Ab Initio Molecular Dynamics Simulation of the Aqueous Ru2+/Ru3+ Redox Reaction: The Marcus Perspective

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.

Free energy calculation of water addition coupled to reduction of aqueous RuO4-

Free energy calculations were carried out for water addition coupled reduction of aqueous ruthenate, RuO4-+H2O+e--->[RuO3(OH)2]2-, using Car-Parrinello molecular dynamics simulations. The full reaction is divided into the reduction of the tetrahedral monoanion, RuO4-+e--->RuO4(2-), followed by water addition, RuO4(2-)+H2O-->[RuO3(OH)2]2-. The free energy of reduction is computed from the fluctuations of the vertical energy gap using the MnO4-+e--->MnO(4)2- reaction as reference. The free energy for water addition is estimated using constrained molecular dynamics methods. While the description of this complex reaction, in principle, involves multiple reaction coordinates, we found that reversible transformation of the reactant into the product can be achieved by control of a single reaction coordinate consisting of a suitable linear combination of atomic distances. The free energy difference of the full reaction is computed to be -0.62 eV relative to the normal hydrogen electrode. This is in good agreement with the experimental value of -0.59 eV, lending further support to the hypothesis that, contrary to the ruthenate monoanion, the dianion is not tetrahedral but forms a trigonal-bipyramidal dihydroxo complex in aqueous solution. We construct an approximate two-dimensional free energy surface using the coupling parameter for reduction and the mechanical constraint for water addition as variables. Analyzing this surface we find that in the most favorable reaction pathway the reduction reaction precedes water addition. The latter takes place via the protonated complex [RuO3(OH)]- and subsequent transport of the created hydroxide ion to the fifth coordination site of Ru.

Ab initio calculation of proton-coupled electron transfer rates using the external-potential representation: A ubiquinol complex in solution

In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schrodinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schrodinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes in this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.

On the position of the highest occupied molecular orbital in aqueous solutions of simple ions

The energies of the highest occupied molecular orbital (HOMO) of four simple microsolvated aqua ion clusters (Na+, Ag+, Cl-, CN-) are computed for varying numbers of water molecules. Extrapolating to infinite hydration numbers we find that these energies approach a value of -6 eV. This limiting one-electron energy is within a margin of +/-1 eV independent of the character of the ion and is 4 eV lower compared to the estimate obtained for the HOMO energy of the ions in aqueous solution under periodic boundary conditions. We argue that this discrepancy must the attributed to a shift in the reference of the one-electron potential of the periodic solvent model.

The Jahn-Teller effect of the Cr2+ ion in aqueous solution:Ab initio QM/MM molecular dynamics simulations

The hydration structure of Cr(2+) has been studied using molecular dynamics (MD) simulations including three-body corrections and combined ab initio quantum mechanical/molecular mechanical (QM/MM) MD simulations at the Hartree-Fock level. The structural properties are determined in terms of radial distribution functions, coordination numbers, and several angle distributions. The mean residence time was evaluated for describing ligand exchange processes in the second hydration shell. The Jahn-Teller distorted octahedral [Cr(H(2)O)(6)](2+) complex was pronounced in the QM/MM MD simulation. The first-shell distances of Cr(2+) are in the range of 1.9-2.8 A, which are slightly larger than those observed in the cases of Cu(2+) and Ti(3+). No first-shell water exchange occurred during the simulation time of 35 ps. Several water-exchange processes were observed in the second hydration shell with a mean residence time of 7.3 ps.

Insight into the solvent effect: A density functional theory study of cisplatin hydrolysis

The solvent effect on reactions in solutions is crucial for many systems. In this study, the reaction barrier with respect to the number of solvent molecules included in the system is systematically studied using density function theory calculations. Our results show that the barriers rapidly converge with respect to the number of solvent molecules. The solvent effect is investigated by calculating cisplatin hydrolysis in several types of solvents. The results are analyzed and a linear relationship between the reaction barrier and the interaction strength of solvent-reactants is found. Insight into the general solvent effect is obtained.

Solvent Reorganization Entropy of Electron Transfer in Polar Solvents

We report the results of molecular dynamics simulations of the solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile at varying temperatures. The simulations confirm the prediction of microscopic solvation theories of a positive reorganization entropy in polar solvents. The results of simulations are analyzed in terms of the splitting of the reorganization entropy into the contributions from the solute-solvent interaction and from the alteration of the solvent structure induced by the solute. These two contributions mutually cancel each other, resulting in the reorganization entropy amounting to only a fraction of each component.

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect, as discussed by the mode-coupling theory. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.

Density Functional Theory Study of Tetrathiafulvalene and Thianthrene in Acetonitrile: Structure, Dynamics, and Redox Properties†

The redox potentials of the organic compounds tetrathiafulvalene (TTF) and thianthrene (TH) in an explicit aprotic polar solvent, acetonitrile, have been computed using ab initio molecular dynamics simulation based on a Gaussian basis set methodology. The density functional description of the pure solvent yields a diffuse and mobile liquid, with structural and dynamical properties that are in good agreement with earlier classical models and experiment. Molecular dynamics simulation of both solute species in their neutral and radical cation states combined with free energy difference calculations result in estimates for the redox potentials of the reactions TH*+ + TTF --> TH + TTF*+ and TH2+ + TTF*+ --> TH*+ + TTF2+. The obtained values are 0.95 +/- 0.06 and 1.09 +/- 0.06 V, respectively, in excellent agreement with experimental data of 0.93 and 1.08 V. Our computational approach is based on Marcus theory, assuming quadratic free energy surfaces. We show that this approximation can still be accurate in systems, such as TH, that undergo a significant change in geometry upon oxidation. Furthermore, despite the different localization of the spin density in the radical cations, results based on self-interaction-corrected functionals and on standard generalized gradient approximations are identical to within 10 meV.

Diabatic free energy curves and coordination fluctuations for the aqueous Ag+∕Ag2+ redox couple: A biased Born-Oppenheimer molecular dynamics investigation

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction Ag(+)-->Ag(2+)+e(-) in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of Ag(+). Diabatic free energy curves of reduced (R) and oxidized (O) states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of Ag(+) and Ag(2+) are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of Ag(+) and find different values for the reorganization free energy of R (1.4 eV) and O (0.9 eV). The computed reorganization free energy of Ag(2+) is in good agreement with the experimental estimate of 0.9-1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for Ag(+) is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation.

On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter

The theory underlying the Car-Parrinello extended-Lagrangian approach to ab initio molecular dynamics (CPMD) is reviewed and reexamined using "heavy" ice as a test system. It is emphasized that the adiabatic decoupling in CPMD is not a decoupling of electronic orbitals from the ions but only a decoupling of a subset of the orbital vibrational modes from the rest of the necessarily coupled system of orbitals and ions. Recent work [J. Chem. Phys. 116, 14 (2002)] has pointed out that, due to the orbital-ion coupling that remains once adiabatic decoupling has been achieved, a large value of the fictitious mass mu can lead to systematic errors in the computed forces in CPMD. These errors are further investigated in the present work with a focus on those parts of these errors that are not corrected simply by rescaling the masses of the ions. It is suggested that any comparison of the efficiencies of Born-Oppenheimer molecular dynamics (BOMD) and CPMD should be performed at a similar level of accuracy. If accuracy is judged according to the average magnitude of the systematic errors in the computed forces, the efficiency of BOMD compares more favorably to that of CPMD than previous comparisons have suggested.

Scanning Tunneling Microscopy, Fourier Transform Infrared Spectroscopy, and Electrochemical Characterization of 2-Naphthalenethiol Self-Assembled Monolayers on the Au Surface: A Study of Bridge-Mediated Electron Transfer in Ru(NH3)62+|Ru(NH3)63+ Redox Reactions

We have studied the structure, adsorption kinetics, and barrier properties of self-assembled monolayers of 2-naphthalenethiol on Au using electrochemical techniques, grazing-angle Fourier transform infrared (FTIR) spectroscopy, and scanning tunneling microscopy (STM). The results of cyclic voltammetric and impedance measurements using redox probes show that 2-naphthalenethiol on Au forms a stable and reproducible, but moderately blocking, monolayer. Annealing of the self-assembled monolayer (SAM)-modified surface at 72 +/- 2 degrees C remarkably improves the blocking property of the monolayer of 2-naphthalenethiol on Au. From the study of kinetics of SAM formation, we find that the self-assembly follows Langmuir adsorption isotherm. Our STM and FTIR results show that the molecules are adsorbed with the naphthalene ring tilted from the surface normal by forming a square root 3 x 3 R30 degrees overlayer structure. From our studies, we conclude that the electron-transfer reaction of ferro/ferricyanide in the freshly formed monolayer occurs predominantly through the pinholes and defects present in the monolayer. However, in the case of thermally annealed specimen, although the ferro/ferricyanide reaction is almost completely blocked, the electron-transfer reaction of hexaammineruthenium(III) chloride is not significantly inhibited. It is proposed that the electron-transfer reaction in the case of the ruthenium redox couple takes place by a tunneling mechanism through the high-electron-density aromatic naphthalene ring acting as a bridge between the monolayer-modified electrode and the ruthenium complex.

Density-functional molecular-dynamics study of the redox reactions of two anionic, aqueous transition-metal complexes

The thermochemistry of the RuO(4)(2-)+MnO(4)(-)-->RuO(4)(-)+MnO(4)(2-) redox reaction in aqueous solution is studied by separate density-functional-based ab initio molecular-dynamics simulations of the component half reactions RuO(4)(2-)-->RuO(4)(-)+e(-) and MnO(4)(2-)-->MnO(4)(-)+e(-). We compare the results of a recently developed grand-canonical method for the computation of oxidation free energies to the predictions by the energy-gap relations of the Marcus theory that can be assumed to apply to these reactions. The calculated redox potentials are in good agreement. The subtraction of the half-reaction free energies gives an estimate of the free energy of the full reaction. The result obtained from the grand-canonical method is -0.4 eV, while the application of the Marcus theory gives -0.3 eV. These should be compared to the experimental value of 0.0 eV. Size effects, in response to increasing the number of water molecules in the periodic model system from 30 to 48, are found to be small ( approximately 0.1 eV). The link to the Marcus theory also has enabled us to compute reorganization free energies for oxidation. For both the MnO(4)(2-) and RuO(4)(2-) redox reactions we find the same reorganization free energy of 0.8 eV (1.0 eV in the larger system). The results for the free energies and further analysis of solvation and electronic structure confirm that these two tetrahedral oxoanions show very similar behavior in solution in spite of the central transition-metal atoms occupying a different row and column in the periodic table.

Time-Dependent Density Functional Theory Description of On-Site Electron Repulsion and Ligand Field Effects in the Optical Spectrum of Hexaaquoruthenium(II) in Solution

Time-dependent density functional theory (TDDFT) and density functional-based molecular dynamics were used to simulate the finite temperature t(2g)5 e(g) <-- t(2g)6 absorption band of the Ru2+ hexahydrate coordination complex in aqueous solution. The (1)T1 <-- (1)A1 and (1)T2 <-- (1)A1 molecular term splitting of this transition, which is not accounted for by the Kohn-Sham excitation spectrum, is shown to be satisfactorily reproduced by TDDFT at the BLYP/ALDA level of theory. Comparison to the spectrum of the Ru2+ (H2O)6 complex in vacuo computed by similar density functional classical molecular dynamics methods leads to the observation that bulk solvation has a negligible effect on the position and the shape of the absorption profile.