Ab Initio Calculation of Homogeneous Outer Sphere Electron Transfer Rates: Application to M(OH2)63+/2+ Redox Couples

Probing time-resolved plasma-driven solution electrochemistry in a falling liquid film plasma reactor: Identification of HO2- as a plasma-derived reducing agent

Many applications involving plasma-liquid interactions depend on the reactive processes occurring at the plasma-liquid interface. We report on a falling liquid film plasma reactor allowing for in situ optical absorption measurements of the time-dependence of the ferricyanide/ferrocyanide redox reactivity, complemented with ex situ measurement of the decomposition of formate. We found excellent agreement between the measured decomposition percentages and the diffusion-limited decomposition of formate by interfacial plasma-enabled reactions, except at high pH in thin liquid films, indicating the involvement of previously unexplored plasma-induced liquid phase chemistry enabled by long-lived reactive species. We also determined that high pH facilitates a reduction-favoring environment in ferricyanide/ferrocyanide redox solutions. In situ conversion measurements of a 1:1 ferricyanide/ferrocyanide redox mixture exceed the measured ex situ conversion and show that conversion of a 1:1 ferricyanide/ferrocyanide mixture is strongly dependent on film thickness. We identified three dominant processes: reduction faster than ms time scales for film thicknesses >100 µm, •OH-driven oxidation on time scales of <10 ms, and reduction on 15 ms time scales for film thickness <100 µm. We attribute the slow reduction and larger formate decomposition at high pH to HO2- formed from plasma-produced H2O2 enabled by the high pH at the plasma-liquid interface as confirmed experimentally and by computed reaction rates of HO2- with ferricyanide. Overall, this work demonstrates the utility of liquid film reactors in enabling the discovery of new plasma-interfacial chemistry and the utility of atmospheric plasmas for electrodeless electrochemistry.

Direct Calculation of Electron Transfer Rates with the Binless Dynamic Histogram Analysis Method

Umbrella sampling molecular dynamics simulations are widely used to enhance sampling along the reaction coordinates of chemical reactions. The effect of the artificial bias can be removed using methods such as the dynamic weighted histogram analysis method (DHAM), which in addition to the global free energy profile also provides kinetic information about barrier-crossing rates directly from the Markov matrix. Here we present a binless formulation of DHAM that extends DHAM to high-dimensional and Hamiltonian-based biasing to allow the study of electron transfer (ET) processes, for which enhanced sampling is usually not possible based on simple geometric grounds. We show the capabilities of binless DHAM on examples such as aqueous ferrous-ferric ET and intramolecular ET in the radical anion of benzoquinone-tetrathiafulvalene-benzoquinone (Q-TTF-Q)-. From classical Hamiltonian-based umbrella sampling simulations and electronic coupling values from quantum chemistry calculations, binless DHAM provides ET rates for adiabatic and nonadiabatic ET reactions alike in excellent agreement with experimental results.

An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Oxide- and Silicate-Water Interfaces and Their Roles in Technology and the Environment

Interfacial reactions drive all elemental cycling on Earth and play pivotal roles in human activities such as agriculture, water purification, energy production and storage, environmental contaminant remediation, and nuclear waste repository management. The onset of the 21st century marked the beginning of a more detailed understanding of mineral aqueous interfaces enabled by advances in techniques that use tunable high-flux focused ultrafast laser and X-ray sources to provide near-atomic measurement resolution, as well as by nanofabrication approaches that enable transmission electron microscopy in a liquid cell. This leap into atomic- and nanometer-scale measurements has uncovered scale-dependent phenomena whose reaction thermodynamics, kinetics, and pathways deviate from previous observations made on larger systems. A second key advance is new experimental evidence for what scientists hypothesized but could not test previously, namely, interfacial chemical reactions are frequently driven by "anomalies" or "non-idealities" such as defects, nanoconfinement, and other nontypical chemical structures. Third, progress in computational chemistry has yielded new insights that allow a move beyond simple schematics, leading to a molecular model of these complex interfaces. In combination with surface-sensitive measurements, we have gained knowledge of the interfacial structure and dynamics, including the underlying solid surface and the immediately adjacent water and aqueous ions, enabling a better definition of what constitutes the oxide- and silicate-water interfaces. This critical review discusses how science progresses from understanding ideal solid-water interfaces to more realistic systems, focusing on accomplishments in the last 20 years and identifying challenges and future opportunities for the community to address. We anticipate that the next 20 years will focus on understanding and predicting dynamic transient and reactive structures over greater spatial and temporal ranges as well as systems of greater structural and chemical complexity. Closer collaborations of theoretical and experimental experts across disciplines will continue to be critical to achieving this great aspiration.

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+ /Fe3+ Redox Reaction

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe²⁺ /Fe³⁺ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe²⁺ /Fe³⁺ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe²⁺ /Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.

Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer

We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.

Oxidation-State Constrained Density Functional Theory for the Study of Electron-Transfer Reactions

We propose a new constrained density functional theory (CDFT) approach which directly controls the oxidation state of the target atoms. In this new approach called oxidation-state constrained density functional theory (OS-CDFT), the eigenvalues of the occupation matrix obtained from projecting the Kohn-Sham wave functions onto the valence orbitals are constrained to obtain the desired oxidation states. This approach is particularly useful to study electron transfer problems in transition metal-containing systems due to the multivalent nature of the transition metal ions. The calculation of the forces on the ions and of the coupling constant was implemented under the OS-CDFT scheme to allow efficient and accurate study of electron transfer reactions. We demonstrated the application of this method in the study of different electron transfer reactions including the aqueous ferrous-ferric self-exchange reaction, polaron hopping in the TiO₂ anatase and bismuth vanadate, and photoexcited electron transfer in the sapphire.

Mechanisms and Rates of U(VI) Reduction by Fe(II) in Homogeneous Aqueous Solution and the Role of U(V) Disproportionation

Molecular-level pathways in the aqueous redox transformation of uranium by iron remain unclear, despite the importance of this knowledge for predicting uranium transport and distribution in natural and engineered environments. As the relative importance of homogeneous versus heterogeneous pathways is difficult to probe experimentally, here we apply computational molecular simulation to isolate rates of key one electron transfer reactions in the homogeneous pathway. By comparison to experimental observations the role of the heterogeneous pathway also becomes clear. Density functional theory (DFT) and Marcus theory calculations for all primary monomeric species at pH values ≤7 show for UO₂²⁺ and its hydrolysis species UO₂OH⁺ and UO₂(OH)₂⁰ that reduction by Fe²⁺ is thermodynamically favorable, though kinetically limited for UO₂²⁺. An inner-sphere encounter complex between UO₂OH⁺ and Fe²⁺ was the most stable for the first hydrolysis species and displayed an electron transfer rate constant k_et = 4.3 × 10³ s^-1. Three stable inner- and outer-sphere encounter complexes between UO₂(OH)₂⁰ and Fe²⁺ were found, with electron transfer rate constants ranging from k_et = 7.6 × 10² to 7.2 × 10⁴ s^-1. Homogeneous reduction of these U(VI) hydrolysis species to U(V) is, therefore, predicted to be facile. In contrast, homogeneous reduction of UO₂⁺ by Fe²⁺ was found to be thermodynamically unfavorable, suggesting the possible importance of U(V)-U(V) disproportionation as a route to U(IV). Calculations on homogeneous disproportionation, however, while yielding a stable outer-sphere U(V)-U(V) encounter complex, indicate that this electron transfer reaction is not feasible at circumneutral pH. Protonation of both axial O atoms of acceptor U(V) (i.e., by H₃O⁺) was found to be a prerequisite to stabilize U(IV), consistent with the experimental observation that the rate of this reaction is inversely correlated with pH. Thus, despite prevailing notions that U(V) is rapidly eliminated by homogeneous disproportionation, this pathway is irrelevant at environmental conditions.

Acidity constants and redox potentials of uranyl ions in hydrothermal solutions

We report a first principles molecular dynamics (FPMD) study of the structures, acidity constants (pK_a) and redox potentials (E⁰) of uranyl (UO₂²⁺) from ambient conditions to 573 K.

A molecularly based theory for electron transfer reorganization energy

Using field-theoretic techniques, we develop a molecularly based dipolar self-consistent-field theory (DSCFT) for charge solvation in pure solvents under equilibrium and nonequilibrium conditions and apply it to the reorganization energy of electron transfer reactions. The DSCFT uses a set of molecular parameters, such as the solvent molecule's permanent dipole moment and polarizability, thus avoiding approximations that are inherent in treating the solvent as a linear dielectric medium. A simple, analytical expression for the free energy is obtained in terms of the equilibrium and nonequilibrium electrostatic potential profiles and electric susceptibilities, which are obtained by solving a set of self-consistent equations. With no adjustable parameters, the DSCFT predicts activation energies and reorganization energies in good agreement with previous experiments and calculations for the electron transfer between metallic ions. Because the DSCFT is able to describe the properties of the solvent in the immediate vicinity of the charges, it is unnecessary to distinguish between the inner-sphere and outer-sphere solvent molecules in the calculation of the reorganization energy as in previous work. Furthermore, examining the nonequilibrium free energy surfaces of electron transfer, we find that the nonequilibrium free energy is well approximated by a double parabola for self-exchange reactions, but the curvature of the nonequilibrium free energy surface depends on the charges of the electron-transferring species, contrary to the prediction by the linear dielectric theory.

A double-QM/MM method for investigating donor–acceptor electron-transfer reactions in solution

A double-QM/MM method can explore the distant-dependent phenomena of outer-sphere electron transfer processes. This method allows easy control of donor–acceptor spin-charge densities within the full-reaction scheme.

Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

We present a plane-wave basis set implementation of charge constrained density functional molecular dynamics (CDFT-MD) for simulation of electron transfer reactions in condensed phase systems. Following the earlier work of Wu and Van Voorhis [Phys. Rev. A 72, 024502 (2005)], the density functional is minimized under the constraint that the charge difference between donor and acceptor is equal to a given value. The classical ion dynamics is propagated on the Born-Oppenheimer surface of the charge constrained state. We investigate the dependence of the constrained energy and of the energy gap on the definition of the charge and present expressions for the constraint forces. The method is applied to the Ru2+-Ru3+ electron self-exchange reaction in aqueous solution. Sampling the vertical energy gap along CDFT-MD trajectories and correcting for finite size effects, a reorganization free energy of 1.6 eV is obtained. This is 0.1-0.2 eV lower than a previous estimate based on a continuum model for solvation. The smaller value for the reorganization free energy can be explained by the fact that the Ru-O distances of the divalent and trivalent Ru hexahydrates are predicted to be more similar in the electron transfer complex than for the separated aqua ions.

Isotopically exchangeable concentrations of elements having multiple oxidation states: the case of Fe(II)/Fe(III) isotope self-exchange in coastal lowland acid sulfate soils

Isotope exchange techniques have been used to probe isotopically exchangeable concentrations of Fe (E value) that are in dynamic equilibrium between the aqueous- and solid-phase of coastal lowland acid sulfate soils. Isotope self-exchange between Fe(II) and Fe(III) was rapid and complete in <1 min (p < 0.05) indicating that this reaction was initially occurring solely in the aqueous-phase and the surface of the soil solid-phase. It is further demonstrated that accurate and valid measurements of isotopically exchangeable concentrations of Fe do not require corrections for Fe speciation. This also holds for any element existing in two or more oxidation states which are completely isotopically self-exchangeable in soils. As isotope self-exchange between Fe(II) and Fe(III) is rapid, the distribution coefficient (Kd) and E value determined via this methodology are, therefore, truly representative of Fe regardless of the relative importance of Fe(II) or Fe(III) to the isotopically exchangeable pool of Fe. In the 21 soil samples examined, isotopically exchangeable concentrations of Fe varied from 90 mg/kg to values as high as 3610 mg/kg in acidic, saturated samples collected below the groundwater table from the transition soil horizon. The combination of low Evalues and extremely high Kd values in the upper oxidized layers of these soils indicate that these soil horizons are a relatively insignificant source of transportable (labile) Fe. As such, given our knowledge on the general rates of microbial Fe(III) reduction in, and the hydraulic properties of, the coastal lowland acid sulfate soils of this region, only those soils adjacent to agricultural drains are likely to contribute to the load of Fe entering surrounding aquatic systems.

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids "on-the-fly" QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

Potential phytoavailability of anthropogenic cobalt in soils as measured by isotope dilution techniques

Isotope dilution is a useful technique to determine the potential phytoavailability of an element in soil. This method involves equilibrating an isotope with soil and then sampling the labile metal pool by analysis of the soil solution (E value) or plants growing in the soil (L value). The work reported here was conducted to evaluate the distribution coefficient (Kd), and the potential phytoavailability (E value) of cobalt (Co) in eight soils subjected to the atmospheric deposition of anthropogenic Co. Multiple regression analyses demonstrated that the K(d) of isotopically exchangeable Co in these soils was best modelled with two parameters: soil pH and organic carbon (OC) content (log Kd=0.85(pH)+1.1(logOC)-5.0, R2=0.94, p<0.01). Cobalt E values ranged from 1.5 to 37% of total soil Co concentrations. No evidence was obtained to suggest that Co(III), if present, was isotopically exchangeable in these soils and it was concluded that the Co E values consisted solely of Co(II). Cobalt L values, measured with Triticum aestivum L. (46 days), of two of these soils (varying in soil pH, e.g. 5.0 and 7.2) were statistically (p<0.05) different to E values. However, when changes of bulk soil pH on Co E values were considered, the two values were statistically (p<0.05) similar indicating that processes affecting soil pH during plant growth can alter isotopically exchangeable concentrations of Co.

Kinetics of reduction of Fe(III) complexes by outer membrane cytochromes MtrC and OmcA of Shewanella oneidensis MR-1

Because of their cell surface locations, the outer membrane c-type cytochromes MtrC and OmcA of Shewanella oneidensis MR-1 have been suggested to be the terminal reductases for a range of redox-reactive metals that form poorly soluble solids or that do not readily cross the outer membrane. In this work, we determined the kinetics of reduction of a series of Fe(III) complexes with citrate, nitrilotriacetic acid (NTA), and EDTA by MtrC and OmcA using a stopped-flow technique in combination with theoretical computation methods. Stopped-flow kinetic data showed that the reaction proceeded in two stages, a fast stage that was completed in less than 1 s, followed by a second, relatively slower stage. For a given complex, electron transfer by MtrC was faster than that by OmcA. For a given cytochrome, the reaction was completed in the order Fe-EDTA > Fe-NTA > Fe-citrate. The kinetic data could be modeled by two parallel second-order bimolecular redox reactions with second-order rate constants ranging from 0.872 microM(-1) s(-1) for the reaction between MtrC and the Fe-EDTA complex to 0.012 microM(-1) s(-1) for the reaction between OmcA and Fe-citrate. The biphasic reaction kinetics was attributed to redox potential differences among the heme groups or redox site heterogeneity within the cytochromes. The results of redox potential and reorganization energy calculations showed that the reaction rate was influenced mostly by the relatively large reorganization energy. The results demonstrate that ligand complexation plays an important role in microbial dissimilatory reduction and mineral transformation of iron, as well as other redox-sensitive metal species in nature.

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.

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.

Reorganization free energies for long-range electron transfer in a porphyrin-binding four-helix bundle protein

To explore the possibility of electron transport in a recently designed four-helix bundle protein (Cochran, F. V.; et al. J. Am. Chem. Soc. 2005, 127, 1346), we have computed the reorganization free energy for (i) oxidation of a single Ru-porphyrin cofactor and (ii) electron self-exchange between two Ru-porphyrin cofactors binding to the solvated protein. Sampling the classical electrostatic energy gap for 20 ns, we find that the fluctuations are well described by Gaussian statistics and obtain reorganization free energies of 0.90 +/- 0.04 eV for oxidation and 1.36 +/- 0.08 eV for self-exchange. The latter is 0.1-0.2 eV higher than the experimental estimate for interprotein electron self-exchange in cytochrome b5. As in natural electron carriers, inner-sphere reorganization is very small, 88 meV for self-exchange between two model cofactors computed at the density functional level of theory. Decomposing the outer-sphere reorganization free energy, we find that the solvent (aqueous ionic solution) is the primary outer-sphere medium for oxidation, contributing 0.60 eV (69%). The protein contributes only 0.27 eV (31%). For self-exchange, the solvent contribution, 0.68 eV (54%), and the protein contribution, 0.59 eV (46%), are almost equally important. The large solvent contribution is due to the slow decay of dipole reorientation of the solvent as a function of distance to the cofactor, implying that the change in the electric field upon electron transfer is not as effectively screened by the four-helix bundle protein. However, ranking the residues according to their free energy contributions, it is suggested that the reorganization free energy can be decreased by about 0.2 eV if two glutamine residues in the vicinity of the cofactor are mutated into less polar amino acids.

Electronic Coupling between Heme Electron-Transfer Centers and Its Decay with Distance Depends Strongly on Relative Orientation

A method for calculating the electron-transfer matrix element V(RP) using density functional theory Kohn-Sham orbitals is presented and applied to heme dimers of varying relative orientation. The electronic coupling decays with increased iron separation according to V(RP) = V(0)(RP)exp(-beta r/2) with a distance dependence parameter beta approximately 2 A(-1) for hemes with parallel porphyrins and either 1.1 or 4.0 A(-1) when the porphyrin planes are perpendicular, depending on the alignment of the iron d(pi) orbital. These findings are used to interpret the observed orientation of the hemes in tetraheme redox proteins such as Flavocytochrome c(3) fumarate reductase (Ifc(3), PDB code 1QJD) of Shewanella frigidimarina, another flavocytochrome from the same bacterium (Fcc(3), 1E39) and a small tetraheme cytochrome of Shewanella oneidensis strain MR1 (1M1P). Our results show that shifting and rotating the hemes controls the adiabaticity of the three electron hopping steps.

Kinetics of Triscarbonato Uranyl Reduction by Aqueous Ferrous Iron: A Theoretical Study

Uranium is a pollutant whose mobility is strongly dependent on its oxidation state. While U(VI) in the form of the uranyl cation is readily reduced by a range of natural reductants, by contrast complexation of uranyl by carbonate greatly reduces its reduction potential and imposes increased electron transfer (ET) distances. Very little is known about the elementary processes involved in uranium reduction from U(VI) to U(V) to U(IV) in general. In this study, we examine the theoretical kinetics of ET from ferrous iron to triscarbonato uranyl in aqueous solution. A combination of molecular dynamics (MD) simulations and density functional theory (DFT) electronic structure calculations is employed to compute the parameters that enter into Marcus' ET model, including the thermodynamic driving forces, reorganization energies, and electronic coupling matrix elements. MD simulations predict that two ferrous iron atoms will bind in an inner-sphere fashion to the three-membered carbonate ring of triscarbonato uranyl, forming the charge-neutral ternary Fe(2)UO(2)(CO(3))(3)(H(2)O)(8) complex. Through a sequential proton-coupled electron-transfer mechanism (PCET), the first ET step converting U(VI) to U(V) is predicted by DFT to occur with an electronic barrier that corresponds to a rate on the order of approximately 1 s(-1). The second ET step converting U(V) to U(IV) is predicted to be significantly endergonic. Therefore, U(V) is a stabilized end product in this ET system, in agreement with experiment.

Realistic quantitative descriptions of electron transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics

A general approach to calculate the diabatic surfaces for electron-transfer reactions is presented, based on first-principles molecular dynamics of the active centers and their surrounding medium. The excitation energy corresponding to the transfer of an electron at any given ionic configuration (the Marcus energy gap) is accurately assessed within ground-state density-functional theory via a novel penalty functional for oxidation-reduction reactions that appropriately acts on the electronic degrees of freedom alone. The self-interaction error intrinsic to common exchange-correlation functionals is also corrected by the same penalty functional. The diabatic free-energy surfaces are then constructed from umbrella sampling on large ensembles of configurations. As a paradigmatic case study, the self-exchange reaction between ferrous and ferric ions in water is studied in detail.

Molecular dynamics investigation of ferrous-ferric electron transfer in a hydrolyzing aqueous solution: calculation of the pH dependence of the diabatic transfer barrier and the potential of mean force

We present a molecular model for ferrous-ferric electron transfer in an aqueous solution that accounts for electronic polarizability and exhibits spontaneous cation hydrolysis. An extended Lagrangian technique is introduced for carrying out calculations of electron-transfer barriers in polarizable systems. The model predicts that the diabatic barrier to electron transfer increases with increasing pH, due to stabilization of the Fe3+ by fluctuations in the number of hydroxide ions in its first coordination sphere, in much the same way as the barrier would increase with increasing dielectric constant in the Marcus theory. We have also calculated the effect of pH on the potential of mean force between two hydrolyzing ions in aqueous solution. As expected, increasing pH reduces the potential of mean force between the ferrous and ferric ions in the model system. The magnitudes of the predicted increase in diabatic transfer barrier and the predicted decrease in the potential of mean force nearly cancel each other at the canonical transfer distance of 0.55 nm. Even though hydrolysis is allowed in our calculations, the distribution of reorganization energies has only one maximum and is Gaussian to an excellent approximation, giving a harmonic free energy surface in the reorganization energy F(DeltaE) with a single minimum. There is thus a surprising amount of overlap in electron-transfer reorganization energies for Fe(2+)-Fe(H2O)6(3+), Fe(2+)-Fe(OH)(H2O)5(2+), and Fe(2+)-Fe(OH)2(H2O)+ couples, indicating that fluctuations in hydrolysis state can be viewed on a continuum with other solvent contributions to the reorganization energy. There appears to be little justification for thinking of the transfer rate as arising from the contributions of different hydrolysis states. Electronic structure calculations indicate that Fe(H2O)6(2+)-Fe(OH)n(H2O)(6-n)(3-n)+ complexes interacting through H3O2- bridges do not have large electronic couplings.

Reaction of hydroquinone with hematite

The rate of reaction of hematite with quinones and the quinone moieties of larger molecules may be an important factor in limiting the rate of reductive dissolution of hematite, especially by iron-reducing bacteria. It is possible that the rate of reductive dissolution of hematite in the presence of excess hydroquinone at pH 2.5 may be limited by the electron-transfer rate. Here, a reductive dissolution rate was measured and compared to electron-transfer rates calculated using Marcus theory. An experimental rate constant was measured at 9.5 x 10 (-6) s(-1) and the reaction order with respect to the hematite concentration was found to be 1.1. Both the dissolution rate and the reaction order of hematite concentration compare well with previous measurements. Of the Marcus theory calculations, the inner-sphere part of the reorganization energy and the electronic coupling matrix element for hydroquinone self-exchange electron transfer are calculated using ab initio methods. The second order self-exchange rate constant was calculated to be 1.3 x 10 (7) M(-1)s(-1), which compares well with experimental measurements. Using previously published data calculated for hexaquairon(III)/(II), the calculated electron-transfer rate for the cross reaction with hydroquinone also compares well to experimental measurements. A hypothetical reductive dissolution rate is calculated using the first-order electron-transfer rate constant and the concentration of total adsorbed quinone. Three different models of the hematite surface are used as well as multiple estimates for the reduction potential, the surface charge, and the adsorption density of hydroquinone. No calculated dissolution rate is less than five orders of magnitude faster than the experimentally measured one.

Reorganization energy associated with small polaron mobility in iron oxide

The reorganization energy is an important quantity controlling electron transfer rates. The internal contribution arising from the energy to reorganize donor/acceptor bonds can be evaluated by the "direct" and "4-point" methods. We examine how spatial separation leading to the noninteracting character of the donor and acceptor affects the reorganization energy. We show that the direct method captures contributions from interaction of the donor and acceptor while the 4-point method does not, and the two methods converge at large separation. Comparing reorganization energies determined by the two methods yields a measure of the degree of interaction between the initial and final states. The analysis is illustrated in the characterization of small polarons in iron oxides.

An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes

We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required "on-the-fly" and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U(d) and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron transfer occurring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment. (