Electron Transfer-from Isolated Molecules to Biomolecules

Theory and Electrochemistry of Cytochrome c

Extensive simulations of cytochrome c in solution are performed to address the apparent contradiction between large reorganization energies of protein electron transfer typically reported by atomistic simulations and much smaller values produced by protein electrochemistry. The two sets of data are reconciled by deriving the activation barrier for electrochemical reaction in terms of an effective reorganization energy composed of half the Stokes shift (characterizing the medium polarization in response to electron transfer) and the variance reorganization energy (characterizing the breadth of electrostatic fluctuations). This effective reorganization energy is much smaller than each of the two components contributing to it and is fully consistent with electrochemical measurements. Calculations in the range of temperatures between 280 and 360 K combine long, classical molecular dynamics simulations with quantum calculations of the protein active site. The results agree with the Arrhenius plots for the reaction rates and with cyclic voltammetry of cytochrome c immobilized on self-assembled monolayers. Small effective reorganization energy, and the resulting small activation barrier, is a general phenomenology of protein electron transfer allowing fast electron transport within biological energy chains.

Looking at Photoinduced Charge Transfer Processes in the IR: Answers to Several Long-Standing Questions

Because of its crucial role in many areas of science and technology, photoinduced electron transfer is the most investigated photochemical reaction. Despite this, several important questions remain open. We present recent efforts to answer some of them, which concern both inter- and intramolecular processes. The decisive factor that allowed these issues to be successfully addressed was the use of time-resolved infrared (TRIR) spectroscopy. Many different transient species, such as tight and loose ion pairs (TIPs and LIPs) and exciplexes, have been invoked to explain the dynamics of intermolecular photoinduced charge separation reactions (i.e., electron transfer between two neutral species) and the production of free ions. However, their structures are essentially unknown, and their exact roles in the reaction mechanism are unclear. Indeed, the commonly used transient electronic absorption spectroscopy does not give much structural insight and cannot clearly distinguish ion pairs from free ions, at least in the visible region. Unambiguous spectral signatures of TIPs, LIPs, and exciplexes could be observed in the IR using electron donor/acceptor (D/A) pairs with adequate vibrational marker modes. The ability to spectrally distinguish these intermediates allowed their dynamics to be disentangled and their roles to be determined. Structural information could be obtained using polarization-resolved TRIR spectroscopy. Our investigations reveal that moderately to highly exergonic reactions result in the formation of both TIPs and LIPs. TIPs are not only generated upon direct charge-transfer excitation of DA complexes, as usually assumed, but are also formed upon static quenching with reactant pairs at distances and orientations enabling charge separation without diffusion. On the other hand, dynamic quenching produces primarily LIPs. In the case of highly exergonic reactions, strong indirect evidence for the generation of ion pairs in an electronic excited state was found, accounting for the absence of an inverted region. Finally, weakly exergonic reactions produce predominantly exciplexes, which can evolve further into ion pairs or recombine to the neutral ground state. The high sensitivity of specific vibrational modes to the local electronic density was exploited to visualize the photoinduced charge flow in symmetric A-(π-D)₂- and D-(π-A)₂-type molecules developed for their two-photon absorption properties. The electronic ground state and Franck-Condon S₁ state of these molecules are purely quadrupolar, but the strong solvatochromism of their fluorescence points to a highly dipolar relaxed S₁ state. This has been explained in terms of excited-state symmetry breaking induced by solvent and/or structural fluctuations. However, real-time observation of this process was missing. Direct visualization of symmetry-breaking charge transfer was achieved using TRIR spectroscopy by monitoring vibrations localized in the two arms of these molecules. A transition from a purely quadrupolar state to a symmetry-broken state on the timescale of solvent relaxation could be clearly observed in polar solvents, indicating that symmetry breaking occurs primarily via solvent fluctuations. In the case of the D-(π-A)₂ molecule, this breaking results in different basicities at the two A ends and consequently in different affinities for H-bonds, which in turn leads to the formation of an asymmetric tight H-bonded complex in highly protic solvents.

Computational Studies on Structural, Excitation, and Charge-Transfer Properties of Ureidopeptidomimetics

Peptides with ureido group enclosing backbones are considered peptidomimetics and are known for their higher stabilities, biocompatibilities, antibiotic, inhibitor, and charge-transduction activities. These peptidomimetics have some unique applications, which are quite different from those of natural peptides. Hence, it is imperative to appreciate their properties at a microscopic level. In this regard, this work outlines, in detail, the charge transfer (CT) properties, hole-migration dynamics, and electronic structures of various experimentally comprehended ureidopeptidomimetic models using density functional theory (DFT). Time-dependent DFT and complete active space self-consistent field computations on basic models provide the necessary evidence for the viability of CT from the end enfolding the ureido group to the other end with a carboxylate entity. This donor-to-acceptor CT has been reflected in excitation studies, in which the higher intensity band corresponds to CT from the π orbital of the ureido group to the π* orbital of the carboxylate entity. Further, hole-migration studies have shown that charge can evolve from the ureido end, whereas the hole generated at the carboxylate end does not migrate. However, hole migration has been reported to occur from both ends (amino and carboxylate ends) in glycine oligopeptides, and our studies show that the ability to transfer and migrate charge can be tuned by modifying the donor and acceptor functional groups in both the neutral and cationic charge states. We have analyzed the possibility of hole migration following ionization using DFT-based wave-packet propagation and found its occurrence on a ∼2-5 fs time scale, which reflects the charge-transduction ability of peptidomimetics.

Influence of Coherent Tunneling and Incoherent Hopping on the Charge Transfer Mechanism in Linear Donor-Bridge-Acceptor Systems

The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.

Dissipation enhanced vibrational sensing in an olfactory molecular switch

Motivated by a proposed olfactory mechanism based on a vibrationally activated molecular switch, we study electron transport within a donor-acceptor pair that is coupled to a vibrational mode and embedded in a surrounding environment. We derive a polaron master equation with which we study the dynamics of both the electronic and vibrational degrees of freedom beyond previously employed semiclassical (Marcus-Jortner) rate analyses. We show (i) that in the absence of explicit dissipation of the vibrational mode, the semiclassical approach is generally unable to capture the dynamics predicted by our master equation due to both its assumption of one-way (exponential) electron transfer from donor to acceptor and its neglect of the spectral details of the environment; (ii) that by additionally allowing strong dissipation to act on the odorant vibrational mode, we can recover exponential electron transfer, though typically at a rate that differs from that given by the Marcus-Jortner expression; (iii) that the ability of the molecular switch to discriminate between the presence and absence of the odorant, and its sensitivity to the odorant vibrational frequency, is enhanced significantly in this strong dissipation regime, when compared to the case without mode dissipation; and (iv) that details of the environment absent from previous Marcus-Jortner analyses can also dramatically alter the sensitivity of the molecular switch, in particular, allowing its frequency resolution to be improved. Our results thus demonstrate the constructive role dissipation can play in facilitating sensitive and selective operation in molecular switch devices, as well as the inadequacy of semiclassical rate equations in analysing such behaviour over a wide range of parameters.

Projection of the Dynamics of Electron Transfer Reaction in Dual Space onto the One-Dimensional Slower Reaction Coordinate Axis

We have derived here for the first time an exact dynamical equation within the domain of classical mechanics for the time dependent density distribution function of one-dimensional reaction coordinate (RC) in the condensed phase for electron transfer reaction by projecting the dynamics of slower modes in multidimensional Liouville space starting with a given set of coordinates of the faster modes. After the faster modes were ensemble averaged, the dynamics of the whole system solely depends on the slower RC. To simplify the complicated equation into a tractable form, benchmark approximations are employed to reduce the formally exact equation into an equation similar to the Smoluchowski equation with a delocalized sink term. As a test case, a Hamiltonian for the solute-solvent system modeled by quadratic functions for fast-relaxing vibrational and slow-relaxing polarization modes, respectively, has been considered. Interestingly, our simplified kinetic equation corresponding to this model Hamiltonian is transformed into the well-known phenomenological Sumi-Marcus equation.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.

Golden rule kinetics of transfer reactions in condensed phase: the microscopic model of electron transfer reactions in disordered solid matrices

The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k(B)T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 < 1 - 3) and for low (ξ0 ≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode∕medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the present approach to the Marcus ET theory and to the quantum-statistical reaction rate theory [V. G. Levich and R. R. Dogonadze, Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim. 124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.

Efficient algorithms for the simulation of non-adiabatic electron transfer in complex molecular systems: application to DNA

In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

Free radical scavenging by natural polyphenols: atom versus electron transfer

Polyphenols (synthetically modified or directly provided by human diet) scavenge free radicals by H-atom transfer and may thus decrease noxious effects due to oxidative stress. Free radical scavenging by polyphenols has been widely theoretically studied from the thermodynamic point of view whereas the kinetic point of view has been much less addressed. The present study describes kinetic-based structure-activity relationship for quercetin. This compound is very characteristic of the wide flavonoid subclass of polyphenols. H-atom transfer is a mechanism based on either atom or electron transfer. This is analyzed here by quantum chemical calculations, which support the knowledge acquired from experimental studies. The competition between the different processes is discussed in terms of the nature of the prereaction complexes, the pH, the formation of activated-deprotonated forms, and the atom- and electron-transfer efficiency. The role of the catechol moiety and the 3-OH group of quercetin as scavengers of different types of free radicals (CH3OO(•), CH3O(•), (•)OH, and (•)CH2OH) is rationalized. Identifying the exact mechanism and accurately evaluating kinetics is of fundamental importance to understand antioxidant behavior in physiological environments.

Quantum origins of molecular recognition and olfaction in Drosophila

The standard model for molecular recognition of an odorant is that receptor sites discriminate by molecular geometry as evidenced that two chiral molecules may smell very differently. However, recent studies of isotopically labeled olfactants indicate that there may be a molecular vibration-sensing component to olfactory reception, specifically in the spectral region around 2300 cm(-1). Here, we present a donor-bridge-acceptor model for olfaction which attempts to explain this effect. Our model, based upon accurate quantum chemical calculations of the olfactant (bridge) in its neutral and ionized states, posits that internal modes of the olfactant are excited impulsively during hole transfer from a donor to acceptor site on the receptor, specifically those modes that are resonant with the tunneling gap. By projecting the impulsive force onto the internal modes, we can determine which modes are excited at a given value of the donor-acceptor tunneling gap. Only those modes resonant with the tunneling gap and are impulsively excited will give a significant contribution to the inelastic transfer rate. Using acetophenone as a test case, our model and experiments on D. melanogaster suggest that isotopomers of a given olfactant give rise to different odorant qualities. These results support the notion that inelastic scattering effects may play a role in discriminating between isotopomers but that this is not a general spectroscopic effect.

Polaron formation: Ehrenfest dynamics vs. exact results

We use a one-dimensional tight binding model with an impurity site characterized by electron-vibration coupling, to describe electron transfer and localization at zero temperature, aiming to examine the process of polaron formation in this system. In particular we focus on comparing a semiclassical approach that describes nuclear motion in this many vibronic-states system on the Ehrenfest dynamics level to a numerically exact fully quantum calculation based on the Bonca-Trugman method [J. Bonča and S. A. Trugman, Phys. Rev. Lett. 75, 2566 (1995)]. In both approaches, thermal relaxation in the nuclear subspace is implemented in equivalent approximate ways: In the Ehrenfest calculation the uncoupled (to the electronic subsystem) motion of the classical (harmonic) oscillator is simply damped as would be implied by coupling to a Markovian zero temperature bath. In the quantum calculation, thermal relaxation is implemented by augmenting the Liouville equation for the oscillator density matrix with kinetic terms that account for the same relaxation. In both cases we calculate the probability to trap the electron by forming a polaron and the probability that it escapes to infinity. Comparing these calculations, we find that while both result in similar long time yields for these processes, the Ehrenfest-dynamics based calculation fails to account for the correct time scale for the polaron formation. This failure results, as usual, from the fact that at the early stage of polaron formation the classical nuclear dynamics takes place on an unphysical average potential surface that reflects the distributed electronic population in the system, while the quantum calculation accounts fully for correlations between the electronic and vibrational subsystems.

Engineered proteins: redox properties and their applications

Oxidoreductases and metalloproteins, representing more than one third of all known proteins, serve as significant catalysts for numerous biological processes that involve electron transfers such as photosynthesis, respiration, metabolism, and molecular signaling. The functional properties of the oxidoreductases/metalloproteins are determined by the nature of their redox centers. Protein engineering is a powerful approach that is used to incorporate biological and abiological redox cofactors as well as novel enzymes and redox proteins with predictable structures and desirable functions for important biological and chemical applications. The methods of protein engineering, mainly rational design, directed evolution, protein surface modifications, and domain shuffling, have allowed the creation and study of a number of redox proteins. This review presents a selection of engineered redox proteins achieved through these methods, resulting in a manipulation in redox potentials, an increase in electron-transfer efficiency, and an expansion of native proteins by de novo design. Such engineered/modified redox proteins with desired properties have led to a broad spectrum of practical applications, ranging from biosensors, biofuel cells, to pharmaceuticals and hybrid catalysis. Glucose biosensors are one of the most successful products in enzyme electrochemistry, with reconstituted glucose oxidase achieving effective electrical communication with the sensor electrode; direct electron-transfer-type biofuel cells are developed to avoid thermodynamic loss and mediator leakage; and fusion proteins of P450s and redox partners make the biocatalytic generation of drug metabolites possible. In summary, this review includes the properties and applications of the engineered redox proteins as well as their significance and great potential in the exploration of bioelectrochemical sensing devices.

Perfluorinated aromatic spacers for sensitizing europium(III) centers in dinuclear oligomers: better than the best by chemical design?

Transfer news: the use of a simple method allows the various sensitization steps in Eu(III) -containing complexes to be deciphered. Incorporation of an increasing number of electron-withdrawing fluorine atoms on the rigid and electronically tunable phenyl spacer between two tridentate binding units (see picture, red O, dark blue N) affects the quantum yield, intersystem crossing, and energy-transfer processes in a rational way.

Resolving the Electron Transfer Kinetics in the Bacterial Reaction Center by Pulse Polarized 2-D Photon Echo Spectroscopy

At the heart of photosynthesis is excitation energy transfer toward and charge separation within highly conserved reaction centers (RCs). The function principles of RCs in purple bacteria offer a blueprint for an optoelectronic device, which efficiently utilizes the near-IR region of the solar spectrum. We present theoretical modeling of the nonlinear optical response of the bacterial RC B. viridis incorporating electron and energy transfer on equal footing. The splitting of special pair excitons P is the origin of distinct cross peaks, which allow monitoring of the kinetics of charge separation. The xxyy - xyxy signal, obtained from sequences of orthogonal polarized laser pulses, highlights the kinetics of the secondary, subpicosecond electron transfer from the accessory bacteriochlorophyll BClL to the bacteriopheophytine BPL. The increased selectivity is explained by the relative orientation of exciton transitions. The technique can resolve complex kinetics in congested signals of photosynthetic complexes that are otherwise hardly accessible.

Electronic coupling for charge transfer in donor-bridge-acceptor systems. Performance of the two-state FCD model

Electronic coupling is a key parameter that determines the rate of electron transfer reactions and electrical conductivity of molecular wires. To examine the performance of a two-state approach based on the orthogonal transformation of adiabatic states to diabatic states, we compare the effective donor-acceptor coupling V(DA) computed with three different approaches in model donor-bridge-acceptor (D-B-A) systems. It is found that V(DA) derived with the two-state method accounts properly for both the direct and superexchange interactions. The approach becomes, however, less accurate with the increasing energy difference of the donor and acceptor states. We suggest a simple diagnostic to identify the situation when the estimated coupling might be inaccurate and consider how to improve the performance of the two-state scheme in such a case.

Orbital-Symmetry-Dependent Electron Transfer through Molecules Assembled on Metal Substrates

Femtosecond charge-transfer dynamics in self-assembled monolayers of cyano-terminated ethane-thiolate on gold substrates was investigated with the core hole clock method. By exploiting symmetry selection rules rather than energetic selection, electrons from the nitrogen K-shell are state-selectively excited into the two symmetry-split π* orbitals of the cyano end group with X-ray photons of well-defined polarization. The charge-transfer times from these temporarily occupied orbitals to the metal substrate differ significantly. Theoretical calculations show that these two π* orbitals extend differently onto the alkane backbone and the anchoring sulfur atom, thus causing the observed dependence of the electron-transfer dynamics on the symmetry of the orbital.

TOWARD THE MECHANISM OF LONG-RANGE CHARGE TRANSFER IN DNA: THEORIES AND MODELS

This article reviews our recent theoretical development toward understanding the interplay of electronic structure and dephasing effects on charge transfer/transport through molecular donor-bridge-acceptor systems. Both the generalized scattering matrix and Green's function formalisms for partially incoherent tunneling processes are summarized. Presented is also an exact mapping between the kinetic rate constants and the electric conductances in evaluation of chemical yields of sequential charge transfer in the presence of competing branching reactions. As an important example, the mechanism of long-range charge transfer in DNA in aqueous solution is investigated with a quantum chemistry implementation of the generalized Green's function formalism. A time scale of about 5 ps is found for the partially incoherent tunneling through a thymine/adenine π-stack in DNA. Numerical results further show that while the carrier oxidative charge does hop sequentially over all guanine sites in a DNA duplex, its tunneling over thymine/adenine bridge base pairs deviates substantially from the superexchange regime. Presented are also evidences for the involvement of both intrastrand and interstrand pathways in the ground state hole charge transfer in DNA.

A new approach to decoherence and momentum rescaling in the surface hopping algorithm

As originally proposed, the fewest switches surface hopping (FSSH) algorithm does not allow for decoherence between wavefunction amplitudes on different adiabatic surfaces. In this paper, we propose an inexpensive correction to standard FSSH dynamics wherein we explicitly model the decoherence of nuclear wave packets on distinct electronic surfaces. Our augmented fewest switches surface hopping approach is conceptually simple and, thus far, it has allowed us to capture several key features of the exact quantum results. Two points in particular merit attention. First, we obtain the correct branching ratios when a quantum particle passes through more than one region of nonadiabatic coupling. Second, our formalism provides a new and natural approach for rescaling nuclear momenta after a surface hop. Both of these features should become increasingly important as surface hopping schemes are applied to higher-dimensional problems.

Coherent site-directed transport in complex molecular networks: an effective Hamiltonian approach

Defining the conditions for coherent site-directed transport from an electron donor to a specific acceptor through tunneling barriers in a network of multiple donor/acceptors sites is an important step toward controlling electronic processes in molecular networks. The required analysis is most challenging since the entire network in essentially involved in coherent transport. In this work we introduce an efficient approach for formulating an effective donor/acceptor coupling in terms of the entire network parameters. The approach is based on implementation of Feshbach projection operators to map the entire network Hamiltonian onto a subspace defined by two specific donor and acceptor sites. This nonperturbative approach enables to define regimes of network parameters in which the effective donor-acceptor coupling is optimal. This is demonstrated numerically for simple models of molecular networks.

Quantum Smoluchowski equation: a systematic study

The strong-friction regime at low temperatures is analyzed systematically starting from the formally exact path-integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher-order quantum corrections to the original quantum Smoluchowski equation [J. Ankerhold, P. Pechukas, and H. Grabert, Phys. Rev. Lett. 87, 086802 (2001); J. Ankerhold and H. Grabert, Phys. Rev. Lett. 101, 119903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher-order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.

Collective effects in charge transfer within a hybrid organic-inorganic system

A collective electron transfer (ET) process was discovered by studying the current noise in a field effect transistor with light-sensitive gate formed by nanocrystals linked by organic molecules to its surface. Fluctuations in the ET through the organic linker are reflected in the fluctuations of the transistor conductivity. The current noise has an avalanche character. Critical exponents obtained from the noise power spectra, avalanche distributions, and the dependence of the average avalanche size on avalanche duration are consistent with each other. A plausible model is proposed for this phenomenon.

Unified expression for the rate constant of the bridged electron transfer derived by renormalization

Electron transfer (ET) from a donor to an acceptor through an energetically close intermediary state on a midway molecule is a process found often in natural and artificial solar-energy capturing systems such as photosynthesis. This process has often been thought of in terms of opposing "superexchange" and "sequential or hopping" mechanisms, and the recent theory of Sumi and Kakitani (SK) [J. Phys. Chem. B 105, 9603 (2001)] has shown an interpolation between these mechanisms. In their theory, however, dynamics governing the most interesting intermediary region between them has artificially been introduced by phenomenologies. The dynamics is played by decoherence among electronic states, their decay, and thermalization of phonons in the medium. The present work clarifies the dynamics on a microscopic basis by means of renormalization in electronic coupling among the states, and gives a complete unified expression of the rate constant of the ET. It merges to that given by the SK theory in the semiclassical approximation for phonons interacting with an electron transferred.