On the microscopic theory of polar solvation dynamics

Electron-Induced Proton Transfer

The pathway of activationless proton transfer induced by an electron-transfer reaction is studied theoretically. Long-range electron transfer produces highly nonequilibrium medium polarization that can drive proton transfer through an activationless transition during the process of thermalization, dynamically altering the screening of the electron-proton Coulomb interaction by the medium. The cross electron-proton reorganization energy is the main energy parameter of the theory, which exceeds in magnitude the proton-transfer reorganization energy roughly by the ratio of the electron-transfer to proton-transfer distance. This parameter, which can be either positive or negative, is related to the difference in pK_a values in two electron-transfer states. The relaxation time of the medium is on the (sub)picosecond time scale, which establishes the characteristic time for activationless proton transfer. Microscopic calculations predict substantial retardation of the collective relaxation dynamics compared to the continuum estimates due to the phenomenology analogous to de Gennes narrowing. Nonequilibrium medium configuration promoting proton transfer can be induced by either thermal or photoinduced charge transfer.

A Surrogate for Debye-Waller Factors from Dynamic Stokes Shifts

We show that the short-time behavior of time-resolved fluorescence Stokes shifts (TRSS) are similar to that of the intermediate scattering function obtained from neutron scattering at q near the peak in the static structure factor for glycerol. This allows us to extract a Debye-Waller (DW) factor analog from TRSS data at times as short as 1 ps in a relatively simple way. Using the time-domain relaxation data obtained by this method we show that DW factors evaluated at times ≥ 40 ps can be directly influenced by α relaxation and thus should be used with caution when evaluating relationships between fast and slow dynamics in glassforming systems.

Terahertz response of dipolar impurities in polar liquids: on anomalous dielectric absorption of protein solutions

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein's hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that "elastic ferroelectric bag" of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.

Electrostatic fluctuations in cavities within polar liquids and thermodynamics of polar solvation

We present the results of numerical simulations of the fluctuations of the electrostatic potential and electric field inside cavities created in the fluid of dipolar hard spheres. We found that the thermodynamics of polar solvation changes dramatically when the cavity size becomes about 4-5 times larger than the size of the liquid particle. The range of small cavities can be reasonably understood within the framework of current solvation models. On the contrary, the regime of large cavities is characterized by a significant softening of the cavity interface resulting in a decay of the fluctuation variances with the cavity size much faster than anticipated by both the continuum electrostatics and microscopic theories. For instance, the variance of the electrostatic potential at the cavity center decays with the cavity radius R0 approximately as 1R{0};{4-6} instead of the 1R{0} scaling expected from the standard electrostatics. Our results suggest that cores of nonpolar molecular assemblies in polar liquids lose solvation strength much faster than is traditionally anticipated.

Photoinduced Vibrational Coherence Transfer in Molecular Dimers

At short times that are faster than dephasing, photoinduced evolution of the vibrational subsystem in an electron-phonon molecular structure depends strongly on the electronic evolution. As the electronic population shifts between the donor and acceptor states, in the diabatic description the state with the largest population determines the equilibrium positions and frequencies of the vibrational modes, which oscillate continuously and without loss of coherence. The vibrational coherence transfer between the electronic states detected recently in a number of systems is described theoretically by application of the quantized Hamiltonian dynamics (QHD) formalism [J. Chem. Phys. 2000, 113, 6557] to the coupled electronic and vibrational degrees of freedom of a model heterodimer. The observed coherent modulation of the frequency of the probe signal is represented with simple analytic and numeric QHD models.

Comparisons of Measured Rate Constants with Spectroscopically Determined Electron-Transfer Parameters

This work involves comparison of rate constants measured for an intervalence (IV) compound with electron-transfer parameters derived from its optical absorption spectrum. The temperature-dependent rate constants for the radical cation having 3-tert-butyl-2,3-diazabicyclo[2.2.2]oct-2-yl (hydrazine) charge-bearing units attached para to a tetramethylbenzene bridge (1+) were previously measured. In this study, resonance Raman is used to calculate the magnitudes of the distortions of normal modes of vibration caused by excitation into the intervalence absorption band. These data produce a vibrational reorganization energy lambdavsym of 9250 cm(-1), and averaged single-mode omegav for use in the Golden Rule equation of 697 cm(-1). Zhu-Nakamura theory has been used to calculate preexponential factors for analysis of the previously measured variable temperature optical spectra using quartic-enhanced intervalence bands to extract the total reorganization energy and the intramolecular electron-transfer rate constants for intramolecular electron transfer using electron spin resonance. In contrast to using the Golden Rule equation, separation of lambda into solvent and vibrational components is not significant for these data. The Zhu-Nakamura theory calculations produce ln(k/T) versus 1/T slopes that are consistent with the experimental data for electronic couplings that are somewhat larger than the values obtained from the optical spectra using Hush's method.

Solvent response and dielectric relaxation in supercooled butyronitrile

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming dipolar liquid butyronitrile near its glass transition temperature T(g)=95 K. The Stokes shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical linewidth changes along the solvation coordinate in a nonmonotonic fashion. These features are characteristic of solvation in viscous solvents and clearly indicate heterogeneous dynamics, i.e., spatially distinct solvent response times. Using the dielectric relaxation data of viscous butyronitrile as input, a microscopic model of dipolar solvation captures the relaxation time, the relaxation dispersion, and the amplitude of the dynamical Stokes shift remarkably well.

Dynamical Arrest of Electron Transfer in Liquid Crystalline Solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.

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.

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.

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.