zwitterions [(-)OAr-BH(+)]. The rate constant for heterogeneous electron transfer from HOAr-NH(2) to a platinum electrode has been derived from electrochemical measurements. For oxidations of HOAr-NH(2), the dependence of the solution rate constants on driving force, on temperature, and on the nature of the oxidant, and the correspondence between the homogeneous and heterogeneous rate constants, are all consistent with the application of adiabatic Marcus theory. The CPET reorganization energies, lambda = 23-56 kcal mol(-)(1), are large in comparison with those for electron transfer reactions of aromatic compounds. The reactions are not highly non-adiabatic, based on minimum values of H(rp) derived from the temperature dependence of the rate constants. These are among the first detailed analyses of CPET reactions where the proton and electron move to different sites.     

Pump-probe spectroscopy with phase-locked pulses in the condensed phase: decoherence and control of vibrational wavepackets

Electronic and vibrational coherences of Cl2 embedded in solid Ar are investigated by exciting to the B state with a phase-locked pulse pair from an unbalanced Michelson interferometer, where the chirp difference matches the B state anharmonicity. Recording the A' --> X fluorescence after relaxation is compared to probing to charge transfer states by a third pulse. The three-pulse experiment delivers more details on the decoherence processes. The signal modulation due to phase tuning up to the third vibrational round-trip time indicates that the electronic coherence in the B <-- X transition is preserved for more than 660 fs in the solid Ar environment where many body electronic interactions take place. Vibrational coherence lasts longer than 3 ps according to the observed half revival of the wavepacket. Control of the coupling between wavepacket motion and lattice oscillation is demonstrated by tuning the relative phase between the phase-locked pulses, preparing wavepackets predominantly composed of either zero-phonon lines or phonon side bands.     

Modulating charge-transfer interactions in topologically different porphyrin-C60 dyads

Control over the interchromophore separation, their angular relationship, and the spatial overlap of their electronic clouds in several ZnP-C(60) dyads (ZnP=zinc porphyrin) is used to modulate the rates of intramolecular electron transfer. For the first time, a detailed analysis of the charge transfer absorption and emission spectra, time-dependent spectroscopic measurements, and molecular dynamics simulations prove quantitatively that the same two moieties can produce widely different electron-transfer regimes. This investigation also shows that the combination of ZnP and C(60) consistently produces charge recombination in the inverted Marcus region, with reorganization energies that are remarkably low, regardless of the solvent polarity. The time constants of electron transfer range from the mus to the ps regime, the electronic couplings from a few tens to several hundreds of cm(-1), and the reorganization energies remain below 0.54 eV and can be as low as 0.16 eV.