Dynamics of electron transfer in bacterial photosynthesis

Dynamic Formation of Metal-Based Traps in Photoexcited Colloidal Quantum Dots and Their Relevance for Photoluminescence

Trap states play a crucial role in the design of colloidal quantum dot (QD)-based technologies. The presence of these in-gap states can either significantly limit the efficiency of devices (e.g., in solar cells or LEDs) or play a pivotal role in the functioning of the technology (e.g., in catalysis). Understanding the atomistic nature of traps is therefore of the highest importance. Although the mechanism through which undercoordinated chalcogenide atoms can lead to trap states in II-VI QDs is generally well understood, the nature of metal-based traps remains more elusive. Previous research has shown that reduction of metal sites in negatively charged QDs can lead to in-gap states. Here, we use density functional theory to show that metal-based traps are also formed in charge-neutral but photoexcited CdSe QDs. It is found that Cd-Cd dimers and the concomitant trap states are transient in nature and appear and disappear on the picosecond time scale. Subsequent nonradiative recombination from the trap is shown to be much faster than radiative recombination, indicating that dimer-related trap states can quench the photoluminescence. These results are expected to be transferable to other II-VI materials and highlight the importance of surface redox reactions for the optical properties of QDs. Moreover, they show that photoexcitation can lead to atomic rearrangements on the surface and thus create transient in-gap states.

Vibrational decoherence induced by ultrafast intramolecular charge separation of an asymmetric bianthryl derivative

Coherent wavepacket oscillation accompanying the ultrafast photoexcited intramolecular charge separation (CS) of 9,9'-bianthryl (BA) and 10-cyano-9,9'-bianthryl (CBA) in a room temperature ionic liquid, N,N-diethyl-N-methyl-N-(methoxyethyl)ammonium tetrafluoroborate (DemeBF₄), was investigated by femtosecond time-resolved transient absorption spectroscopy. The frequency of the coherent oscillation observed for CBA in nonpolar n-hexane solution (Hex) was 377 cm^-1, while this oscillation was undetectable in DemeBF₄. For BA in DemeBF₄, coherent oscillation with a frequency of 394 cm^-1 was observed, which is similar to that for CBA in Hex. CS of CBA occurs in the ultrashort time range of ≤100 fs, while that of BA occurs in a few picosecond range [E. Takeuchi et al., J. Phys. Chem. C 120, 14502-14512 (2016)]. Hence, the oscillation of CBA in Hex and that of BA in DemeBF₄ are assigned to the molecular vibration in the locally excited state, while this oscillation dephases instantaneously for CBA in DemeBF₄ due to the ultrafast CS and no oscillation was generated in the CS state. This result suggests that the CS reaction is not mediated by a specific intramolecular vibration in the CS state but occurs incoherently through higher levels of multiple vibrational modes.

Reorganization energies of the electron transfer reactions involving quinones in the reaction center of Rhodobacter sphaeroides

In framework of the continuum electrostatics theory, the reorganization energies of the electron transfers Q_A^--Q_B (fast phase), Bph^--Q_A, P⁺-Q_A^-, and P⁺-Q_B^- in the photosynthetic bacterial reaction center have been calculated. The calculations were based on the static dielectric permittivity spatial distribution derived from the data on the electrogenesis, with the corresponding characteristic times relatively close to the reaction times of Q_A^--Q_B (fast phase) and Bph^--Q_A but much shorter than those times of the latter two recombination reactions. The calculated reorganization energies were reasonably close to the experimental estimates for Q_A^--Q_B (fast phase) and Bph^--Q_A but substantially lower than those of P⁺-Q_A^- and P⁺-Q_B^-. A higher effective dielectric permittivity contributes to this effect, but the dominant contribution is most probably made by a non-dielectric relaxation, especially for the P⁺-Q_B^- recombination influenced by the proton transfer. This situation calls for reconsidering of the current electron transfer rate estimates.

Excited state electron and energy relays in supramolecular dinuclear complexes revealed by ultrafast optical and X-ray transient absorption spectroscopy

The kinetics of photoinduced electron and energy transfer in a family of tetrapyridophenazine-bridged heteroleptic homo- and heterodinuclear copper(i) bis(phenanthroline)/ruthenium(ii) polypyridyl complexes were studied using ultrafast optical and multi-edge X-ray transient absorption spectroscopies. This work combines the synthesis of heterodinuclear Cu(i)-Ru(ii) analogs of the homodinuclear Cu(i)-Cu(i) targets with spectroscopic analysis and electronic structure calculations to first disentangle the dynamics at individual metal sites by taking advantage of the element and site specificity of X-ray absorption and theoretical methods. The excited state dynamical models developed for the heterodinuclear complexes are then applied to model the more challenging homodinuclear complexes. These results suggest that both intermetallic charge and energy transfer can be observed in an asymmetric dinuclear copper complex in which the ground state redox potentials of the copper sites are offset by only 310 meV. We also demonstrate the ability of several of these complexes to effectively and unidirectionally shuttle energy between different metal centers, a property that could be of great use in the design of broadly absorbing and multifunctional multimetallic photocatalysts. This work provides an important step toward developing both a fundamental conceptual picture and a practical experimental handle with which synthetic chemists, spectroscopists, and theoreticians may collaborate to engineer cheap and efficient photocatalytic materials capable of performing coulombically demanding chemical transformations.

Theory of Triplet Excitation Transfer in the Donor-Oxygen-Acceptor System: Application to Cytochrome b6f

Theoretical consideration is presented of the triplet excitation dynamics in donor-acceptor systems in conditions where the transfer is mediated by an oxygen molecule. It is demonstrated that oxygen may be involved in both real and virtual intramolecular triplet-singlet conversions in the course of the process under consideration. Expressions describing a superexchange donor-acceptor coupling owing to a participation of the bridging twofold degenerate oxygen's virtual singlet state are derived and the transfer kinetics including the sequential (hopping) and coherent (distant) routes are analyzed. Applicability of this theoretical description to the pigment-protein complex cytochrome b6f, by considering the triplet excitation transfer from the chlorophyll a molecule to distant β-carotene, is discussed.

Reactant-product quantum coherence in electron transfer reactions

We investigate the physical meaning of quantum superposition states between reactants and products in electron transfer reactions. We show that such superpositions are strongly suppressed and, to leading orders of perturbation theory, do not pertain in electron transfer reactions. This is because of the intermediate manifold of states separating the reactants from the products. We provide an intuitive description of these considerations with Feynman diagrams. We also discuss the relation of such quantum coherences to understanding the fundamental quantum dynamics of spin-selective radical-ion-pair reactions.

Charge transfer in model peptides: obtaining Marcus parameters from molecular simulation

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.

Novel mechanism for temperature-independent transitions in flexible molecules: role of thermodynamic fluctuations

A novel physical mechanism is proposed to explain the temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states. It is shown that at room temperatures, stochastic broadening of molecular energy levels predominates the energy of low-frequency vibrations accompanying the transition. This leads to a cancellation of temperature dependence in the stochastically averaged rate constants. As an example, a physical interpretation of temperature-independent onset of P2X{3} receptor desensitization in neuronal membranes is provided.

The Quantum Solvation, Adiabatic versus Nonadiabatic, and Markovian versus Non-Markovian Nature of Electron-Transfer Rate Processes

In this work, we revisit the electron-transfer rate theory, with particular interests in the distinct quantum solvation effect and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theor. Comput. Chem. 2006, 5, 685. Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier crossing to tunneling and from barrierless to quantum barrier crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.

On the quantum theory of electron transfer: Effect of potential surfaces of the reactants and products

In this study the electron transfer theory for the high frequency intramolecular mode and low frequency medium mode has been rederived using different methods. For a single-mode case when the reactant surface is not in a thermal equilibrium but in a thermocoherent state the authors have derived the rate and discussed about the quantum features of the rate. In the limit of very low and very high temperatures the expressions are derived analytically and compared with the case of thermal distribution. Secondly, a Franck-Condon factor for a multimode displaced, distorted, and Duschinsky rotated adiabatic potential surfaces has been derived to obtain the rate. Lastly, a systematic investigation is made to show the temperature dependence on the rate due to displacement, distortion, and Duschinsky rotation of the harmonic potential energy surfaces of the reactant and product manifold.

Electron transfer in proteins: nonorthogonal projections onto donor-acceptor subspace of the Hilbert space

We develop nonorthogonal projectors, called Löwdin projectors, to construct an effective donor-acceptor system composed of localized donor (D) and acceptor (A) states of a long-distance electron transfer problem. When these states have a nonvanishing overlap with the bridge states these projectors are non-Hermitian and there are various possible effective two-level systems that can be built. We show how these can be constructed directly from the Schrödinger or Dyson equation projected onto the D-A subspace of the Hilbert space and explore these equations to determine the connection between Hamiltonian and Green function partitioning. We illustrate the use of these effective two-level systems in estimating the electron transfer rate in the context of a simple electron transfer model.

Electron Transfer in Self-Assembled Orthogonal Structures

Two new molecular dyads, comprising pyrromethene (bodipy) and 2,2':6',2"-terpyridine (terpy) subunits, have been synthesized and fully characterized. Absorption and fluorescence spectral profiles are dominated by contributions from the bodipy unit. Zinc(II) cations bind to the vacant terpy ligand to form both 1:1 and 1:2 (cation:ligand) complexes, as evidenced by X-ray structural data, NMR and spectrophotometric titrations. Attachment of the cations is accompanied by a substantial decrease in fluorescence from the bodipy chromophore due to intramolecular electron transfer across the orthogonal structure. At low temperature, nuclear tunneling occurs and the rate of electron transfer is essentially activationless. However, activated electron transfer is seen at higher temperatures and allows calculation of the corresponding reorganization energy and electronic coupling matrix element. In both cases, charge recombination is faster than charge separation.

Stepwise assembly of acceptor--sigma spacer--donor monolayers: preparation and electrochemical characterization

Self-assembled monolayers comprising benzoquinone--methylene spacer--ferrocene molecules have been prepared on gold surfaces using a stepwise assembly procedure. A base monolayer of cystamine is formed on a gold surface. Benzoquinone is then attached to the amine end of the cystamine monolayer by a Michael's addition reaction. Subsequently, a diaminoalkane spacer of varying length is introduced. Finally, ferrocene is attached to the diamonoalkane spacer through an amide bond to complete the acceptor--sigma spacer--donor assembly. The distance between the two redox moieties has been varied systematically by altering the length of the alkyl chain spacer present between them. The quinone attachment to the cystamine monolayer leads to two different redox forms, a mono- and a diamino derivative. The pKa values have been evaluated for both of the derivatives. The monomolecular layer assembly has been characterized extensively using electrochemical techniques and the electrochemical kinetic parameters have been evaluated at different stages of modification.

Probability current in protein electron transfer reactions: A Green function pathway model

In a biological electron transfer reaction problem we have found distinct electron probability current representations of macromolecular currents, amino acid and interamino acid currents, atomic and interatomic currents. We present a general interatomic current approach to obtain the electron probability current from donor to acceptor sites, and vice versa. Symmetric (or antisymmetric) renormalizable interatomic currents provide exact (or approximate) effective tunneling matrix element between donor and acceptor states. The electron probability currents allow us to investigate stationary tunneling pathways through protein bridge medium, from molecular to subatomic resolution at any level of electronic description of the biological structure. Analytical comparison among interatomic pathway models is presented and we found equivalent interatomic current representations with distinct dependence on the tunneling energy from the weak to strong coupling between protein bridge and the donoracceptor sites.

Dynamics of electron transfer pathways in cytochrome C oxidase

Cytochrome c oxidase mediates the final step of electron transfer reactions in the respiratory chain, catalyzing the transfer between cytochrome c and the molecular oxygen and concomitantly pumping protons across the inner mitochondrial membrane. We investigate the electron transfer reactions in cytochrome c oxidase, particularly the control of the effective electronic coupling by the nuclear thermal motion. The effective coupling is calculated using the Green's function technique with an extended Huckel level electronic Hamiltonian, combined with all-atom molecular dynamics of the protein in a native (membrane and solvent) environment. The effective coupling between Cu(A) and heme a is found to be dominated by the pathway that starts from His(B204). The coupling between heme a and heme a(3) is dominated by a through-space jump between the two heme rings rather than by covalent pathways. In the both steps, the effective electronic coupling is robust to the thermal nuclear vibrations, thereby providing fast and efficient electron transfer.

Low dielectric response in enzyme active site

The kinetics of charge transfer depend crucially on the dielectric reorganization of the medium. In enzymatic reactions that involve charge transfer, atomic dielectric response of the active site and of its surroundings determines the efficiency of the protein as a catalyst. We report direct spectroscopic measurements of the reorganization energy associated with the dielectric response in the active site of alpha-chymotrypsin. A chromophoric inhibitor of the enzyme is used as a spectroscopic probe. We find that water strongly affects the dielectric reorganization in the active site of the enzyme in solution. The reorganization energy of the protein matrix in the vicinity of the active site is similar to that of low-polarity solvents. Surprisingly, water exhibits an anomalously high dielectric response that cannot be described in terms of the dielectric continuum theory. As a result, sequestering the active site from the aqueous environment inside low-dielectric enzyme body dramatically reduces the dielectric reorganization. This reduction is particularly important for controlling the rate of enzymatic reactions.

Electron transfer: classical approaches and new frontiers

Electron transfer, under conditions of weak interaction and a medium acting as a passive thermal bath, is very well understood. When electron transfer is accompanied by transient chemical bonding, such as in interfacial coordination electrochemical mechanisms, strong interaction and molecular selectivity are involved. These mechanisms, which take advantage of "passive self-organization," cannot yet be properly described theoretically, but they show substantial experimental promise for energy conversion and catalysis. The biggest challenge for the future, however, may be dynamic, self-organized electron transfer. As with other energy fluxes, a suitable positive feedback mechanism, through an active molecular environment, can lead to a (transient) decrease of entropy equivalent to an increase of molecular electronic order for the activated complex. A resulting substantial increase in the rate of electron transfer and the possibility of cooperative transfer of several electrons (without intermediates) can be deduced from phenomenological theory. The need to extend our present knowledge may be derived from the observation that chemical syntheses and fuel utilization in industry typically require high temperatures (where catalysis is less relevant), whereas corresponding processes in biological systems are catalyzed at environmental conditions. This article therefore focuses on interfacial or membrane-bound electron transfer and investigates an aspect that nature has developed to a high degree of perfection: self-organization.

Electron transfer and electronic energy relaxation under high hydrostatic pressure

The following question has been addressed in the present work. How external high (up to 8 kbar) hydrostatic pressure acts on photoinduced intramolecular electron transfer and on exciton relaxation processes? Unlike phenomena, as they are, have been studied in different systems: electron transfer in an artificial Zn-porphyrin-pyromellitimide (ZnP-PM) supramolecular electron donor-acceptor complex dissolved in toluene measured at room temperature; exciton relaxation in a natural photosynthetic antenna protein called FMO protein measured at low temperatures, between 4 and 100 K. Spectrally selective picosecond time-resolved emission technique has been used to detect pressure-induced changes in the systems. The following conclusions have been drawn from the electron transfer study: (i) External pressure may serve as a potential and sensitive tool not only to study, but also to control and tune elementary chemical reactions in solvents; (ii) Depending on the system parameters, pressure can both accelerate and inhibit electron transfer reactions; (iii) If competing pathways of the reaction are available, pressure can probably change the branching ratio between the pathways; (iv) The classical nonadiabatic electron transfer theory describes well the phenomena in the ZnP-PM complex, assuming that the driving force or/and reorganisation energy depend linearly on pressure; (v) A decrease in the ZnP-PM donor-acceptor distance under pressure exerts a minor effect on the electron transfer rate. The effect of pressure on the FMO protein exciton relaxation dynamics at low temperatures has been found marginal. This may probably be explained by a unique structure of the protein [D.E. Trondrud, M.F. Schmid, B.W. Matthews, J. Mol. Biol. 188 (1986) p. 443; Y.-F. Li, W. Zhou, E. Blankenship, J.P. Allen, J. Mol. Biol., submitted]. A barrel made of low compressibility beta-sheets may, like a diving bell, effectively screen internal bacteriochlorophyll a molecules from external influence of high pressure. The origin of the observed slow pico = and subnanosecond dynamics of the excitons at the exciton band bottom remains open. The phenomenon may be due to weak coupling of phonons to the exciton states or/and to low density of the relevant low-frequency ( approximately 50 cm(-1)) phonons. Exciton solvation in the surrounding protein and water-glycerol matrix may also contribute to this effect. Drastic changes of spectral, kinetic and dynamic properties have been observed due to protein denaturation, if the protein was compressed at room temperature and then cooled down, as compared to the samples, first cooled and then pressurised.