A frequency-resolved cavity model (FRCM) for treating equilibrium and non-equilibrium solvation energies

Substituent Effects on Photochemistry of Anthracene-Phenol-Pyridine Triads Revealed by Multireference Calculations

Inverted region behavior for concerted proton-coupled electron transfer (PCET) was recently demonstrated for biomimetic anthracene-phenol-pyridine molecular triads. Photoexcitation of the anthracene to a locally excited state (LES) is followed by concerted electron transfer from the phenol to the anthracene and proton transfer from the phenol to the pyridine, forming a relatively long-lived charge separated state (CSS). The long-lived CSS and the inverted region behavior associated with the decay from the CSS to the ground state through charge recombination were experimentally observed only for triads with certain substituents on the anthracene and the pyridine. To explain this distinction, we computed the proton potential energy curves in four substituted triads using the complete active space self-consistent-field method and multireference perturbation theory, including solvent effects with a dielectric continuum model. The calculations revealed a local electron-proton transfer (LEPT) state, in which both the electron and proton transfer from the phenol to the pyridine. When the LEPT state is lower in energy than the CSS, it may provide an alternative pathway for fast decay from the LES to the ground state and thereby preclude detection of the CSS and the inverted region behavior. These calculations predict that substituents stabilizing negative charge on the pyridine and destabilizing negative charge on the anthracene will favor the LEPT pathway, while substituents with the reverse effects will favor the CSS pathway, which could exhibit inverted region behavior. These insights about the stabilization of energy-storing charge-separated states have implications for designing and controlling PCET reactions in artificial photosynthetic systems and other energy conversion processes.

Charge carrier mobility in one-dimensional aligned π-stacks of conjugated small molecules with a benzothiadiazole central unit

A theoretical study is applied to gain insight into the microscopic electron and hole transport in benzothiadiazole-cored molecular semiconductors either with furan or thiophene flanks arranged in π-stacks. For the characterization of the energetics of the reduction and oxidation processes and their impact on the molecular geometry, the internal reorganization energy is defined for isolated molecules in the gas phase. The outer-shell reorganization energy is evaluated within the frequency-resolved cavity model and as an electrostatic contribution within the polarizable continuum model. The intermolecular electronic coupling interaction for the Marcus charge hopping is calculated using the energy splitting in dimer method, the generalized Mulliken-Hush approach and the fragment charge difference scheme. In order to probe the relation between the charge hopping rate/charge carrier mobility and the molecular organization within the π-stacks, different stacking modes are investigated: (i) dimers with a perfect registry, i.e. segregated stacking motif, when molecules are placed face-to-face, and (ii) dimers forming slipped cofacial orientations with longitudinal and transverse shifts, i.e. mixed stacking motif. Besides, the effects of molecular planarity and rigidity, influencing internal molecular relaxation upon charging, the effects of non-covalent interactions within stacks and the heteroatom replacement on the charge carrier mobility are studied. The results obtained in the simulations of one-dimensional aligned π-stacks of molecular semiconductors are compared with available experimental data for small conjugated benzothiadiazole-cored molecules with thiophene flanks and benzothiadiazole-quaterthiophene-based copolymers.

The role of acid–base equilibria in formal hydrogen transfer reactions: tryptophan radical repair by uric acid as a paradigmatic case

The sequential proton gain electron transfer and proton electron sequential transfer mechanisms play the most important roles in tryptophan repair by uric acid.

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.

Long Range Proton-Coupled Electron Transfer Reactions of Bis(imidazole) Iron Tetraphenylporphyrins Linked to Benzoates

Concerted proton-electron transfer (CPET) reactions in iron carboxy-tetraphenylporphyrin complexes have been investigated using both experimental and theoretical methods. Synthetic heme models abstract H⁺ and e^- from the hydroxylamine TEMPOH or an ascorbate derivative, and the kinetics of the TEMPOH reaction indicate concerted transfer of H⁺ and e^-. Phenylene linker domains vary the electron donor/acceptor separation by approximately 4 Å. The rate data and extensive molecular simulations show that the electronic coupling decay constant (β) depends on conformational flexibility and solvation associated with the linker domain. Our best estimate of β is 0.23 ± 0.07 Å^-1, a value that is near the low end of the range (0.2-0.5 Å^-1) established for electron transfer reactions involving related linkers. This is the first analysis of β for a CPET reaction.

Electron transfer within self-assembling cyclic tetramers using chlorophyll-based donor-acceptor building blocks

The synthesis and photoinduced charge transfer properties of a series of Chl-based donor-acceptor triad building blocks that self-assemble into cyclic tetramers are reported. Chlorophyll a was converted into zinc methyl 3-ethylpyrochlorophyllide a (Chl) and then further modified at its 20-position to covalently attach a pyromellitimide (PI) acceptor bearing a pyridine ligand and one or two naphthalene-1,8:4,5-bis(dicarboximide) (NDI) secondary electron acceptors to give Chl-PI-NDI and Chl-PI-NDI(2). The pyridine ligand within each ambident triad enables intermolecular Chl metal-ligand coordination in dry toluene, which results in the formation of cyclic tetramers in solution, as determined using small- and wide-angle X-ray scattering at a synchrotron source. Femtosecond and nanosecond transient absorption spectroscopy of the monomers in toluene-1% pyridine and the cyclic tetramers in toluene shows that the selective photoexcitation of Chl results in intramolecular electron transfer from (1*)Chl to PI to form Chl(+•)-PI(-•)-NDI and Chl(+•)-PI(-•)-NDI(2). This initial charge separation is followed by a rapid charge shift from PI(-•) to NDI and subsequent charge recombination of Chl(+•)-PI-NDI(-•) and Chl(+•)-PI-(NDI)NDI(-•) on a 5-30 ns time scale. Charge recombination in the Chl-PI-NDI(2) cyclic tetramer (τ(CR) = 30 ± 1 ns in toluene) is slower by a factor of 3 relative to the monomeric building blocks (τ(CR) = 10 ± 1 ns in toluene-1% pyridine). This indicates that the self-assembly of these building blocks into the cyclic tetramers alters their structures in a way that lengthens their charge separation lifetimes, which is an advantageous strategy for artificial photosynthetic systems.

Probing quantum and dynamic effects in concerted proton-electron transfer reactions of phenol-base compounds

The oxidation of three phenols, which contain an intramolecular hydrogen bond to a pendent pyridine or amine group, has been shown, in a previous experimental study, to undergo concerted proton-electron transfer (CPET). In this reaction, the electron is transferred to an outer-sphere oxidant, and the proton is transferred from the oxygen to nitrogen atom. In the present study, this reaction is studied computationally using a version of Hammes-Schiffer's multistate continuum theory where CPET is formulated as a transmission frequency between neutral and cation vibrational-electronic states. The neutral and cation proton vibrational wave functions are computed from one-dimensional potential energy surfaces (PESs) for the transferring proton in a fixed heavy atom framework. The overlap integrals for these neutral/cation wave functions, considering several initial (i.e., neutral) and final (i.e., cation) vibrational states, are used to evaluate the relative rates of oxidation. The analysis is extended to heavy atom configurations with various proton donor-acceptor (i.e., O-N) distances to assess the importance of heavy atom "gating". Such changes in d(ON) dramatically affect the nature of the proton PESs and wave functions. Surprisingly, the most reactive configurations have similar donor-acceptor distances despite the large (~0.2 Å) differences in the optimized structures. These theoretical results qualitatively reproduce the experimental faster reactivity of the reaction of the pyridyl derivative 1 versus the CH(2)-pyridyl 2, but the computed factor of 5 is smaller than the experimental 10(2). The amine derivative is calculated to react similarly to 1, which does not agree with the experiments, likely due to some of the simplifying assumptions made in applying the theory. The computed kinetic isotope effects (KIEs) and their temperature dependence are in agreement with experimental results.

SOLVENT REORGANIZATION ENERGY WITH DIELECTRIC GREEN FUNCTIONAL AND ITS APPLICATION TO RETURN ELECTRON TRANSFER IN TETRACYANOETHYLENE-HEXAMETHYLBENZENE SYSTEM

Based on classical electrodynamics, the proper integral formula for general cases is adopted to estimate the electrostatic free energy difference between two given states, e.g. equilibrium and non-equilibrium states in the charging process of solute molecule in solution. With adequate consideration of the change of dielectric property in establishing the non-equilibrium state, the electrostatic free energy for this state can be obtained in a form differing from the traditional theories. The general formula of the solvent reorganization energy is derived according to the definition of the free energy difference between the non-equilibrium and equilibrium states due to the same electronic state of the solute molecule. Applying it to the two-sphere model and single-sphere model, we obtain the new expressions of the solvent reorganization energy, which are convenient to be used in practice. In the investigation of the return electron transfer of tetracyanoethylene-hexmethylbenzene system, good results can be obtained by using our expression when they are compared with those from the experiment.

SOLVATION ENERGY OF NONEQUILIBRIUM POLARIZATION: OLD QUESTION, NEW ANSWER

Although an old question, the electrostatic free energy of nonequilibrium solvation in a continuous dielectric has recently been disputed. Here we show that the nonequilibrium solvation energy can be obtained without any ambiguity by imposing a suitable external electric field with its source localized in the ambient so as to bring the nonequilibrium into an equilibrium state but constrain its charge distribution, polarization, and entropy unchanged. As an application, a two-sphere cavity model is proposed for estimating the solvent reorganization energy, which solves the longstanding issue that it tends to be overestimated by a factor of two by the popular continuum models.

Theoretical analysis of the unusual temperature dependence of the kinetic isotope effect in quinol oxidation

In this paper we present theoretical calculations on model biomimetic systems for quinol oxidation. In these model systems, an excited-state [Ru(bpy)(2)(pbim)](+) complex (bpy = 2,2'-dipyridyl, pbim = 2-(2-pyridyl)benzimidazolate) oxidizes a ubiquinol or plastoquinol analogue in acetonitrile. The charge transfer reaction occurs via a proton-coupled electron transfer (PCET) mechanism, in which an electron is transferred from the quinol to the Ru and a proton is transferred from the quinol to the pbim(-) ligand. The experimentally measured average kinetic isotope effects (KIEs) at 296 K are 1.87 and 3.45 for the ubiquinol and plastoquinol analogues, respectively, and the KIE decreases with temperature for plastoquinol but increases with temperature for ubiquinol. The present calculations provide a possible explanation for the differences in magnitudes and temperature dependences of the KIEs for the two systems and, in particular, an explanation for the unusual inverse temperature dependence of the KIE for the ubiquinol analogue. These calculations are based on a general theoretical formulation for PCET reactions that includes quantum mechanical effects of the electrons and transferring proton, as well as the solvent reorganization and proton donor-acceptor motion. The physical properties of the system that enable the inverse temperature dependence of the KIE are a stiff hydrogen bond, which corresponds to a high-frequency proton donor-acceptor motion, and small inner-sphere and solvent reorganization energies. The inverse temperature dependence of the KIE may be observed if the 0/0 pair of reactant/product vibronic states is in the inverted Marcus region, while the 0/1 pair of reactant/product vibronic states is in the normal Marcus region and is the dominant contributor to the overall rate. In this case, the free energy barrier for the dominant transition is lower for deuterium than for hydrogen because of the smaller splittings between the vibronic energy levels for deuterium, and the KIE increases with increasing temperature. The temperature dependence of the KIE is found to be very sensitive to the interplay among the driving force, the reorganization energy, and the vibronic coupling in this regime.

Buffer-Assisted Proton-Coupled Electron Transfer in a Model Rhenium−Tyrosine Complex

The mechanism for tyrosyl radical generation in the [Re(P-Y)(phen)(CO)3]PF6 complex is investigated with a multistate continuum theory for proton-coupled electron transfer (PCET) reactions. Both water and the phosphate buffer are considered as potential proton acceptors. The calculations indicate that the model in which the proton acceptor is the phosphate buffer species HPO(4)2- can successfully reproduce the experimentally observed pH dependence of the overall rate and H/D kinetic isotope effect, whereas the model in which the proton acceptor is water is not physically reasonable for this system. The phosphate buffer species HPO4(2-) is favored over water as the proton acceptor in part because the proton donor-acceptor distance is approximately 0.2 A smaller for the phosphate acceptor due to its negative charge. The physical quantities impacting the overall rate constant, including the reorganization energies, reaction free energies, activation free energies, and vibronic couplings for the various pairs of reactant/product vibronic states, are analyzed for both hydrogen and deuterium transfer. The dominant contribution to the rate arises from nonadiabatic transitions between the ground reactant vibronic state and the third product vibronic state for hydrogen transfer and the fourth product vibronic state for deuterium transfer. These contributions dominate over contributions from lower product states because of the larger vibronic coupling, which arises from the greater overlap between the reactant and product vibrational wave functions. These calculations provide insight into the fundamental mechanism of tyrosyl radical generation, which plays an important role in a wide range of biologically important processes.

Molecular simulations of outersphere reorganization energies in polar and quadrupolar solvents. The case of intramolecular electron and hole transfer

Outersphere reorganization energies (lambda) for intramolecular electron and hole transfer are studied in anion- and cation-radical forms of complex organic substrates (p-phenylphenyl-spacer-naphthyl) in polar (water, 1,2-dichloroethane, tetrahydrofuran) and quadrupolar (supercritical CO2) solvents. Structure and charge distributions of solute molecules are obtained at the HF/6-31G(d,p) level. Standard Lennard-Jones parameters for solutes and the nonpolarizable simple site-based models of solvents are used in molecular dynamics (MD) simulations. Calculation of lambda is done by means of the original procedure, which treats electrostatic polarization of a solvent in terms of a usual nonpolarizable MD scheme supplemented by scaling of reorganization energies at the final stage. This approach provides a physically relevant background for separating inertial and inertialless polarization responses by means of a single parameter epsilon(infinity), optical dielectric permittivity of the solvent. Absolute lambda values for hole transfer in 1,2-dichloroethane agree with results of previous computations in terms of the different technique (MD/FRCM, Leontyev, I. V.; et al. Chem. Phys. 2005, 319, 4). Computed lambda values for electron transfer in tetrahydrofuran are larger than the experimental values by ca. 2.5 kcal/mol; for the case of hole transfer in 1,2-dichloroethane the discrepancy is of similar magnitude provided the experimental data are properly corrected. The MD approach gives nonzero lambda values for charge-transfer reaction in supercritical CO2, being able to provide a uniform treatment of nonequilibrium solvation phenomena in both quadrupolar and polar solvents.

Molecular Simulation of Solvent-Induced Stokes Shift in Absorption/Emission Spectra of Organic Chromophores

The values of steady-state solvatochromic Stokes shifts (SS) in absorption/emission electronic spectra of organic chromophores are studied theoretically in the framework of the Hush-Marcus model. Charge distributions for chromophore solutes in their S0 and S1 states are found by means of conventional quantum-chemical methods combined with the continuum PCM approach for treating solvation effects. The solvent reorganization energies, which are expected to correlate with the solvent-induced part of 1/2 SS, are found in a molecular dynamics (MD) simulation which invokes a novel method for separation of the inertial piece of the electrostatic response (Vener, et al. J. Phys. Chem. B 2006, 110, 14950). Computations, performed in two solvents (acetonitrile and benzene), consider three organic dyes: coumarin 153 as a benchmark system and two other chromophores, for which experimental spectra are also reported. The results are found to be in reasonable agreement with the experiment. A consistent treatment of nonlinear effect in the solvent response, promoted by the polarizability of solutes and contributing to the solvent reorganization energies (Ingrosso, et al. J. Phys. Chem. B 2005, 109, 3553), improves the results of computations.

Chemical approaches to artificial photosynthesis. 2

The goal of artificial photosynthesis is to use the energy of the sun to make high-energy chemicals for energy production. One approach, described here, is to use light absorption and excited-state electron transfer to create oxidative and reductive equivalents for driving relevant fuel-forming half-reactions such as the oxidation of water to O2 and its reduction to H2. In this "integrated modular assembly" approach, separate components for light absorption, energy transfer, and long-range electron transfer by use of free-energy gradients are integrated with oxidative and reductive catalysts into single molecular assemblies or on separate electrodes in photelectrochemical cells. Derivatized porphyrins and metalloporphyrins and metal polypyridyl complexes have been most commonly used in these assemblies, with the latter the focus of the current account. The underlying physical principles--light absorption, energy transfer, radiative and nonradiative excited-state decay, electron transfer, proton-coupled electron transfer, and catalysis--are outlined with an eye toward their roles in molecular assemblies for energy conversion. Synthetic approaches based on sequential covalent bond formation, derivatization of preformed polymers, and stepwise polypeptide synthesis have been used to prepare molecular assemblies. A higher level hierarchial "assembly of assemblies" strategy is required for a working device, and progress has been made for metal polypyridyl complex assemblies based on sol-gels, electropolymerized thin films, and chemical adsorption to thin films of metal oxide nanoparticles.

A Theoretical Investigation of Charge Transfer in Several Substituted Acridinium Ions

We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken-Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide range of torsional angles. Nevetheless, the initial and final cationic states remain reasonably well-localized over this range, and thus TICT state formation is unlikely in these systems. Finally, a version of the GMH model based on Koopmans' Theorem is developed and found to yield coupling elements generally within a factor of 2 of the many-electron GMH for a sample acridinium system, but with overestimated adiabatic and diabatic dipole moment differences.

Solvent Dependence of the Spectra and Kinetics of Excited-State Charge Transfer in Three (Alkylamino)benzonitriles

Steady-state absorption and emission spectra and emission decay kinetics are reported for 4-aminobenzonitrile (ABN), 4-(1-azetidinyl)benzonitrile (P4C), 4-(1-pyrrolidinyl)benzonitrile (P5C), and 4-(1-piperidinyl)benzonitrile (P6C) in 24 room temperature solvents. In solvents of modest to high polarity, P4C, P5C, and P6C exhibit dual fluorescence and emission decays characteristic of the transformation from an initially prepared (LE) state to a more polar charge transfer (CT) state, whereas ABN does not undergo this reaction. The frequencies of the steady-state absorption and emission spectra of all of these solutes can be rationalized using a dielectric continuum description of the solvent and considering only the minima on the reactive surfaces, which are assumed to involve both an intramolecular (twisting) and a solvation coordinate. Characteristics of the gas-phase solutes deduced from this analysis are in good agreement with electronic structure calculations and indicate that differences in their spectra mainly reflect differences in the relative energies of the gas-phase LE and CT states. The relative yields of LE and CT emission are not described as satisfactorily by this model, and reasons for this failure are discussed. The kinetics of the LE --> CT reaction vary considerably with solute and solvent. In many solvents, the emission decays of P4C are reasonably described by a simple two-state kinetic scheme with time-independent rate constants. In P5C and P6C multiexponential decays are observed that reflect time-dependent shifts of the component spectra as well as time-dependent reaction rates. A simplified analysis of these complex dynamics provides estimates for both the free energy change Delta(r)G and (average) LE --> CT rate constant k(f) for a wide range of solute and solvent combinations. The driving force for reaction (-Delta(r)G) follows the order P6C > P5C > P4C and increases with increasing solvent polarity. The reaction rates are correlated to Delta(r)G and follow the opposite trend. The relationships observed between k(f) and Delta(r)G suggest that static solvent effects, i.e., barrier height changes, are the primary determinants of the solvent dependence in P4C. Correlations between barrier-corrected rates and solvation times suggest that dynamical solvent effects contribute substantially to the solvent dependence of the rates in P5C, and especially P6C.

Continuous medium theory for nonequilibrium solvation: III. Solvation shift by monopole approximation and multipole expansion in spherical cavity

According to the classical electrodynamics, a new and reasonable method about electrostatic energy decomposition of the solute-solvent system has been proposed in this work by introducing the concept of spring energy. This decomposition in equilibrium solvation gives the clear comprehension for different parts of total electrostatic free energy. Logically extending this cognition to nonequilibrium leads to the new formula of electrostatic free energy of nonequilibrium state. Furthermore, the general solvation shift for light absorption/emission has been reformulated and applied to the ideal sphere case with the monopole approximation and multipole expansion. Solvation shifts in vertical ionizations of atomic ions of some series of main group elements have been investigated with monopole approximation, and the variation tendency of the solvation shift versus atomic number has been discussed. Moreover, the solvation shift in photoionization of nitrate anion in glycol has been investigated by the multipole expansion method.

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.

Theoretical studies of proton-coupled electron transfer reactions

A theoretical formulation for proton-coupled electron transfer (PCET) is described. This theory allows the calculation of rates and kinetic isotope effects and provides insight into the underlying fundamental principles of PCET reactions. Applications of this theory to PCET reactions in iron bi-imidazoline complexes, oxoruthenium polypyridyl complexes, osmium-benzoquinone systems, amidinium-carboxylate salt bridges, DNA-acrylamide complexes, and ruthenium polypyridyl-tyrosine systems are summarized. The mechanistic insight gained from theoretical calculations on these model systems is relevant to PCET in more complex biological processes such as photosynthesis and respiration.

Continuous medium theory for nonequilibrium solvation: II. Interaction energy between solute charge and reaction field and single-sphere model for spectral shift

On the basis of continuous medium theory, a model for evaluation of spectral shifts in solution has been developed in this work. The interaction energy between solute dipole and reaction field and the self-energy of the reaction field have been formulated through derivations. Applying the interaction energy expression together with the point dipole approximation to the case of spherical cavity produces new formulations of spectral shifts. The same expression of electrostatic free energy of the nonequilibrium state is achieved by integrating the change of the electrostatic free energy for a charging process. Moreover, generalized formulations evaluating spectral shifts have been established in the charge-potential notation, and the reduction of them to the point dipole case consistently leads to the same formulations of spectral shifts as those by interaction energy approach. Mutual supports provide convincing evidences for the reliability of the present results. In this work, attentions are particularly paid to the conclusion of zero self-energy of the reaction field, which is different from the previous theory. Reasoning and arguments are given on this point. From the present derivations, it is concluded that the spectral shifts of light absorption and emission were theoretically exaggerated in the past, in particular, by a factor of 2 for the spectral shift sum.

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.

Proton-coupled electron transfer in a model for tyrosine oxidation in photosystem II

Theoretical calculations of a model for tyrosine oxidation in photosystem II are presented. In this model system, an electron is transferred to ruthenium from tyrosine, which is concurrently deprotonated. This investigation is motivated by experimental measurements of the dependence of the rates on pH and temperature (Sjödin et al. J. Am. Chem. Soc. 2000, 122, 3932). The mechanism is proton-coupled electron transfer (PCET) at pH < 10 when the tyrosine is initially protonated and is single electron transfer (ET) for pH > 10 when the tyrosine is initially deprotonated. The PCET rate increases monotonically with pH, whereas the single ET rate is independent of pH and is 2 orders of magnitude faster than the PCET rate. The calculations reproduce these experimentally observed trends. The pH dependence for the PCET reaction arises from the decrease in the reaction free energies with pH. The calculations indicate that the larger rate for single ET arises from a combination of factors, including the smaller solvent reorganization energy for ET and the averaging of the coupling for PCET over the reactant and product hydrogen vibrational wave functions (i.e., a vibrational overlap factor in the PCET rate expression). The temperature dependence of the rates, the solvent reorganization energies, and the deuterium kinetic isotope effects determined from the calculations are also consistent with the experimental results.

Theoretical investigation of large kinetic isotope effects for proton-coupled electron transfer in ruthenium polypyridyl complexes

A theoretical investigation of proton-coupled electron transfer in ruthenium polypyridyl complexes is presented. The three reactions studied are as follows: (1) the comproportionation reaction of [(bpy)(2)(py)Ru(IV)O](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(bpy)(2)(py)Ru(III)OH](2+); (2) the comproportionation reaction of [(tpy)(bpy)Ru(IV)O](2+) and [(tpy)(bpy)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(III)OH](2+); and (3) the cross reaction of [(tpy)(bpy)Ru(III)OH](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(II)OH(2)](2+) and [(bpy)(2)(py)Ru(III)OH](2+). This investigation is motivated by experimental measurements of rates and kinetic isotope effects for these systems (Binstead, R. A.; Meyer, T. J. J. Am. Chem. Soc. 1987, 109, 3287. Farrer, B. T.; Thorp, H. H. Inorg. Chem. 1999, 38, 2497.). These experiments indicate that the second reaction is nearly one order of magnitude faster than the first reaction, and the third reaction is in the intermediate regime. The experimentally measured kinetic isotope effects for these three reactions are 16.1, 11.4, and 5.8, respectively. The theoretical calculations elucidate the physical basis for the experimentally observed trends in rates and kinetic isotope effects, as well as for the unusually high magnitude of the kinetic isotope effects. In this empirical model, the proton donor-acceptor distance is predicted to be largest for the first reaction and smallest for the third reaction. This prediction is consistent with the degree of steric crowding near the oxygen proton acceptor for the three reactions. The second reaction is faster than the first reaction since a smaller proton donor-acceptor distance leads to a larger overlap between the reactant and product proton vibrational wave functions. The intermediate rate of the third reaction is determined by a balance among several competing factors. The observed trend in the kinetic isotope effects arises from the higher ratio of the hydrogen to deuterium vibrational wave function overlap for larger proton donor-acceptor distances. Thus, the kinetic isotope effect increases for larger proton donor-acceptor distances. The unusually high magnitude of the kinetic isotope effects is due in part to the close proximity of the proton transfer interface to the electron donor and acceptor. This proximity results in strong electrostatic interactions that lead to a relatively small overlap between the reactant and product vibrational wave functions.

Comparison of hydride, hydrogen atom, and proton-coupled electron transfer reactions

A comparison of hydride, hydrogen atom, and proton-coupled electron transfer reactions is presented. Herein, hydride and hydrogen atom transfer refer to reactions in which the electrons and protons transfer between the same donor and acceptor, while proton-coupled electron transfer (PCET) refers to reactions in which the electrons and protons transfer between different centers. Within these definitions, hydride and hydrogen atom transfer reactions are typically electronically adiabatic, hence evolving on a single electronic surface. In contrast, PCET reactions are often electronically nonadiabatic since the electron transfers a longer distance through a proton transfer interface. For all three types of reactions, solute reorganization is important, particularly the hydrogen donor--acceptor mode. Solvent reorganization is critical for hydride transfer and PCET, which involve significant solute charge redistribution, but not for hydrogen atom transfer. Theoretical descriptions and simulation methodology for all three types of reactions are presented, as well as experimentally relevant applications to hydride transfer in enzymes and PCET in solution.

Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazoline complexes

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.