Solvent Control of Electron Transfer Reactions

Direct observation of coherent femtosecond solvent reorganization coupled to intramolecular electron transfer

It is well known that the solvent plays a critical role in ultrafast electron-transfer reactions. However, solvent reorganization occurs on multiple length scales, and selectively measuring short-range solute-solvent interactions at the atomic level with femtosecond time resolution remains a challenge. Here we report femtosecond X-ray scattering and emission measurements following photoinduced charge-transfer excitation in a mixed-valence bimetallic (FeⁱⁱRuⁱⁱⁱ) complex in water, and their interpretation using non-equilibrium molecular dynamics simulations. Combined experimental and computational analysis reveals that the charge-transfer excited state has a lifetime of 62 fs and that coherent translational motions of the first solvation shell are coupled to the back electron transfer. Our molecular dynamics simulations identify that the observed coherent translational motions arise from hydrogen bonding changes between the solute and nearby water molecules upon photoexcitation, and have an amplitude of tenths of ångströms, 120-200 cm^-1 frequency and ~100 fs relaxation time. This study provides an atomistic view of coherent solvent reorganization mediating ultrafast intramolecular electron transfer.

Molecular dynamics simulations of the dielectric properties of fructose aqueous solutions

The static dielectric permittivity and dielectric relaxation properties of fructose aqueous solutions of different concentrations ranging from 1.0 to 4.0 mol l(-1) are investigated by means of molecular dynamics simulations. The contributions from intra- and interspecies molecular correlations were computed individually for both the static and frequency-dependent dielectric properties, and the results were compared with the available experimental data. Simulation results in the time- and frequency-domains were analyzed and indicate that the presence of fructose has little effect on the position of the fast, high-frequency (>500 cm(-1)) components of the dielectric response spectrum. The low-frequency (<0.1 cm(-1)) components, however, are markedly influenced by sugar concentration. Our analysis indicates that fructose-fructose and fructose-water interactions strongly affect the rotational-diffusion regime of molecular motions in the solutions. Increasing fructose concentration not only enhances sugar-sugar and sugar-water low frequency contributions to the dielectric loss spectrum but also slows down the reorientational dynamics of water molecules. These results are consistent with previous computer simulations carried out for other disaccharide aqueous solutions.

A spherical cavity model for quadrupolar dielectrics

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field, and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have a small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager's theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures.

Do H-bonds explain strong ion aggregation in ethylammonium nitrate + acetonitrile mixtures?

Binary mixtures of the protic ionic liquid ethylammonium nitrate (EAN) and acetonitrile (AN) were studied at 25 °C over the entire composition range by means of broadband dielectric spectroscopy covering 0.2 ≤ ν/GHz ≤ 89. The dielectric spectra could be decomposed into two relaxation processes, both of which proved to be composite modes. For dilute solutions the higher-frequency Debye relaxation centered at ∼60 GHz is associated with the rotational diffusion of AN molecules, whereas at higher salt concentrations ultra-fast intermolecular vibrations and librations of EAN dominate the process. For EAN-rich solutions the lower-frequency relaxation is mainly due to jump reorientation of the ethylammonium cation, whereas contact ion pairs (CIPs) dominate this mode for dilute solutions. From the relaxation amplitudes effective solvation numbers and ion-pair concentrations were determined. For vanishing EAN mole fraction, xEAN → 0, an effective cation solvation number of ∼7 was found which steeply drops until xEAN ≈ 0.2 but shows only moderate decrease later on. The obtained association constant for EAN, K0(A) = 970 L mol(-1), exceeds that of other 1 : 1 electrolytes in AN by a factor of ∼30-50. This observation, as well as the fact that CIPs are formed despite strong cation solvation, indicates that ion pairing is mainly driven by the formation of strong hydrogen bonds between anions and cations.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.

ESR-Investigations on the Dynamic Solvent Effects of Degenerate Electron Exchange Reactions. Part I: Cyanobenzenes

The rates of degenerate electron exchange (electron self-exchange) of various cyanobenzenes have been measured by EPR line broadening technique in nine different solvents at room temperature. The molecules studied comprise besides benzene-1,2-dicarbonitrile, benzene-1,4-dicarbonitrile and benzene-1,2,4,5-tetracarbonitrile, the two isomeric tricyanobenzenes, benzene-1,2,3-tricarbonitrile and benzene-1,2,4-tricarbonitrile, the anion radicals of which have not been characterized before.

The experimentally observed rates vary from 4.5 × 108 to 44.0 × 108 M−1 s−1 and show the pronounced dependence on the longitudinal relaxation times, τL, of the solvents. The solvent dynamical effect so manifested is confirmed with remarkable clarity using solvents spanning a wide range of τL-values, which comprise acetonitrile (0.2 ps) and o-dichlorobenzene (6.0 ps) at its extremes. The rate constants are compared with Marcus theory using the continuum model (CM) and the mean spherical approximation (MSA) for the outer sphere reorganization energies and Nelson’s method for the inner sphere reorganization energies. Furthermore, an estimation of the resonance splitting energies, V RP, is given based on the experimental rates.

Quadrupolar solvatochromism: 4-amino-phthalimide in toluene

We present calculations of the temperature dependence of the solvent reorganization energy of 4-amino-phthalimide chromophore in quadrupolar toluene. The reorganization energy is a sum of the contributions from quadrupolar and induction solvation. We employ several calculation formalisms in order to evaluate their performance against the experiment. The point-dipole and full atomic distributions of solute charge are compared to show that the point-dipole approximation works well for this chromophore. We also show that most of the reorganization entropy comes from the quadrupolar response. Induction solvation amounts to about 10% of the entropy. Both the reorganization energy and the reorganization entropy are greatly affected by the local solute-solvent density profile (density reorganization) which contributes about half of their values. The induction reorganization energy is strongly affected by the microscopic, nonlocal nature of the density fluctuations of the solvent around the solute.

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.

Three-centered model of ultrafast photoinduced charge transfer: Continuum dielectric approach

A theoretical description of photoinduced charge transfer involves explicit treating both the optical formation of the nuclear wave packet on the excited free energy surface and its ensuing dynamics. The reaction pathway constitutes two-stage charge transfer between three centers. Manifestations of fractional charge transfer at first stage are explored. An expression for time dependent rate constant of photoinduced charge transfer is found in the framework of the linear dielectric continuum model of the medium. The model involves both the intramolecular vibrational reorganization and the Coulombic interaction of the transferred charge with the medium polarization fluctuations and allows to express the rate in terms of intramolecular reorganization parameters and complex dielectric permittivity. The influence of the vibrational coherent motion in the locally excited state on the charge transfer dynamics has been explored. The dependence of the ultrafast photoinduced charge transfer dynamics on the excitation pulse carrier frequency (spectral effect) has been investigated. The spectral effect has been shown to depend on quantity of the fractional charge.

Dynamic salt effect on intramolecular charge-transfer reactions

The dynamic salt effect in charge-transfer reactions is investigated theoretically in this paper. Free-energy surfaces are derived based on a nonequilibrium free-energy functional. Reaction coordinates are clearly defined. The solution of the reaction-diffusion equation leads to a rate constant depending on the time correlation function of the reaction coordinates. The time correlation function of the ion-atmosphere coordinate is derived from the solution of the Debye-Falkenhagen equation. It is shown that the dynamic salt effect plays an important role in controlling the rate of charge-transfer reactions in the narrow-window limit but is balanced by the energetics and the dynamics of the polar-solvent coordinate. The simplest version of the theory is compared with an experiment, and the agreement is fairly good. The theory can also be extended to charge-transfer in the class of electrolytes that has come to be called "ionic fluids."

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.

On the microscopic theory of polar solvation dynamics

A microscopic model of the time-resolved Stokes shift is developed. The model calculates the solvation dynamics by combining the atomic resolution of the solute structure with dipolar dynamics from the polarization structure factors of the homogeneous solvent. Calculations are made for coumarin 153 and quinoxaline optical dyes with atomic geometries and charge distributions taken from quantum calculations. Stokes shift dynamics is calculated and compared to experiment in high-temperature acetonitrile and methanol and in low-temperature 2-methyl-tetrahydrofurane using dielectric relaxation data from experiment.

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

Dipole solvation in dielectrics

This paper presents an exact solution for the free energy of linear solvation of a dipolar solute in an arbitrary dielectric material with a microscopic spectrum of polarization fluctuations. The solution is given in terms of wave vector-dependent longitudinal and transverse structure factors of the polarization fluctuations in the pure dielectric. Good agreement with computer simulations of dipole solvation in dipolar and dipolar--quadrupolar liquids is achieved.

Nonlinear Approach to Nonequilibrium Solvation

We investigate an alternative approach to the study of the solvent response to the sudden change in the charge distribution of a solute molecule. The theory avoids the assumption that the response induced in the solvent is linear with respect to the solute perturbation. Our method focuses on the nonequilibrium characteristic function g