Simultaneous analyses of photoinduced electron transfer in the wild type and four single substitution isomers of the FMN binding protein from Desulfovibrio vulgaris, Miyazaki F

The mechanism of photoinduced electron transfer (PET) from the aromatic amino acids (Trp32, Tyr35 and Trp106) to the excited flavin mononucleotide (FMN) in the wild type (WT) and four single amino acid substitution isomers (E13T, E13Q, W32A and W32Y) of FMN binding protein (FBP) from the Desulfovibrio vulgaris (Miyazaki F) were simultaneously analyzed (Method A) with the Marcus-Hush (MH) theory and Kakitani-Mataga (KM) theory using ultrafast fluorescence dynamics of these proteins. In addition, the PET mechanism of the WT, E13T and E13Q FBP systems (Method B) were also analyzed with both MH and KM theories. The KM theory could describe all of the experimental fluorescence decays better than the MH theory by both Methods A and B. The PET rates were found to largely depend on the electrostatic energies between photo-products, isoalloxazine (Iso) anion and the PET donor cations, and the other ionic groups, and hence on static dielectric constants. The dielectric constant (ε(0)(DA)) around the PET donors and acceptor was separately determined from those (ε(0)(j), j = WT, E13T, E13Q, W32Y and W32A) in the domain between the Iso anion or the donor cations and the other ionic groups in the proteins. The values of ε(0)(DA) were always lower than those of ε(0)(j), which is reasonable because no amino acid exists between the PET donors and acceptor in all systems. The values of the dielectric constants ε(0)(j) (j = WT, E13T and E13Q) were similar to those obtained previously from the analysis of the crystal structures and the average lifetimes of these FBP proteins. Energy gap law in the FBP systems was examined. An excellent parabolic function of the logarithms of the PET rates was obtained against the total free energy gap. The PET in these FBP isomers mostly took place in the so-called normal region, and partly in the inverted region.     

Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling T(DA) of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate T(DA). Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable T(DA) for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.     

Ab initio calculation for inner reorganization energy of gas-phase electron transfer in organic molecule–ion systems

A series of electron transfer (ET) reactions between some organic molecules have been investigated through ab initio calculations. Biphenyl (Bp) and 9,9^′-dimethylfluorene anion radicals are chosen as the donor, whereas several organic molecules with different redox abilities are chosen as the acceptor. The inner reorganization energy and the endothermicity of the ET reactions in those molecule–ion systems have been estimated through the HFSCF and complete active space multiconfiguration SCF calculations. Double-well potentials for the gas-phase ET reactions have been constructed using the linear reaction coordinate, and the results show that the quinone-containing ET reactions are in Marcus' inverted region. It has been found that the inner reorganization energies are different for various donor-acceptor couples, unlike the experimentally fitted ones. The contribution from the inter-ring torsional motion in Bp to the inner reorganization energy has been evaluated from the energy difference of the biphenyl-acceptor and the dimethylfluorine-acceptor systems. Comparisons with the experimentally observed results have been made.     

Electron transfer reactions of fluorotyrosyl radicals

The complex Re(bpy)(CO)3CN is an excited state oxidant of tyrosine upon deprotonation of the tyrosyl phenol. A series of Re(bpy-FnY)(CO)3CN complexes ([Re]-FnY: [Re]-Y, [Re]-3-FY, [Re]-3,5-F2Y, [Re]-2,3-F2Y, [Re]-2,3,5-F3Y, [Re]-2,3,6-F3Y, and [Re]-F4Y) have been prepared so as to vary the FnY*/FnY- reduction potential and thus the driving force for electron transfer in this system. Time-resolved emission and nanosecond absorption spectroscopies have been used to measure the rates for charge separation, CS, and charge recombination, CR, for each complex. A driving force analysis reveals that CS is well described by Marcus' theory for ET, is strongly driving force dependent (activated), and occurs in the normal region for ET. CR, on the other hand, is weakly driving force dependent (near activationless) and occurs in the inverted region for ET. These data demonstrate that fluorotyrosines will be powerful probes for unraveling charge transport mechanisms in enzymes that utilize tyrosyl radicals.     

Non-Condon效应对电子转移速率影响的理论模拟及其在有机半导体中的应用

随着Condon近似下各种电子转移理论的不断发展与完善和人们对non-Condon效应在电子转移过程中重要作用认识的逐步深入,已建立了几个理论模型来研究这种效应对电子转移速率的影响.本文主要总结了近两年来我们在non-Condon效应电子转移理论方面的工作,首先阐述了指数型、高斯型以及直线型non-Condon电子转移速率的全量子表达式,然后运用该理论模型以及分子动力学模拟计算了二噻吩四硫富瓦烯（DT-TTF）有机半导体的迁移率.此外,还进一步利用数值模拟详细研究了这三种线型的non-Condon效应在量子尺度上对电子转移速率的影响.     

Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach

Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H(2)O)(6)(2+/3+) and Ru(H(2)O)(6)(2+/3+). The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.     

Average electron tunneling route of the electron transfer in protein media

We present a new theoretical method to determine and visualize the average tunneling route of the electron transfer (ET) in protein media. In this, we properly took into account the fluctuation of the tunneling currents and the quantum-interference effect. The route was correlated with the electronic factor in the case of ET by the elastic tunneling mechanism. We expanded by the interatomic tunneling currents 's. Incorporating the quantum-interference effect into the mean-square interatomic tunneling currents, denoted as , we could express as a sum of variant Planck's over 2pi(2). Drawing the distribution of on the protein structure, we obtain the map which visually represents which parts of bonds and spaces most significantly contribute to . We applied this method to the ET from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobacter sphaeroides. We obtained 's by a combined method of molecular dynamics simulations and quantum chemical calculations. In calculating , we found that much destructive interference works among the interatomic tunneling currents even after taking the average. We drew the map by a pipe model where atoms a and b are connected by a pipe with width proportional to the magnitude of . We found that two groups of 's, which are mutually coupled with high correlation in each group, have broad pipes and form the average tunneling routes, called Trp route and Met route. Each of the two average tunneling routes is composed of a few major pathways in the Pathways model which are fused at considerable part to each other. We also analyzed the average tunneling route for the ET by the inelastic tunneling mechanism.     

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.     

Anomalous temperature-isotope dependence in proton-coupled electron transfer

Motivated by the experiments of Hodgkiss et al. [J. Phys. Chem. (submitted)] on electron transfer (ET) through a H-bonding interface, we present a new theoretical model for proton-coupled electron transfer (PCET) in the condensed phase, that does not involve real proton transfer. These experiments, which directly probe the joint T-isotope effects in coupled charge transfer reactions, show anomalous T dependence in k(H)k(D), where k(H) and k(D) are the ET rates through the H-bonding interface with H-bonded protons and deuterons, respectively. We address the anomalous T dependence of the k(H)k(D) in our model by attributing the modulation of the electron tunneling dynamics to bath-induced fluctuations in the proton coordinate, so that the mechanism for coupled charge transfer might be better termed vibrationally assisted ET rather than PCET. We argue that such a mechanism may be relevant to understanding traditional PCET processes, i.e., those in which protons undergo a transfer from donor to acceptor during the course of ET, provided there is an appropriate time scale separating both coupled charge transfers. Likewise, it may also be useful in understanding long-range ET in proteins, where tunneling pathways between redox cofactors often pass through H-bonded amino acid residues, or other systems with sufficiently decoupled proton and electron donating functionalities.     

Interference, fluctuation, and alternation of electron tunneling in protein media. 1. Two tunneling routes in photosynthetic reaction center alternate due to thermal fluctuation of protein conformation

Electron tunneling routes for the electron transfer from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobactor sphaeroides are investigated by a combined method of molecular dynamics simulations for the protein conformation fluctuation and quantum chemical calculations for the electronic states of the donor, acceptor, and protein medium. The analysis of the tunneling route is made by mapping interatomic electron tunneling currents for each protein conformation. We found that there are two dominant routes mainly passing through Trp(M252) (Trp route) or mainly passing through Met(M218) (Met route). Actual electron tunneling pathways alternate between the two routes, depending on the protein conformation which varies with time. When either the Trp route or the Met route dominates, the electron tunneling matrix element /T(DA)/ becomes large. When both the Trp route and the Met route dominate, /T(DA)/ becomes very small due to the destructive interference of the electron tunneling currents between the two routes. We found that a linear relationship exists between the value of /T(DA)/ and the inverse of the degree of destructive interference Q for a wide range of values (ca. 3-10(3) for Q). A similar relationship was also found previously for electron transfer in ruthenium-modified azurins, suggesting that this relationship holds true in general. From these results, we are led to the conclusion that /T(DA)/ cannot exceed a maximum value at Q = 1, even if much variation of /T(DA)/ happens due to the fluctuation of protein conformation. We also conclude that the property of the electron transfer alternates between constructive and destructive interference, due to the fluctuation of protein conformation. It is impossible to keep a system in either constructive or destructive interference because thermal fluctuation of protein conformation takes place.     

反转区电子转移速率的理论研究

利用级联方程方法研究了反转区的电子转移速率与电子态耦合常数以及溶剂弛豫时间的关系.结果表随着电子态间耦合强度的增加,反应速率先增加然后减小,而随着溶剂弛豫时间的减小反应速率增加.我们将这些结果与近似理论费米黄金规则、Landau-Zener公式进行了比较,由于费米金规则基于一阶微扰论,所以只适用于耦合常数较小的情况.而Landau-Zener公式假设电子在跃迁区域弹道运动,在电子态耦合大的情况下也存在问题.     

Synthesis of directly linked zinc(II) porphyrin-imide dyads and energy gap dependence of intramolecular electron transfer reactions

A series of zinc(II) porphyrin-imide dyads (ZP-Im), in which an electron donating ZP moiety is directly connected to an electron accepting imide moiety in the meso position, have been prepared for the examination of energy gap dependence of intramolecular electron transfer reactions with large electronic coupling. The nearly perpendicular conformation of the imide moiety towards the porphyrin plane has been revealed by Xray crystal structures. The energy gap for charge separation, 1ZP* - Im --> ZP+ - Im-, is varied by changing the electron accepting imide moiety to cover a range of about 0.8 eV in DMF. Definitive evidence for electron transfer has been obtained in three solvents (toluene, THF, and DMF) through picosecond-femtosecond transient absorption studies, which have allowed us to determine the rates of photoinduced charge separation, 1ZP* - Im --> ZP+ - Im-, and subsequent thermal charge recombination ZP+ - Im- --> ZP - Im. The free-energy gap dependence (energy gap law) has been probed from the normal to the nearly top region for the charge separation rate alone, and only the inverted region for the charge recombination rate. Although both of the energy gap dependencies can be approximately reproduced by means of the simplified semiclassical equation, when we take into consideration the effect of the high frequency vibrations replaced by one mode of averaged frequency, many features, including the effects of solvent polarity and the electron tunneling matrix element on the energy gap law, differ considerably from those of the previously studied porphyrin-quinone systems, which have weaker interchromophore electronic interactions.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Semiclassical treatments of electron transfer rate from weak to strong electronic coupling regime

Electron transfer (ET) rate is a fundamental parameter to characterize ET processes in physical, chemical, material and biologic sciences. It is affected by a number of quantum phenomena, such as nuclear tunneling, curve crossing, quantum interference, and the coupling to the environment. It is thus a challenge to accurately evaluate the ET rate since one has to incorporate both quantum effects and dissipation. In this review article, we present several semiclassical theories proposed in our group to cover the regime from weak to strong electronic coupling. Their applications to some concrete systems are also shown.     

Noise-assisted quantum electron transfer in photosynthetic complexes

Electron transfer (ET) between primary electron donor and acceptor is modeled in the photosynthetic complexes. Our model includes (i) two discrete energy levels associated with donor and acceptor, which are directly interacting and (ii) two continuum manifolds of electron energy levels (“sinks”), each interacting with the donor and acceptor. We also introduce external (classical) noise which acts on both donor and acceptor. We derive a closed system of integro-differential equations which describes the non-Markovian quantum dynamics of the ET. A region of parameters is found in which the ET dynamics can be simplified, and described by coupled ordinary differential equations. Using these simplified equations, both cases of sharp and flat redox potentials are analyzed. We analytically and numerically obtain the characteristic parameters that optimize the ET rates and efficiency in this system. In particular, we demonstrate that even for flat redox potential a simultaneous influence of sink and noise can significantly increase the efficiency of the ET. We discuss a relation between our approach and the Marcus theory of ET.     

Theoretical investigation of the hydrogen abstraction reaction of the OH radical with CH3CHF2 (HFC152-a): a dual level direct density functional theory dynamics study

The hydrogen abstraction reaction of the OH radical with CH(3)CHF(2) (HFC152-a) has been studied theoretically over a wide temperature range, 200-3000 K. Two different reactive sites of the molecule, CH(3) and CHF(2) groups have been investigated precisely, and results confirm that CHF(2) position of the molecule is a highly reactive site. In this study, three recently developed hybrid density functional theories, namely, MPWB1K, MPW1B95, and MPW1K, are used. The MPWB1K/6-31+G(d,p) method gives the best result for kinetic calculations, including barrier heights, reaction path information and geometry of transition state structures and other stationary points. To refine the barrier height of each channel, a single point energy calculation was performed in MPWB1K/MG3S method. The obtained rate constants by dual level direct dynamics with the interpolated single point energy method (VTST-ISPE) using DFT quantum computational methods, are consistent with available experimental data. The canonical variational transition state theory (CVT) with the zero-curvature and also the small-curvature tunneling correction methods is used to calculate the rate constants. Over the temperature range 200-3000 K, the variation effect, tunneling contribution, branching ratio of each channel are calculated. The rate constants and their temperature dependency in the form of a fitted three-parameter Arrhenius expression are k(1)(T) = 2.00 x 10(-19)(T)(2.24) exp(-1273/T), k(2)(T) = 1.95 x 10(-19)(T)(2.46) exp(-2374/T), and k(T) = 3.13 x 10(-19)(T)(2.47) exp(- 1694/T) cm(3) molecule(-1) s(-1). For the H abstraction from the CHF(2) group, a nonclassical reflection effect is detected as a dominant quantum effect.     

Bridge-dependent electron transfer in porphyrin-based donor-bridge-acceptor systems.

Photoinduced electron transfer in donor-bridge-acceptor systems with zinc porphyrin (or its pyridine complex) as the donor and gold(III) porphyrin as the acceptor has been studied. The porphyrin moieties were covalently linked with geometrically similar bridging chromophores which vary only in electronic structure. Three of the bridges are fully conjugated pi-systems and in a fourth, the conjugation is broken. For systems with this bridge, the quenching rate of the singlet excited state of the donor was independent of solvent and corresponded to the rate of singlet energy transfer expected for a F?rster mechanism. In contrast, systems with a pi-conjugated bridging chromophore show a solvent-dependent quenching rate that suggests electron transfer in the Marcus normal region. This is supported by picosecond transient absorption measurements, which showed formation of the zinc porphyrin radical cation only in systems with pi-conjugated bridging chromophores. On the basis of the Marcus and Rehm-Weller equations, an electronic coupling of 5-20 cm(-)(1) between the donor and acceptor is estimated for these systems. The largest coupling is found for the systems with the smallest energy gap between the donor and bridge singlet excited states. This is in good agreement with the coupling calculated with quantum mechanical methods, as is the prediction of an almost zero coupling in the systems with a nonconjugated bridging chromophore.     

Free energy landscapes of electron transfer system in dipolar environment below and above the rotational freezing temperature

Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape.