Calculated Electron Transfer Rate Research Articles

Mechanisms of Electron Transfer Rate Modulations in Cytochrome P450 BM3.

Bacterial cytochromes P450 BM3 (CYP450 BM3) catalyze reactions of industrial importance. Despite many successful biotransformations, robust (re)design for novel applications remains challenging. Rational design and evolutionary approaches are not always successful, highlighting a lack of complete understanding of the mechanisms of electron transfer (ET) modulations. Thus, the full potential of CYP450 reactions remains under-exploited. In this work, we report the first molecular dynamics (MD)-based explicit prediction of BM3 ET parameters (reorganization energies; λ and ET free energies; ΔG°), and log ET rates (log kET) using the Marcus theory. Overall, the calculated ET rates for the BM3 wild-type (WT), mutants (F393 and L86), ligand-bound state, and ion concentrations agree well with experimental data. In ligand-free (LF) BM3, mutations modulate kET via ET ΔG°. Simulations show that the experimental ET rate enhancement is due to increased driving force (more negative ΔG°) upon ligation. This increase is related to the protein reorganization required to accommodate the ligand in the binding pocket rather than binding interactions with the ligand. Our methodology (CYPWare 1.0) automates all the stages of the MD simulation step-up, energy calculations, and estimation of ET parameters. CYPWare 1.0 and this work thus represent an important advancement in the CYP450 ET rate predictions, which has the potential to guide the redesign of ET enzymes. This program and a Web tool are available on GitHub for academic research.

Electrocatalytic activity of doped graphene: Quantum-mechanical theory view

Based on the quantum-mechanical theory of electron transfer (ET), the parameter was proposed to describe the electrochemical activity of doped graphenes. The parameter is calculated using the density of states (DOS), local density of state (LDOS) values, which are in turn obtained from the density functional theory (DFT) calculations and reorganization energies of redox system. DOS describes the contribution of the electronic structure of the electrode to the ET process, while the LDOS describes the electron density contribution of the atoms at some distance from the surface electrode. Reorganization energy corresponds to the restriction of solvation shell and bonds in redox system due to ET process. The overall contribution of these parameters enables a comprehensive assessment of the activity that is acceptable for semi-quantitative analysis. Calculations have shown that the proposed activity parameter correlates well with the calculated ET rate constants.Theoretical study of the oxygen reduction reaction (ORR) on graphene doped with p-elements in the framework of quantum-mechanical theory showed that ET activity decreases in series P-Gr > S-Gr > N-Gr > B-Gr > O-Gr > Gr. According to our estimates, the mixed or adiabatic regime of ET is probably observed on doped graphenes for all steps of ORR. Using N- and B-graphenes as an example and activity parameter, the influence of the applied potential and the atomic fraction of the doped element on the ET activity are studied.

Ferrocene Molecular Architectures Grafted on Si(111): A Theoretical Calculation of the Standard Oxidation Potentials and Electron Transfer Rate Constant.

The standard oxidation potential and the electron transfer (ET) rate constants of two silicon-based hybrid interfaces, Si(111)/organic-spacer/Ferrocene, are theoretically calculated and assessed. The dynamics of the electrochemical driven ET process is modeled in terms of the classical donor/acceptor scheme within the framework of “Marcus theory”. The ET rate constants, , are determined following calculation of the electron transfer matrix element, , together with the knowledge of the energy of the neutral and charge separated systems. The recently introduced Constrained Density Functional Theory (CDFT) method is exploited to optimize the structure and determine the energy of the charge separated species. Calculated ET rate constants are and , in the case of the short and long organic-spacer, respectively.

Photoinduced electron transfer from Eu(II)-complexes to organic molecules: Rate and mechanistic investigation

Abstract Photoinduced electron transfer (PET) from europium(II)-complexes to variety of organic electron acceptors has been investigated in tetrahydrofuran (THF), 1,2-dimethoxyethane (DME) and acetonitrile (ACN). Laser flash photolysis (LFP) study indicates the formation of radical cation of the donor {Eu (II)} and radical/radical anion of corresponding acceptors, confirming the photoinduced electron transfer. Time resolved luminescence quenching experiments showed that rate constants of forward electron transfer are in the range of 10 8 –10 9 M −1 s −1 . Furthermore, experimentally obtained rate constants are in good agreement with calculated electron transfer rate constants using Marcus equation with a reorganization energy ( λ ) of 45 kcal/mol. Interestingly, the excited state decay from radical ion pair formed in Eu(II)-ketone systems revealed that back electron transfer (BET) rate constants are 4–5 order of magnitude less ( k bet = 10 4 –10 5 s −1 ) compared to that of forward electron transfer, under the present experimental conditions. The significant decrease in rate is attributed to the large energy barrier for the back electron transfer process, which involves transformation of an otherwise stable trivalent lanthanide to its thermodynamically less stable divalent oxidation state. This investigation reveals, for the first time, that divalent europium complexes are promising candidates for generating long lived charge separated states in the excited state in the presence of suitable acceptors.

A computational protocol to predict suitable redox mediators for substitution of NAD(P)H in P450 monooxygenases

P450s catalyze a wide spectrum of stereo- and regioselective reactions like hydroxylations, epoxidations and dehydrogenations. Therefore biotransformations with P450s are of great relevance to organic synthesis. The use of isolated enzymes offers advantages over the use of whole cells. A key issue for catalytic applications of isolated P450s is the demand for a continuous electron supply to the heme-group. Mediator driven bioelectrocatalysis can help to overcome this problem. For mediator driven bioelectrocatalysis the identification of a suitable mediator is crucial for the fast development of an efficient electro enzymatic process. To this end we have developed a computational screening method based on using freely available software. Calculated electron transfer rates were compared with measured product formation rates. The novel in silico procedure allows a faster identification of suitable mediators for electrochemically driven P450 catalyzed reactions and can be used as screening tool. It may also lead to a massive reduction of experimental effort for the development of bioelectrochemical reaction systems in the future.

Electron transfer kinetics at single-walled carbon nanotube paper: The role of band structure

The role of band structure of individual tubules from single-walled carbon nanotube paper in the electron transfer process was considered within Gerischer–Marcus theory using Raman scattering spectroscopy, cyclic voltammetry and electrochemical impedance spectroscopy data. A heterogeneous electron transfer rate of 1.06 × 10 − 3 cm s was observed for ferri/ferrocyanid. A position of the Raman radial breathing mode was used for determination of the chiral vectors of tubules being in resonance with excitation laser light of 1.17 eV. For these tubules, the calculated electron transfer rates are similar. It has been shown that nanotube electronic states away from the Fermi level contribute to the electron transfer kinetics due to the broad distribution of the redox states in electrolyte.

Heterogeneous reduction of U 6+ by structural Fe 2+ from theory and experiment

Computational and experimental studies were performed to explore heterogeneous reduction of U 6+ by structural Fe 2+ at magnetite (Fe 3O 4) surfaces. Molecular Fe–Fe–U models representing a uranyl species adsorbed in a biatomic bidentate fashion to an iron surface group were constructed. Various possible charge distributions in this model surface complex were evaluated in terms of their relative stabilities and electron exchange rates using ab initio molecular orbital methods. Freshly-cleaved, single crystals of magnetite with different initial Fe 2+/Fe 3+ ratios were exposed to uranyl-nitrate solution (pH ∼ 4) for 90 h. X-ray photoelectron spectroscopy and electron microscopy indicated the presence of a mixed U 6+/U 5+ precipitate heterogeneously nucleated and grown on stoichiometric magnetite surfaces, but only the presence of sorbed U 6+ and no precipitate on sub-stoichiometric magnetite surfaces. Calculated electron transfer rates indicate that sequential multi-electron uranium reduction is not kinetically limited by conductive electron resupply to the adsorption site. Both theory and experiment point to structural Fe 2+ density, taken as a measure of thermodynamic reducing potential, and sterically accessible uranium coordination environments as key controls on uranium reduction extent and rate. Uranium incorporation in solid phases where its coordination is constrained to the uranate type should widen the stability field of U 5+ relative to U 6+. If uranium cannot acquire 8-fold coordination then reduction may proceed to U 5+ but not necessarily U 4+.

Carbon Nanotube Mat as Mediator-Less Glucose Sensor Electrode

In this paper, the direct electron transfer of glucose oxidase (GOx) on carbon nanotube (CNT) mat electrode is demonstrated. Because of the electrical conductivity and mechanical strength of CNT mat, it can be used as an electrode as well as a catalyst support. Therefore, the preparation process for the CNT mat based sensor electrode is simpler than that of the conventional CNT dispersed sensor electrodes. GOx was covalently immobilized on the oxidized CNT mat, which is connected to a wire by using silver paste and epoxy glue. Attenuated Total Reflectance Fourier Transform-Infrared (ATR-FTIR) result shows transmittance peaks at 1637 cm(-1) and 1525 cm(-1) which are corresponding to the band I and II of amide. Cyclic voltammetric shows a pair of well-defined redox peaks with the average formal potential of -0.425 V (vs. Ag/AgCl reference electrode) in the phosphate buffered saline solution (1 x PBS, pH 7.4). Calculated electron transfer rate constant and the surface density of GOx were 1.71 s(-1) and (3.27 +/- 0.20) x 10(-13) mol/cm2, respectively. Cyclic voltammograms of GOx-CNT mat in glucose solution show that the immobilized GOx retains its catalytic activity to glucose. The amperometric sensor response showed a linear dependence on the glucose concentration in the range of 0.2 mM to 2.18 mM with a detection sensitivity of 4.05 microA mM(-1) cm(-2). The Michaelis-Menten constant of the immobilized GOx was calculated to be 2.18 mM.

Surface Grafting of Ferrocene-Containing Triazene Derivatives on Si(100)

Ferrocene-containing molecules have been grafted to Si(100) surfaces to form monolayers and multilayers via a triazene derivative and its subsequent diazonium chemistry. The growth of the ferrocene-containing films was controlled by molecular concentrations and reaction times. Results from ellipsometry showed that the film thicknesses were in the range of subnanometer to several nanometers. X-ray photoelectron spectroscopy has confirmed the structural integrity of ferrocene in the films. Electrochemical studies of the ferrocene-containing multilayer have shown a reversible one-electron wave of the ferrocene/ferrocenium couple. The multilayer coverage was found to be 2.8 × 10−9 mol cm−2. The calculated electron transfer rate constant was 164 s−1.

Three-dimensional representations of photo-induced electron transfer rates in pyrene-(CH2)n-N,N′-dimethylaniline systems obtained by three electron transfer theories

The observed rates of photo-induced electron transfer (ET) from N,N′-dimethylaniline (DMA) to the excited pyrene (Py) in confined systems of pyrene-(CH2)n-N,N′- dimethylaniline (PnD: n=1–3) were studied by molecular dynamic simulation (MD) and three kinds of electron transfer theories. ET parameters contained in Marcus theory (M theory), Bixon and Jortner theory (BJ theory) and Kakitani and Mataga theory (KM theory) were determined so as to fit the calculated fluorescence intensities with those obtained by the observed ET rates, according to a non-linear least squares method. Three-dimensional profiles of logarithm of calculated ET rates depending on two of three ET parameters, R, ɛ0 and −ΔG° were systematically examined with best-fit ET parameters of P1D. Bell shape dependencies of ET rate were predicted on R and on ɛ0, and on −ΔG° as well, by M theory and KM theory. The profiles of logarithm of ET rate calculated by BJ theory exhibited oscillatory dependencies not only on −ΔG°, but also on R and on ɛ0. Relationship between ET state and charge transfer complex was discussed with BJ theory.

Laser Flash Photolysis Studies on the Model System for Photo-Oxidation-Induced Polycondensation Polyimides with Fullerene C60

Laser flash photolysis studies were carried out to elucidate the quenching mechanism of the triplet state of fullerene C60 (3C60*) by furan-substituted diimides, which are the model compounds for photosensitive polyimides based on the photo-oxidation-induced polycondensation (POP) reaction. The decay kinetics of transient 3C60* triplet-triplet absorption at 740 nm revealed that the model diimides quenched 3C60* in γ-butyrolactone, with the quenching rate constants, kq(obsd), being determined to be on the order of 105 to 106 M-1·s-1. The free-energy changes for electron transfer from the model diimides to 3C60*, ΔGet, and the calculated electron transfer rate constants, kq(calcd), were also evaluated from the Rehm-Weller equation using the oxidation potentials for the model diimides. The kq(obsd) values were found to be, on the whole, correlated with ΔGet and to be in fair agreement with the kq(calcd) values. These results indicate that the quenching reaction occurs primarily by electron transfer from the diimide to 3C60*. Furthermore, the kq(obsd) value for benzyl 2-furoate, which constitutes a part of the model diimide molecule was found to be small compared with those for the model diimides. We therefore drew the conclusions that the electron transfer occurs predominantly from the benzimido moiety to 3C60*, not from the furoate moiety and, consequently, the furoate moiety may not take part in electron transfer.

Intermolecular electron transfer between coumarin dyes and aromatic amines in Triton-X-100 micellar solutions: evidence for Marcus inverted region.

Photoinduced electron transfer (ET) between coumarin dyes and aromatic amines has been investigated in Triton-X-100 micellar solutions and the results have been compared with those observed earlier in homogeneous medium. Significant static quenching of the coumarin fluorescence due to the presence of high concentration of amines around the coumarin fluorophore in the micelles has been observed in steady-state fluorescence studies. Time-resolved studies with nanosecond resolutions mostly show the dynamic part of the quenching for the excited coumarin dyes by the amine quenchers. A correlation of the quenching rate constants, estimated from the time-resolved measurements, with the free energy changes (DeltaG0) of the ET reactions shows the typical bell shaped curve as predicted by Marcus outer-sphere ET theory. The inversion in the ET rates for the present systems occurs at an exergonicity (-DeltaG0) of approximately 0.7-0.8 eV, which is unusually low considering the polarity of the Palisade layer of the micelles where the reactants reside. Present results have been rationalized on the basis of the two dimensional ET model assuming that the solvent relaxation in micellar media is much slower than the rate of the ET process. Detailed analysis of the experimental data shows that the diffusional model of the bimolecular quenching kinetics is not applicable for the ET reactions in the micellar solutions. In the present systems, the reactions can be better visualized as equivalent to intramolecular electron transfer processes, with statistical distribution of the donors and acceptors in the micelles. A low electron coupling (Vel) parameter is estimated from the correlation of the experimentally observed and the theoretically calculated ET rates, which indicates that the average donor--acceptor separation in the micellar ET reactions is substantially larger than for the donor--acceptor contact distance. Comparison of the Vel values in the micellar solution and in the donor--acceptor close contact suggests that there is an intervention of a surfactant chain between the interacting donor and acceptor in the micellar ET reaction.

Adiabatic electron transfer: comparison of modified theory with experiment.

The radical cations of properly designed bishydrazines allow comparison of observed and calculated electron transfer rate constants. These compounds have rate constants small enough to be measured by dynamic electron spin resonance spectroscopy and show charge transfer bands corresponding to vertical excitation from the energy well for the charge occurring upon one hydrazine unit to that for the electron-transferred species. Analysis of the data for all six compounds studied indicates that the shape of the adiabatic surface on which electron transfer occurs can be obtained from the charge transfer band accurately enough to successfully predict the electron transfer rate constant and that explicit tunneling corrections are not required for these compounds.

Electron transfer via bridges

In this paper we explore the energetic control of sequential and superexchange electron transfer (ET) mechanisms on the basis of quantum-mechanical simulations and calculations for long-range ET in DBA systems, where the donor (D) and the acceptor (A) are separated by a bridge (B). We studied ET dynamics in a Franck–Condon (FC) system characterized by three multi-dimensional displaced harmonic potential surfaces, where an initial single vibronic doorway state |α〉 (with energy Eα) in the DBA (≡D) electronic state is coupled to the mediating {|β〉} vibronic quasicontinuum of the D+B−A (≡B) electronic state, which in turn is coupled to the final {|γ〉} vibronic quasicontinuum of the D+BA− (≡A) electronic state. The level structure was described by the vibrational frequencies (for a four-mode harmonic system) and the energy gaps ΔGDB and ΔGDA between the origins of the corresponding electronic states (with nα=1–50, nβ=1000–2000, and nγ=1000–2000 states in the {|α〉}, {|β〉}, and {|γ〉} manifolds, respectively), while the couplings were characterized by the spectral densities and by the pair correlations (specified in terms of correlation parameters ηαα′ and ηββ′) between states belonging to the same manifold. The correlation parameters ηαα′ (α,α′=1–40) for the doorway-quasicontinuum coupling and ηββ′ (β,β′=150–190) for the interquasicontinuum coupling are considerably lower than unity (|ηαα′|⩽0.4 and |ηββ′|⩽0.3), obeying propensity rules with the highest values of |ηαα′| and |ηββ′| which correspond to a single vibrational quantum difference, while for multimode changes between α and α′ or between β and β′ very low values of |ηαα′| or |ηββ′| are exhibited. Radiationless transitions theory was applied for quantum-mechanical simulations based on the dynamcis of wave packets of molecular eigenstates for resonance (ΔGDB<Eα) and for off-resonance (ΔGDB>Eα) coupling. Resonance |α〉–{|β〉}–{|γ〉} coupling results in two-step sequential ET kinetics for all doorway states |α〉, manifesting phase erosion due to weakly correlated intercontinuum coupling, without the need of intermediate state phonon induced thermalization. Off-resonance |α〉–{|β〉} coupling in conjunction with {|β〉}–{|γ〉} resonance interactions results in unistep superexchange ET kinetics. The simulated sequential ET rates and the superexchange rate are in good agreement with the calculated quantum-mechanical rates obtained using the electronic couplings and FC densities. The energy-gap (ΔGDB) dependence of the simulated and the calculated ET rates from a single doorway state reveal a “transition” from sequential to superexchange ET with increasing ΔGDB. For a finite-temperature system, characterized by a fixed ΔGDB (>0) small energy gap, the thermally averaged rate from a canonical ensemble of doorway states will result in the superposition of both superexchange and sequential mechanisms.

Electron transfer rates of metallorganic complexes

We use a density matrix formalism to investigate intramolecular electron transfer (ET). Dissipation is provided by a heat bath having the environmental degrees of freedom. We assign the calculated ET rates to different ET mechanisms. Variation of key parameters leads to transition between different ET regimes.

A perturbation molecular orbital theory of electron-transfer rates

Perturbation molecular orbital (PMO) theory is used to approximate the electronic matrix element in the semiclassical expression for the rate of nonadiabatic electron transfer (ET). The resulting expression gives a satisfactory account of the intramolecular ET rate data reported by Closs, Miller, and co-workers. We develop the idea of electron-transfer efficiency for the contribution of electron transfer to the observed kinetics of ion–molecule collisions followed by electron transfer. Electron-transfer efficiency comes from the calculated ET rate divided by the maximum calculated ET rate. Electron-transfer efficiency values are also obtained by dividing the observed reaction rate by the collision rate, calculated by the PMO treatment of ion–molecule collision rates. We applied this approach to data on electron transfer from sulfurhexafluoride or perfluoromethylcyclohexane anions to aromatic acceptors. The structural reorganization energies, λs, for these reactions were 0.016 and 0.046 eV, respectively. The vibrational reorganization energies, λv, for the reactions were 1.01 and 1.00 eV, respectively. Electron transfer from either of the donor anions to fluoranil occurs in the inverted region.

Internal return in the photochemistry of ring-substituted 1-(1-naphthyl)ethyl esters of phenylacetic acid

The photochemistry in methanol of the esters 12a–d has been studied in order to determine the importance of internal return of both ion pair and radical pair intermediates. The efficiency of internal return, determined by monitoring 18O exchange between the alcohol and carbonyl oxygens, was shown to be substituent dependent, varying from approximately 10% for the 4,7-dimethoxy substrate to nearly 50% for the 4-cyano case. The corresponding ground state solvolysis reactions gave about 10% internal return and, within experimental error, were substituent independent. Internal return was also examined by racemization of the chiral center in 12a and 12d. In summary, these combined results reveal that internal return probably occurs mainly through a contact (not solvent-separated) radical pair. More important, internal return has little effect on previously calculated electron transfer rate constants for converting the radical pair to the ion pair. Therefore, the previously reported Marcus' correlations are valid. Keywords: photochemistry of benzylic esters, internal return, photosolvolysis, electron transfer, radical pairs.

An a b i n i t i o study of aqueous Fe2+–Fe3+ electron transfer

The tunneling rate for the transfer of an electron from an Fe2+ to an Fe3+ ion is determined by a Hamiltonian matrix element, which has been calculated for interionic distances in the range 5.10–7.22 Å. The ions were either alone, or surrounded by water molecules. The calculations were made by computing the electronic wave function of the system by the complete active space self-consistent field (CASSCF) method, and then evaluating the relevant matrix element for this wave function interacting with a symmetry image of itself, representing the final state. Basis set dependence, and in particular the effect of bond functions, was investigated, as well as the effect of removing some water molecules or replacing them with point charges. The results seem to indicate that earlier calculated values, which are frequently used, of the tunneling rate may be too large by as much as a factor of 10. If so, then the agreement between earlier calculated electron transfer rates and experimental data may be explained by compensating deficiencies in the assumed statistical distribution of interionic distances.