Electron Transfer Reactions In Solution Research Articles

Simulating Electron Transfer Reactions in Solution: Radical-Polar Crossover.

Single-electron transfer (SET) promotes a wide variety of interesting chemical transformations, but modeling of SET requires a careful treatment of electronic and solvent effects to give meaningful insight. Therefore, a combined constrained density functional theory and molecular mechanics (CDFT/MM) tool is introduced specifically for SET-initiated reactions. Mechanisms for two radical-polar crossover reactions involving the organic electron donors tetrakis(dimethylamino)ethylene (TDAE) and tetrathiafulvalene (TTF) were studied with the new tool. An unexpected tertiary radical intermediate within the TDAE system was identified, relationships between kinetics and substitution in the TTF system were explained, and the impact of the solvent environments on the TDAE and TTF reactions were examined. The results highlight the need for including solvent dynamics when quantifying SET kinetics and thermodynamics, as a free energy difference of >20 kcal/mol was observed. Overall, the new method informs mechanistic analysis of SET-initiated reactions and therefore is envisioned to be useful for studying reactions in the condensed phase.

An X-ray investigation of stereoselectivity in the interactions of [Co(en)3]3+ with [Co(ox)3]3- (en is ethane-1,2-diamine and ox is oxalate).

The X-ray structure of racemic tris(ethane-1,2-diamine-κ2N,N')cobalt(III) tris(oxalato-κ2O1,O2)cobaltate(III) pentahydrate, [Co(C2H8N2)3][Co(C2O4)3]·5H2O or [Co(en)3][Co(ox)3]·5H2O, has been determined. Hydrogen-bonding interactions along the C3-axis of the [Co(en)3]3+ cation with the [Co(ox)3]3- anion are heterochiral, while those perpendicular to this axis are homochiral. Implications for the interpretation of chiral discriminations and induction in electron-transfer reactions in solution are discussed.

Assessing the correctness of pressure correction to solvation theories in the study of electron transfer reactions.

Liquid state theories have emerged as a numerically efficient alternative to costly molecular dynamics simulations of electron transfer reactions in solution. In a recent paper [Jeanmairet et al., Chem. Sci. 10, 2130-2143 (2019)], we introduced the framework to compute the energy gap, free energy profile, and reorganization free energy using molecular density functional theory. However, this technique, as other molecular liquid state theories, overestimates the bulk pressure of the fluid. Because of the very high pressure, the predicted free energy is dramatically exaggerated. Several attempts were made to fix this issue, either based on simple a posteriori correction or by introducing bridge terms. By studying two model half reactions in water, Cl → Cl+ and Cl → Cl-, we assess the correctness of these two types of corrections to study electron transfer reactions. We found that a posteriori correction, because it violates the Variational principle, leads to an inconsistency in the definition of the reorganization free energy and should not be used to study electron transfer reactions. The bridge approach, because it is theoretically well grounded, is perfectly suitable for this type of systems.

Solid State Dilution Controls Marcus Inverted Transport in Rectifying Molecular Junctions.

Traditional Marcus theory accounts for electron transfer reactions in solutions, and the polarity of solvent molecule matters for them. How such an environment polarity affects electron transfer reactions in solid-state devices, however, remains uncertain. This paper describes how the Marcus inverted charge transport is influenced by solid-state molecular dilution in large-area tunneling junctions. A monolayer of 2,2'-bipyridyl terminated n-alkanethiolate (SC11BIPY), which rectifies currents via electron hopping within the inverted regime, is diluted with n-alkanethiolate (SCn) of different lengths (n = 8, 10, or 18) or at different surface mole fractions. The dilution introduces nonpolar environments within the monolayer, hinders stabilization of charged BIPY species upon electron hopping, and pushes the equilibrium of BIPY ⇄ BIPY•- process toward the reverse direction. Our work demonstrates that solid-state molecular dilution permits systematic control of the environment polarity of active component in nanoscale devices, much like solvent polarity control in solution, and their performances.

Energy-Storage Applications for a pH Gradient between Two Benzimidazole-Ligated Ruthenium Complexes That Engage in Proton-Coupled Electron-Transfer Reactions in Solution.

The judicious selection of pairs of benzimidazole-ligated ruthenium complexes allowed the construction of a rechargeable proton-coupled electron-transfer (PCET)-type redox battery. A series of ruthenium(II) and -(III) complexes were synthesized that contain substituted benzimidazoles that engage in PCET reactions. The formation of intramolecular Ru-C cyclometalation bonds stabilized the resulting ruthenium(III) complexes, in which pKa values of the imino N-H protons on the benzimidazoles are usually lower than those for the corresponding ruthenium(II) complexes. As a proof-of-concept study for a solution redox battery based on such PCET reactions, the charging/discharging cycles of several pairs of ruthenium complexes were examined by chronopotentiometry in an H-type device with half-cells separated by a Nafion membrane in unbuffered CH3CN/H2O (1/1, v/v) containing 0.1 M NaCl. During the charging/discharging cycles, the pH value of the solution gradually changed accompanied by a change of the open-circuit potential (OCP). The changes for the OCP and pH value of the solution in the anodic and cathodic half-cells were in good agreement with the predicted values from the Pourbaix diagrams for the pairs of ruthenium complexes used. Accordingly, the careful selection of pairs of ruthenium complexes with a sufficient potential gradient and a suitably large pKa difference is crucial: the charge generated between the two ruthenium complexes changes the OCP and the pH difference between the two cells in an unbuffered solution, given that the PCET reactions occur at both electrodes and that discharging leads to the original state. Because the electric energy is stored as a pH gradient between the half-cells, new possibilities for PCET-type rocking-chair redox batteries arise.

Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion.

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes.

Long range electron transfer reactions in solution: An analytically solvable model

We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of large number of potentials which are involved (donor – long bridge – acceptor) in the process. The coupling between these potentials are assumed to be represented by Dirac delta functions. The diffusive motion in this paper is represented by the Smoluchowski equation. Our solution requires the knowledge of the Laplace transform of the Green’s function for the motion in all the uncoupled potentials. For the case where all potentials are parabolic, we have derived a very simple expression for the Green’s function of the whole process under the semi-infinite limit.

Electroinduced Carbene Formation in the Cathodic Reduction of 1,2-Dicarbonyl Compounds via Electron-Transfer to the Solvent

Electrochemical reduction of 9,10-phenanthrenequinone, benzil and acenaphthenequinone in 1,1,1-trichloroethane (TCE)/TBAP under constant potential conditions provides an interesting entry to new coupling products through an electron-transfer reaction in solution to the chlorinated solvent. This electroinduced reaction points out the differences in the reaction pathway followed by these 1,2-dicarbonyl compounds depending on their geometry. The intermediates nature and their behavior, both in solution and at the electrode surface, are discussed.

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

We developed a double-quantum mechanical/molecular mechanical (d-QM/MM) method for investigation of full outer-sphere electron transfer (ET) processes between a donor and an acceptor (DA) in condensed matter. In the d-QM/MM method, which employs the novel concept of multiple QM regions, one can easily specify the number of electrons, spin states and appropriate exchange-correlation treatment in each QM region, which is especially important in the cases of ET involving transition metal sites. We investigated Fe(2+/3+) self-exchange and Fe(3+) + Ru(2+) → Fe(2+) + Ru(3+) in aqueous solution as model reactions, and demonstrated that the d-QM/MM method gives reasonable accuracy for the redox potential, reorganization free energy and electronic coupling. In particular, the DA distance dependencies of those quantities are clearly shown at the density functional theory hybrid functional level. The present d-QM/MM method allows us to explore the intermediate DA distance region, important for long-range ET phenomena observed in electrochemistry (on the solid-liquid interfaces) and biochemistry, which cannot be dealt by the half-reaction scheme with the conventional QM/MM.

Marcus Theory: Thermodynamics CAN Control the Kinetics of Electron Transfer Reactions

Although it is generally true that thermodynamics do not influence kinetics, this is NOT the case for electron transfer reactions in solution. Marcus Theory explains why this is so, using straightforward physical chemical principles such as transition state theory, Arrhenius’ Law, and the Franck-Condon Principle. Here the background and applications of Marcus Theory are presented, with special emphasis given to biological redox reactions. Interesting conclusions that arise from the theory are also discussed. These include the nonlinear contribution of reorganization energy (λ) to the activation free energy (ΔG⧧), as well as the existence of a defined “normal range” of reaction cell potential (ΔE°): Only if ΔE° is within this range does a reaction of lower λ have a lower ΔG⧧; outside of this range, the lower-λ reaction will have the higher ΔG⧧.

Correction to “Isotope Effects on the Nonequilibrium Dyanamics of Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution”

Correction to “Isotope Effects on the Nonequilibrium Dyanamics of Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution”

Isotope Effects on the Nonequilibrium Dynamics of Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution.

The hydrogen/deuterium isotope effects on the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) are investigated with a recently developed nonadiabatic dynamics approach. An ensemble of surface hopping trajectories is propagated according to a Langevin equation on electron-proton vibronic free energy surfaces that depend on a collective solvent coordinate. The calculations illustrate that ultrafast PCET reactions could exhibit a significant normal isotope effect, where PCET is faster for hydrogen than deuterium, but could also exhibit a negligible isotope effect or even a slight inverse isotope effect. The isotope effect is very small or absent when highly excited electron-proton vibronic states dictate the nonadiabatic dynamics and increases with greater participation of lower vibronic states. Thus, although the presence of a significant isotope effect strongly suggests that proton motion is coupled to electron transfer, the absence of an isotope effect does not exclude the possibility that proton transfer accompanies electron transfer in ultrafast photoinduced charge transfer processes.

Role of Solvent Dynamics in Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution

A theoretical formulation for modeling photoinduced nonequilibrium proton-coupled electron transfer (PCET) reactions in solution is presented. In this formulation, the PCET system is described by donor and acceptor electron-proton vibronic free energy surfaces that depend on a single collective solvent coordinate. Dielectric continuum theory is used to obtain a generalized Langevin equation of motion for this collective solvent coordinate. The terms in this equation depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties characterizing the vibronic surfaces. The ultrafast dynamics following photoexcitation is simulated using a surface hopping method in conjunction with the Langevin equation of motion. This methodology is used to examine a series of model photoinduced PCET systems, where the initial nonequilibrium state is prepared by vertical photoexcitation from the ground electronic state to the donor electronic state. Analysis of the dynamical trajectories provides insight into the interplay between the solvent dynamics and the electron-proton transfer for these types of processes. In addition, these model studies illustrate how the coupling between the electron-proton transfer and the solvent dynamics can be tuned by altering the solute and solvent properties.

Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P((1))(X,R,t)) and the product (P((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent. As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

ChemInform Abstract: Computer Simulations of Electron-Transfer Reactions in Solution and in Photosynthetic Reaction Centers

ChemInform Abstract: Computer Simulations of Electron-Transfer Reactions in Solution and in Photosynthetic Reaction Centers

Molecular factor analysis in self-exchange electron transfer reactions in solution

We present a systematic method to access molecular factors and rate constants for self-exchange electron transfer reactions in solution using partial least squares and a number of chosen descriptors. In this work it is shown that the log response for the set of reactions considered can be mostly described in terms of the Intersecting State Model (ISM) when the nonadiabaticity of transfers involving electrons in σ*-orbitals is considered.

Ab initio molecular orbital study of dinitrobenzene radical anions

A theoretical study of 1,3-dinitrobenzene (DNB) radical anion, which exhibits an intramolecular electron transfer reaction in solution, is reported. The geometries of 1,3-DNB and 1,4-DNB radical anions have been optimized as isolated species to reveal their intrinsic properties by using CASSCF theory with the aug-cc-pVDZ basis set. Single-point energy calculations have been carried out at the CASPT2 and CCSD(T) levels. It is demonstrated that the 1,3-DNB radical anion is slightly more stable as an electronically localized structure in the absence of solvent, whereas the 1,4-DNB radical anion has a delocalized structure.

Ultrafast Electron Transfer Dynamics of a Zn(II)porphyrin−Viologen Complex Revisited: S2 vs S1 Reactions and Survival of Excess Excitation Energy

The photoinduced electron transfer reactions in a self-assembled 1:1 complex of zinc(II)tetrasulphonatophenylporphyrin (ZnTPPS(4-)) and methylviologen (MV(2+)) in aqueous solution were investigated with transient absorption spectroscopy. ZnTPPS(4-) was excited either in the Soret or one of the two Q-bands, corresponding to excitation into the S(2) and S(1) states, respectively. The resulting electron transfer to MV(2+) occurred, surprisingly, with the same time constant of τ(FET) = 180 fs from both electronic states. The subsequent back electron transfer was rapid, and the kinetics was independent of the initially excited state (τ(BET) = 700 fs). However, ground state reactants in a set of vibrationally excited states were observed. The amount of vibrationally excited ground states detected increased with increasing energy of the initial excited state, showing that excess excitation energy survived a two-step electron transfer reaction in solution. Differences in the ZnTPSS(•3-)/MV(•+) spectra suggest that the forward electron transfer from the S(2) state at least partially produces an electronically excited charge transfer state, which effectively suppresses the influence of the inverted regime. Other possible reasons for the similar electron transfer rates for the different excited states are also discussed.

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.

Two-Dimensional Free Energy Surfaces for Electron Transfer Reactions in Solution

Change in intermolecular distance between electron donor (D) and acceptor (A) can induce intermolecular electron transfer (ET) even in nonpolar solvent, where solvent orientational polarization is absent. This was shown by making simple calculations of the energies of the initial and final states of ET. In the case of polar solvent, the free energies are functions of both D-A distance and solvent orientational polarization. On the basis of 2-dimensional free energy surfaces, the relation of Marcus ET and exciplex formation is discussed. The transient effect in fluorescence quenching was measured for several D-A pairs in a nonpolar solvent. The results were analyzed by assuming a distance dependence of the ET rate that is consistent with the above model.