A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.     

Solvent reorganization in electron and ion transfer reactions near a smooth electrified surface: a molecular dynamics study

Molecular dynamics simulations of electron and ion transfer reactions near a smooth surface are presented, analyzing the effect of the geometrical constraint of the surface and the interfacial electric field on the relevant solvation properties of both a monovalent negative ion and a neutral atom. The simulations show that, from the solvation point of view, ion adsorption is an uphill process due to the need to shed off the ion's solvation shell and displace water from the surface. Atom adsorption, on the other hand, has only a small barrier, related to the molecularity of the solvent. Both the electrostatic interaction of the ion with the solvent and the ion's solvent reorganization energy (the relevant parameter in the Marcus electron transfer theory) decrease as the surface is approached, whereas these parameters are not sensitive to the distance from the surface for the atom. This is a consequence of the importance of long-range electrostatic interactions for ion solvation and the importance of short-range interactions for atom solvation. The electric field either attracts or repels an ion to or from the surface, but the field has no influence on the solvent reorganization energy. By including the quantum-mechanical electron transfer between the metal surface and the ion/atom in solution in the MD simulation by using a model Hamiltonian, we calculated two-dimensional free energy surfaces for ion adsorption allowing for partial charge transfer, based on a fully molecular picture of ion solvation near the surface.     

Charge separation reaction in clusters of polar molecules: MD simulations

Rate constant of intermolecular electron transfer (ET) in a photoexcited donor-acceptor model system solvated by a cluster of polar molecules has been expressed in terms of the statistical distribution of the electrostatic potential energy difference between the reacting sites. This distribution has been calculated for a particular case of acetonitrile clusters a ≈120 K by MD computer simulation. The MD values of the cluster reorganization energy and the ET rate constant have been compared with the corresponding MD results for the donor-acceptor pair solvated in bulk acetonitrile and with theoretical predictions based on the continuum model.     

Energetics of Photoinduced Electron Transfer in the Indole-O2 Cluster in Gas Phase: Possible Consequences for Photoexcited Tryptophan in Solution

Abstract— A direct process for an activationless electron transfer from photoexcited tryptophan to molecular oxygen is proposed. By photodetachment of mass-selected indole-O_2- clusters in gas phase a neutral indole₊ O_2- charge-separated exciplex state is found at 2.25 0.2 eV above the neutral ground state. By theory also, the existence of an excited charge separated state at 3.05 0.2 eV is postulated. In gas phase both charge-separated cluster states are energetically below the first singlet states ₁L_b and ₁L_a and the lower even below the first triplet state T₁ of indole. In gas-phase clusters these energetics imply a very efficient quenching of photoexcited indole by fast electron transfer to oxygen. We discuss a similar mechanism for tryptophan-O₂ in aqueous environment and find it without activation barrier and presumably extremely fast. In the collisional tryptophan_*-O₂ complex the efficiency and the time scale of the charge transfer process should be mostly solvent independent. In polar solvent a complete charge separation and free superoxide formation are expected. We correlate this model with previous fluorescence and phosphorescence quenching data of excited tryptophan by O₂ and propose electron transfer to be the relevant process.     

Energy gap law of electron transfer in nonpolar solvents

We investigate the energy gap law of electron transfer in nonpolar solvents for charge separation and charge recombination reactions. In polar solvents, the reaction coordinate is given in terms of the electrostatic potentials from solvent permanent dipoles at solutes. In nonpolar solvents, the energy fluctuation due to solvent polarization is absent, but the energy of the ion pair state changes significantly with the distance between the ions as a result of the unscreened strong Coulomb potential. The electron transfer occurs when the final state energy coincides with the initial state energy. For charge separation reactions, the initial state is a neutral pair state, and its energy changes little with the distance between the reactants, whereas the final state is an ion pair state and its energy changes significantly with the mutual distance; for charge recombination reactions, vice versa. We show that the energy gap law of electron-transfer rates in nonpolar solvents significantly depends on the type of electron transfer.     

A surface science approach to ultrafast electron transfer and solvation dynamics at interfaces

Excess electrons in polar media, such as water or ice, are screened by reorientation of the surrounding molecular dipoles. This process of electron solvation is of vital importance for various fields of physical chemistry and biology as, for instance, in electrochemistry or photosynthesis. Generation of such excess electrons in bulk water involves either photoionization of solvent molecules or doping with e.g. alkali atoms, involving possibly perturbing interactions of the system with the parent-cation. Such effects are avoided when using a surface science approach to electron solvation: in the case of polar adsorbate layers on metal surfaces, the substrate acts as an electron source from where photoexcited carriers are injected into the adlayer. Besides the investigation of electron solvation at such interfaces, this approach allows for the investigation of heterogeneous electron transfer, as the excited solvated electron population continuously decays back to the metal substrate. In this manner, electron transfer and solvation processes are intimately connected at any polar adsorbate-metal interface. In this tutorial review, we discuss recent experiments on the ultrafast dynamics of photoinduced electron transfer and solvation processes at amorphous ice-metal interfaces. Femtosecond time-resolved two-photon photoelectron spectroscopy is employed as a direct probe of the electron dynamics, which enables the analysis of all elementary processes: the charge injection across the interface, the subsequent electron localization and solvation, and the dynamics of electron transfer back to the substrate. Using surface science techniques to grow and characterize various well-defined ice structures, we gain detailed insight into the correlation between adsorbate structure and electron solvation dynamics, the location (bulk versus surface) of the solvation site, and the role of the electronic structure of the underlying metal substrate on the electron transfer rate.     

Environmental control of primary photochemistry in a mutant bacterial reaction center

The core structure of the photosynthetic reaction center is quasisymmetric with two potential pathways (called A and B) for transmembrane electron transfer. Both the pathway and products of light-induced charge separation depend on local electrostatic interactions and the nature of the excited states generated at early times in reaction centers isolated from Rhodobacter sphaeroides. Here transient absorbance measurements were recorded following specific excitation of the Q(y)() transitions of P (the special pair of bacteriochlorophylls), the monomer bacteriochlorophylls (B(A) and B(B)), or the bacteriopheophytins (H(A) and H(B)) as a function of both buffer pH and detergent in a reaction center mutant with the mutations L168 His to Glu and L170 Asn to Asp in the vicinity of P and B(B). At a low pH in any detergent, or at any pH in a nonionic detergent (Triton X-100), the photochemistry of this mutant is faster than, but similar to, wild type (i.e. electron transfer occurs along the A-side, 390 nm excitation is capable of producing short-lived B-side charge separation (B(B)(+)H(B)(-)) but no long-lived B(B)(+)H(B)(-) is observed). Certain buffering conditions result in the stabilization of the B-side charge separated state B(B)(+)H(B)(-), including high pH in the zwitterionic detergent LDAO, even following excitation with low energy photons (800 or 740 nm). The most striking result is that conditions giving rise to stable B-side charge separation result in a lack of A-side charge separation, even when P is directly excited. The mechanism that links B(B)(+)H(B)(-) stabilization to this change in the photochemistry of P in the mutant is not understood, but clearly these two processes are linked and highly sensitive to the local electrostatic environment produced by buffering conditions (pH and detergent).     

The key role of solvation dynamics in intramolecular electron transfer: time-resolved photophysics of crystal violet lactone

The intramolecular electron-transfer reaction in crystal violet lactone in polar aprotic solvents is studied with femtosecond transient absorption spectroscopy. The initially excited charge transfer state (1)CT A is rapidly converted into a highly polar charge transfer state (1)CT B. This ultrafast electron transfer is seen as a solvent-dependent dual fluorescence in steady-state spectra. We find that the electron-transfer process can be followed by a change from a double-peaked transient absorption spectrum to a single-peak one in the low picosecond range. The transient absorption kinetic curves are multiexponential, and the fitted time constants are solvent dependent but do not reproduce the known solvation times. For 6-dimethylaminophthalide, the optically active constituent of crystal violet lactone, only a small temporal evolution of the spectra is found. To explain these findings, we present a model that invokes a time-dependent electron-transfer rate. The rate is determined by the instantaneous separation of the two charge-transfer states. Because of their differing dipole moments, they are dynamically lowered to a different extent by the solvation. When they temporarily become isoenergetic, equal forward and backward transfer rates are reached. The intrinsic electron-transfer ( (1)CT A --> (1)CT B) reaction is probably as fast as that in the structurally analogous malachite green lactone (on the 100 fs time scale). The key element for the dynamics is therefore its control by the solvent, which changes the relative energetics of the two states during the solvation process. With further stabilization of the more polar state, the final equilibrium in state population is reached.     

Fluorescence quenching induced by conformational fluctuations in unsolvated polypeptides

Time-resolved measurements were conducted to relate the fluorescence lifetimes of dye-derivatized polypeptides to local conformational dynamics in trapped, unsolvated peptide ions. This research was performed to better understand the intramolecular interactions leading to the observed increase of fluorescence quenching with temperature and, in particular, how this quenching is related to conformational fluctuations. Dye-derivatized polyproline ions, Dye-[Pro] n -Arg (+)-Trp, are formed by electrospray ionization and trapped in a variable-temperature quadrupole ion trap where they are exposed to a pulsed laser which excites fluorescence. Lifetime data exhibit fluorescence quenching as a result of an interaction between the dye and tryptophan (Trp) side chain. This result is consistent with solution measurements performed for comparison. The lifetime temperature dependence is closely fit over the range 150-463 K by an Arrhenius model of the ensemble averaged quenching rate, k q. Model fits of the measured lifetimes yield a frequency prefactor of approximately 10 (11) s (-1) for k q characteristic of collective motions of the side chains identified in molecular dynamics (MD) simulations. The data fits also yield activation barriers of approximately 0.3 eV, which are comparable to intramolecular electrostatic interactions calculated between the unshielded charge on the Arg residue and the dye. As a result, the quenching rate appears to be determined by the rate of conformational fluctuations and not by the rate of a specific quenching mechanism. The peptide sequence of Dye-Trp-[Pro] n -Arg (+) was also studied and identified a dependence of the quenching rate on the electrostatic field in the vicinity of the dye, Trp pair. Molecular dynamics simulations were performed over the range of experimental measurements to study trajectories relevant to the quenching interaction. The MD simulations indicate that as the temperature is increased, conformational fluctuations in the presence of strong electrostatic fields of the charged Arg (+) residue can result in both (a) an increased number of dye and Trp separations <8 A and (b) increased exothermicity for electron transfer reactions between the dye and Trp. Consequently, the MD simulations are consistent with increased fluorescence quenching with temperature resulting from the occurrence of conformers having specific positions of the dye, Trp, and Arg (+). As a result, the fluorescence lifetime provides a local probe of conformational fluctuations averaged over the ion ensemble.     

Model Reactions for Photosynthesis—Photoinduced Charge and Energy Transfer between Covalently Linked Porphyrin and Quinone Units

Photosynthesis is one of the fascinating fields of current interdisciplinary research. It seems miraculous that nature, in the process of evolution, has managed to bring about the process of photosynthesis. The first step involves a charge separation at the reaction centers, which proceeds with 100% quantum yield from the photoexcited singlet state of the bacteriochlorophyll donor, despite the fact that the wasteful deactivation of the electron into the ground state should be highly favored. Biomimetic model compounds (that is, those which resemble the pigments nature has developed) have been constructed from porphyrins and quinones. These model systems have allowed the study of the factors contributing to the highly efficient charge separation. This report focuses on recent developments in the study of electron transfer in porphyrinoquinones. Some of the results of these investigations may not be not fully understood and are often the subject of controversial discussions.     

Theoretical investigation of charge transfer excitation and charge recombination in acenaphthylene–tetracyanoethylene complex

Ab initio calculations were performed to investigate the charge separation and charge recombination processes in the photoinduced electron transfer reaction between tetracyanoethylene and acenaphthylene. The excited states of the charge‐balanced electron donor–acceptor complex and the singlet state of ion pair complex were studied by employing configuration interaction singles method. The equilibrium geometry of electron donor–acceptor complex was obtained by the second‐order Møller–Plesset method, with the interaction energy corrected by the counterpoise method. The theoretical study of ground state and excited states of electron donor–acceptor complex in this work reveals that the S₁ and S₂ states of the electron donor–acceptor complexes are excited charge transfer states, and charge transfer absorptions that corresponds to the S₀ → S₁ and S₀ → S₂ transitions arise from π–π* excitations. The charge recombination in the ion pair complex will produce the charge‐balanced ground state or excited triplet state. According to the generalized Mulliken–Hush model, the electron coupling matrix elements of the charge separation process and the charge recombination process were obtained. Based on the continuum model, charge transfer absorption and charge transfer emission in the polar solvent of 1,2‐dichloroethane were investigated. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 23–35, 2003     

Theoretical study of proton coupled electron transfer reaction in the light state of the AppA BLUF photoreceptor

The BLUF (blue light sensor using flavin adenine dinucleotide) domain is widely studied as a prototype for proton coupled electron transfer (PCET) reactions in biological systems. In this work, the photo-induced concerted PCET reaction from the light state of the AppA BLUF domain is investigated. To model the simultaneous transfer of two protons in the reaction, two-dimensional potential energy surfaces for the double proton transfer are first calculated for the locally excited and charge transfer states, which are then used to obtain the vibrational wave function overlaps and the vibrational energy levels. Contributions to the PCET rate constant from each pair of vibronic states are then analyzed using the theory based on the Fermi's golden rule. We show that, the recently proposed light state structure of the BLUF domain with a tautomerized Gln63 residue is consistent with the concerted transfer of one electron and two protons. It is also found that, thermal fluctuations of the protein structure, especially the proton donor-acceptor distances, play an important role in determining the PCET reaction rate. © 2018 Wiley Periodicals, Inc.     

The effects of charge transfer on the aqueous solvation of ions

Ab initio-based charge partitioning of ionic systems results in ions with non-integer charges. This charge-transfer (CT) effect alters both short- and long-range interactions. Until recently, the effects of CT have been mostly neglected in molecular dynamics (MD) simulations. The method presented in this paper for including charge transfer between ions and water is consistent with ab initio charge partitioning and does not add significant time to the simulation. The ions of sodium, potassium, and chloride are parameterized to reproduce dimer properties and aqueous structures. The average charges of the ions from MD simulations (0.900, 0.919, and -0.775 for Na(+), K(+), and Cl(-), respectively) are consistent with quantum calculations. The hydration free energies calculated for these ions are in agreement with experimental estimates, which shows that the interactions are described accurately. The ions also have diffusion constants in good agreement with experiment. Inclusion of CT results in interesting properties for the waters in the first solvation shell of the ions. For all ions studied, the first shell waters acquire a partial negative charge, due to the difference between water-water and water-ion charge-transfer amounts. CT also reduces asymmetry in the solvation shell of the chloride anion, which could have important consequences for the behavior of chloride near the air-water interface.     

Molecular simulations of outersphere reorganization energies in polar and quadrupolar solvents. The case of intramolecular electron and hole transfer

Outersphere reorganization energies (lambda) for intramolecular electron and hole transfer are studied in anion- and cation-radical forms of complex organic substrates (p-phenylphenyl-spacer-naphthyl) in polar (water, 1,2-dichloroethane, tetrahydrofuran) and quadrupolar (supercritical CO2) solvents. Structure and charge distributions of solute molecules are obtained at the HF/6-31G(d,p) level. Standard Lennard-Jones parameters for solutes and the nonpolarizable simple site-based models of solvents are used in molecular dynamics (MD) simulations. Calculation of lambda is done by means of the original procedure, which treats electrostatic polarization of a solvent in terms of a usual nonpolarizable MD scheme supplemented by scaling of reorganization energies at the final stage. This approach provides a physically relevant background for separating inertial and inertialless polarization responses by means of a single parameter epsilon(infinity), optical dielectric permittivity of the solvent. Absolute lambda values for hole transfer in 1,2-dichloroethane agree with results of previous computations in terms of the different technique (MD/FRCM, Leontyev, I. V.; et al. Chem. Phys. 2005, 319, 4). Computed lambda values for electron transfer in tetrahydrofuran are larger than the experimental values by ca. 2.5 kcal/mol; for the case of hole transfer in 1,2-dichloroethane the discrepancy is of similar magnitude provided the experimental data are properly corrected. The MD approach gives nonzero lambda values for charge-transfer reaction in supercritical CO2, being able to provide a uniform treatment of nonequilibrium solvation phenomena in both quadrupolar and polar solvents.     

Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics

Photoinduced proton transfer in the Watson-Crick guanine (G)-cytosine (C) base pair has been studied using Car-Parrinello molecular dynamics (CP-MD). A flexible mechanical constraint acting on all three hydrogen bonds in an unbiased fashion has been devised to explore the free energy profile along the proton transfer coordinate. The lowest barrier has been found for proton transfer from G to C along the central hydrogen bond. The resulting charge transfer excited state lies energetically close to the electronic ground state suggesting the possibility of efficient radiationless decay. It is found that dynamic, finite temperature fluctuations significantly reduce the energy gap between the ground and excited states for this charge transfer product, promoting the internal conversion process. A detailed analysis of the internal degrees of freedom reveals that the energy gap is considerably reduced by out-of-plane molecular vibrations, in particular. Consequently, it appears that considering only the minimum energy path provides an upper-bound estimate of the associated energy gap compared to the full-dimension dynamical reaction coordinate. Furthermore, the first CP-MD simulations of the G-C base pair in liquid water are presented, and the effects of solvation on its electronic structure are analyzed.     

Influence of thermal fluctuations on interfacial electron transfer in functionalized TiO2 semiconductors

The influence of thermal fluctuations on the dynamics of interfacial electron transfer in sensitized TiO2-anatase semiconductors is investigated by combining ab initio DFT molecular dynamics simulations and quantum dynamics propagation of transient electronic excitations. It is shown that thermal nuclear fluctuations speed up the underlying interfacial electron transfer dynamics by introducing nonadiabatic transitions between electron acceptor states, localized in the vicinity of the photoexcited adsorbate, and delocalized states extended throughout the semiconductor material, creating additional relaxation pathways for carrier diffusion. Furthermore, it is shown that room-temperature thermal fluctuations reduce the anisotropic character of charge diffusion along different directions in the anatase crystal and make similar the rates for electron injection from adsorbate states of different character. The reported results are particularly relevant to the understanding of temperature effects on surface charge separation mechanisms in molecular-based photo-optic devices.     

Two-dimensional free-energy surface on the exchange reaction of alkyl chloride/chloride using the QM/MM-MC method

Two-dimensional free-energy surfaces are calculated for alkyl chloride/chloride exchange/inversion reactions: Cl(-)+RCl (R=Me and t-Bu) surrounded by one hundred H(2)O molecules as a model of solvent. The methodology of free-energy calculation by perturbation theory based on a mixed-Hamiltonian model (QM/MM) combined with Monte Carlo sampling of the solvent configurations was used to obtain the changes in solvation free energy. We devised a special procedure to analyze the two-dimensional free-energy surfaces to gain unique insight into the differences in the reaction mechanisms between the two systems. The inversion reaction path for R=t-Bu on the free-energy surface is found to proceed in an asynchronous way within a concerted framework via the ion-pair region. This is in contrast to the R=Me system that proceeds as a typical S(N)2 reaction.     

Simulation of the electron transfer between the tetraheme subunit and the special pair of the photosynthetic reaction center using a microstate description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.     

Primary processes in plant photosynthesis: photosystem I reaction center

The photosystem I (PSI) pigment-protein complex of plants converts light energy into a transmembrane charge separation, which ultimately leads to the reduction of carbon dioxide. Recent studies on the dynamics of primary energy transfer, charge separation, and following electron transfer of the reaction center (RC) of the PSI prepared from spinach are reviewed. The main results of femtosecond transient absorption and fluorescence spectroscopies as applied to the P700-enchied PSI RC are summarized. This specially prepared material contains only 12–14 chlorophylls per P700, which is a special pair of chlorophyll a and has a significant role in primary charge separation. The P700-enriched particles are useful to study dynamics of cofactors, since about 100 light-harvesting chlorophylls are associated with wild PSI RC and prevent one from observing the elementary steps of the charge separation. In PSI RC energy and electron transfer were found to be strongly coupled and an ultrafast up-hill energy equilibration and charge separation were observed upon preferential excitation of P700. The secondary electron-transfer dynamics from the reduced primary electron acceptor chlorophyll a to quinone are described. With creating free energy differences (ΔG₀) for the reaction by reconstituting various artificial quinones and quinoids, the rate of electron transfer was measured. Analysis of rates versus ΔG₀ according to the quantum theory of electron transfer gave the reorganization energy, electronic coupling energy and other factors. It was shown that the natural quinones are optimized in the photosynthetic protein complexes. The above results were compared with those of photosynthetic purple bacteria, of which the structure and functions have been studied most.