Solvent Motions Research Articles

Role of inertial and non-Markovian effects on activated barrier crossing dynamics for charge transfer reactions in solution

Charge transfer processes in a polar solvent, modeled as an activated crossing over a parabolic potential barrier, are studied here through the Grote–Hynes (G–H) theory using the recent microscopic approaches to the dielectric friction based on mode coupling theory. The calculated frequency-dependent friction consisting of the short-range as well as the long-range contributions is used to obtain the barrier crossing rates based on the G–H theory, and for comparison also Kramers' theory using the zero-frequency value of the friction. The effect of considering the inertial and non-Markovian motion of the solvent molecules on the calculated friction as well as the barrier crossing rates is investigated. The inertial component of solvent motion is found to be an important factor.

Diffusive and segmental dynamics in polymer gel electrolytes

Dynamic light scattering data on a polymer gel electrolyte with a complex relaxation behavior is presented. The electrolyte consists of lithium perchlorate dissolved in an ethylene carbonate and propylene carbonate solution that is immobilized with poly(methyl methacrylate). We attribute the observed relaxation processes to two diffusive and one segmental relaxation processes based on the form of the time decay of the intermediate scattering function and the corresponding temperature and wave vector dependencies. The dynamic light scattering results are compared with the ionic conductivity, which reveals a close connection between the fast diffusive motion of the low molecular weight solvent within the gel and the ionic conductivity. This motion is strongly decoupled from and considerably faster than the segmental motion of the polymer matrix. The results indicate that the ionic transport occurs mainly within the low molecular weight solvent.

Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations

Hybl et al. demonstrated a technique for recording two-dimensional Fourier transform electronic correlation and relaxation spectra based on detecting phase modulation of the signal electric field in a noncollinear femtosecond four-wave mixing experiment. A theoretical analysis of 2D correlation and relaxation experiments is presented for a system consisting of two electronic states each having two or more sublevels. The separation between absorption and dispersion mode 2D spectra in these experiments is investigated in detail for nonzero pulse duration and compared to related 2D NMR experiments based on a nonlinear optical definition of coherence order. Phase-twisted peaks, which mix absorption and dispersion line shapes, can occur under some circumstances. A 1D projection of the complex 2D spectrum is shown to equal the transient grating signal field, and the real part of this projection is related to the spectrally resolved pump−probe signal. Calculated 2D spectra for a two-level Bloch model, an underdamped Brownian oscillator, and a few models of polar solvent dynamics based on the correlation function approach to the nonlinear response developed by Mukamel and co-workers are presented. The real parts of the 2D spectra are primarily positive (indicative of ground state bleaching and excited state emission) but contain negative regions arising from excitation of coherent superposition states (e.g. vibrational wavepackets) in both the ground and excited electronic states. Assignment of the 2D spectra displaying wavepacket motion at the vibronic level is discussed, and the manifestations of wavepacket motion and vibrational relaxation in the 2D spectra are explored. As suggested by Hybl et al., an increase in pulse duration is found to affect a 2D spectrum primarily as a spectral filter that limits the range of the spectrum. The Gaussian correlation function characteristic of inertial solvent motion is found to be faithfully reflected in a homogeneous 2D cross width which is nearly independent of pulse duration. An alternative experimental method for obtaining only the real part of 2D spectra is proposed.

Novel U-Shaped Systems Containing an Imide-Functionalized Cleft for the Study of Solvent-Mediated Electron Transfer and Energy Transfer: Synthesis and Binding Studies

A solution to the vexing problem of investigating solvent-mediated electron transfer under conditions of frozen solvent motion may be at hand with the synthesis of novel U-shaped systems such as 1 (R=CO(2)Me) and 2 (R=CH(2)OMe), in which the imide-functionalized cleft provides the point of attachment of the "solvent" molecule, either covalently or by hydrogen bonding.

Role of Nonpolar Forces in Aqueous Solvation: Computer Simulation Study of Solvation Dynamics in Water Following Changes in Solute Size, Shape, and Charge

The coupling between solvent fluctuations and the electronic states of solutes is critically important in charge transfer and other chemical reactions. This has piqued enormous interest in solvation dynamicssthe study of how solvent motions relax changes in a solute’s charge distribution. In nearly every computer simulation of solvation dynamics, the system is modeled by an atomic or molecular solute whose charge (or higher multipole moment) is suddenly changed, and the motions of the solvent molecules that relax the new charge distribution are monitored. Almost none of this work, however, accounts for the fact that most reacting solutes also undergo significant changes in size and shape as well as charge distribution. For the excited states of dye molecules typically used as probes in solvation experiments or for the atoms and molecules that change oxidation state in charge transfer reactions, we expect changes in reactant size on the order of 5 -20%. In this paper, we use computer simulation to explore the differences between dielectric solvation, due to changes in charge distribution, and mechanical solvation, due to changes in size and shape, for a Lennard-Jones sphere in flexible water. The solvation energy for the size changes expected in typical reactions is on the same order as that for the appearance of a fundamental unit of charge, indicating that dielectric and mechanical solvation dynamics should participate at comparable levels. For dielectric solvation, solvent librations dominate the influence spectrum, but we also find a significant contribution from the water bending motion as well as low-frequency translations. The influence spectrum for mechanical solvation, on the other hand, consists solely of low-frequency intermolecular translational motions, leading to mechanical solvation dynamics that are significantly slower than their dielectric counterparts. The spectrum of couplings for various mechanical perturbations (size, shape, or polarizability) depends somewhat on the magnitude of the change, but all types of mechanical relaxation dynamics appear qualitatively similar. This is due to the steepness of the solute solvent interaction potential, which dictates that the majority of the solvation energy for mechanical changes comes from the translational motion of the closest one or two solvent molecules. Finally, we explore the solvation dynamics for combined changes in both size and charge and find that the resulting dynamics depend sensitively on the sign and magnitude of both the size and charge changes. For some size/charge combinations, the translational and rotational motions that lead to relaxation work cooperatively, producing rapid solvation. For other combinations, the key translational and rotational solvent motions for relaxation are antagonistic, leading to a situation where mechanical solvation becomes rate limiting: solvent rotational motions are “frustrated” until after translational relaxation has occurred. All the results are compared with previous experimental and theoretical studies of solvation dynamics, and the implications for solvent-driven chemical reactions are discussed.

Deuterium isotope effect on the solvation dynamics of a dye molecule in methanol and acetonitrile

Solvation dynamics of a dye molecule in methanol, acetonitrile, and their deuterated analogs has been measured by the three-pulse stimulated photon echo peak shift. The effects of deuterium substitution on the stationary fluorescence spectra and the time domain data are found to be significant in both solvents. Moreover, the deuterium isotope effects are contrasted in methanol and acetonitrile. The ultrafast component, found to be 200–260 fs, is not slowed down by the deuterium substitution of the hydroxyl group in methanol, and it is even slightly shortened by deuteration in acetonitrile. The isotope dependence and the time scales suggest that the ultrafast component is not originated from the inertial free rotation of the solvent molecules but from collective dispersive solvent motion, at least for the present system. In addition to the ultrafast and ps solvation time scales usually observed in methanol and acetonitrile, a large amplitude ns component is observed in all solvents. The amplitudes of the ns component are substantially different in isotopomers, showing the opposite trend in methanol and acetonitrile.

Mesoscopic model for solvent dynamics

Complex fluids such as polymers in solution or multispecies reacting systems in fluid flows often can be studied only by employing a simplified description of the solvent motions. A stochastic model utilizing a synchronous, discrete-time dynamics with continuous velocities and local multiparticle collisions is developed for this purpose. An H theorem is established for the model and the hydrodynamic equations and transport coefficients are derived. The results of simulations are presented which verify the properties of the model and demonstrate its utility as a hydrodynamics medium for the study of complex fluids.

Kinetic Pathways of Ion Pair Dissociation in Water

We have successfully applied the transition path sampling method to the deterministic dynamics of a many-body system with long-ranged interactions. The process we investigate, dissociation of a model Na+Cl- ion pair in water, involves a wide range of transition pathways in which collective solvent motions play an important role. Transition states along these pathways encompass a broad distribution of ionic separations. Ion pairs in contact remain associated for ∼20 ps on average, a time scale considerably longer than the ∼3ps predicted by transition state theory with ionic separation as the order parameter. In contrast to theories of barrier crossing based upon frictional effects (with or without memory), we find that the discrepancy between these time scales arises from neglected solvent free energy barriers rather than stochastic buffeting of the ion pair.

Controlling the Adiabaticity of Electron-Transfer Reactions Using Nematic Liquid-Crystal Solvents

Transient absorption studies of intramolecular photoinduced charge separation and thermal charge recombination were carried out on a molecule consisting of a 4-(N-pyrrolidinyl)naphthalene-1,8-imide donor (PyrNI) covalently attached to a pyromellitimide acceptor (PI) dissolved in the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline (MBBA). In the isotropic phase, just above the nematic to isotropic phase transition, ordered microdomains exist that give rise to solvation dynamics that consist of collective reorientational motions of the microdomains and relatively faster reorientations of molecules within the domains. The different temperature dependence of these responses permits the assignment of collective or molecular solvent motions as mediators of the charge separation and recombination reactions. We find for PyrNI−PI in MBBA that charge separation is adiabatic and controlled by the collective microdomain reorientations, whereas the charge recombination is nonadiabatic and controlled by the fast...

Intermolecular Excited‐State Proton Transfer in Clusters of 1‐Naphthol with Water and with Ammonia

AbstractThe excited‐state proton transfer reactions of 1‐naphthol(H2O)n and 1‐naphthol(NH3)n clusters are compared. Both exisiting and new data suggest that the two systems may react in strikingly different fashions, roughly corresponding to non‐adiabatic and adiabatic limiting cases, respectively. In water clusters, the reaction is kinetically limited by solvent motion, and there is a strong dynamic interaction involving the water and two lowest electronic excited states, which thereby invert. In ammonia clusters, the excited states appear to be premixed by the the stronger base, and the reaction may proceed in a rapid manner, resembling intracluster vibrational relaxation, with relatively little solvent reorganization.

Mechanisms of solvation dynamics of polyatomic solutes in polar and nondipolar solvents: A simulation study

Molecular dynamics (MD) simulations of a benzenelike solute in acetonitrile and CO2 (298 K and 52.18 cm3/mol) are used to investigate the molecular basis of solvation dynamics in polar and nondipolar solvents. The solvation response to various charge rearrangements within the benzene solute are simulated in order to mimic the type of electrostatic solvation observed in typical experimental systems. From equilibrium MD simulations the solvation time correlation function [TCF; C(t)] and the corresponding solvation velocity TCF [G(t)] are used to study the mechanisms underlying time-dependent solvation within the linear response limit. Decomposition of G(t) into contributions from rotational and translational solvent velocities reveals that the relative mix of these two types of motion is quite similar in the two solvents but is strongly dependent on the multipolar order (m) of the solute perturbation. The contribution of translational solvent motions to both the short and long time dynamics of C(t) increases from about 10% for a monopolar perturbation (m=0; i.e., a change in net charge) to about 40% for a perturbation of octopolar (m=3) symmetry. Decomposition of both C(t) and G(t) into single-molecule and molecular-pair contributions shows that the collective nature of the solvation response depends markedly on the charge symmetry of both the solvent molecule’s charge distribution and the solute perturbation. In the nondipolar solvent CO2 neither C(t) nor G(t) differ significantly from their single-molecule counterparts—collective effects are therefore of little consequence to solvation in this solvent. However, in the highly dipolar solvent acetonitrile pair contributions to C(t) greatly suppress the magnitude of the solvation response and as a consequence greatly increase the speed of the response over what it would be in their absence. The importance of these intermolecular correlations in acetonitrile decreases substantially with m, such that the “suppression factors” (αs) vary from ∼9 for m=0 to ∼2 for m=3. The intermolecular correlations of primary importance in acetonitrile are of a static rather than a dynamic nature (i.e., pair effects on G(t) are of only secondary importance). This feature makes it possible to employ several approximate relationships to relate the collective dynamics of solvation in polar fluids to simpler single-solvent molecule dynamics.

2E relaxation of Cr(III) complexes in rigid and fluid media

2E decays have been recorded for a group of Cr(III) complexes with varying 4T 2 2E separations in solvents with independently measured relaxation times. Thermal quenching that occurs when solvent motion is slow relative to the excited state decay time leads to non-exponential decay. Comparison of the 2E lifetimes and estimated deviations from exponentiality in a wide range of complex-solvent combinations as a function of temperature suggests a model in which 2 E ⇒ 4 T 2 back-transfer is the dominant decay pathway in most complexes. The back-transfer rate is increased by solvent motion.

Dynamics of Various Metal-Octaethylporphyrins in Solution Studied by Resonance Raman and Low-Temperature Optical Absorption Spectroscopies. Role of the Central Metal

The temperature dependence of the Soret band of various metal-octaethylporphyrins [i.e., Ni(II), Cu(II), and Pd(II)] dissolved in the glass-forming mixture 50% (v/v) isopentane/ethyl ether in the temperature range 300−40 K was studied. Co(II)-octaethylporphyrin dissolved in dichloromethane was also investigated in the temperature range 300−180 K. The aim of the work was to investigate the role of the central metal in the conformational flexibility of porphyrins and in communicating solvent motions to their macrocycle. We used resonance Raman spectroscopy to determine the vibronic coupling of high-frequency modes to the electronic transition into the porphyrin B state. The corresponding coupling of a “bath” of low-frequency porphyrin/solvent motions was taken into account by a temperature-dependent Gaussian width (σ) of the Soret band. Following the approach of Melchers et al. (Biophys. J. 1996, 70, 2092−2099), the mean square fluctuations (MSF) of the central metal atom with respect to the porphyrin plane...

On the dynamics of electrochemical ion-transfer reactions

Abstract A model electrochemical ion-transfer reaction is investigated by molecular dynamics simulations. Non-equilibrium solvation effects can lead to barrier recrossings when the ion passes the transition state. The resulting transmission coefficient, which measures the deviation of the rate from the predictions of the transition state theory, is in good agreement with the Grote–Hynes theory. By contrast, Kramers theory predicts a much lower rate constant. The reaction occurs in the polarization caging regime of Grote–Hynes theory, in which the solvent motion controls the advance of the reaction. Furthermore, the molecular friction depends strongly on the distance from the electrode.

Ultrafast Librational Dynamics of the Hydrated Electron

Photon echo and resonant transient grating experiments on the equilibrated aqueous electron are reported, using 15 fs excitation pulses. Both experiments exhibit clear signatures of wave packet dynamics, attributed to an underdamped solvent motion of about $850\mathrm{cm}{}^{\ensuremath{-}1}$. Experiments in ${D}_{2}\mathrm{O}$ expose the librational nature of this mode. The overall agreement between experiment and quantum-molecular dynamics simulations is good, except for the initial oscillatory dynamics, which have not been predicted.

Wave Packet Dynamics in Ultrafast Spectroscopy of the Hydrated Electron

Hydrated-electron dynamics is examined by frequency-resolved pump−probe experiments using pulses of 13 fs centered at 780 nm. A recurrence at ∼40 fs signifies a strong coupling of the electronic transition to underdamped solvent motions. Wave packet dynamics launched by the pump pulse produces an ultrafast red-shift of the electronic transition by approximately 6500 cm-1. Gross features of the pump−probe experiments are analyzed using a two-level system.

A theory for adiabatic bond breaking electron transfer reactions at metal electrodes

A theory is formulated for bond breaking and electron transfer at metal electrodes, based on an adaptation of the Anderson–Newns Hamiltonian. The model provides an extension of Savéant's model for concerted bond breaking and electron transfer and yields Savéant's predictions in the limit of vanishing electronic coupling. Solvent dynamical effects are investigated by assuming an overdamped solvent motion and a ballistic bond breaking motion. It is found that in a sufficiently slow solvent the transfer coefficient and the activation enthalpy may become temperature dependent, although the effect is probably small for most combinations of redox couples and solvents at room temperature.

The short-time intramolecular dynamics of solutes in liquids. II. Vibrational population relaxation

Events such as the vibrational relaxation of a solute are often well described by writing an effective equation of motion—a generalized Langevin equation—which expresses the surrounding medium’s influence on the intramolecular dynamics in terms of a friction and a fluctuating force acting on the solute. These quantities, though, can be obtained from the instantaneous normal modes (INMs) of the system when the relaxation takes place in a fluid, suggesting that we should be able to analyze in some detail the solvent motions driving the relaxation, at least for short times. In this paper we show that this promise can indeed be realized for the specific case of a vibrating diatomic molecule dissolved in an atomic solvent. Despite the relatively long times typical of vibrational population relaxation, it turns out that understanding the behavior of the vibrational friction at the short times appropriate to INMs (a few hundred femtoseconds) often suffices to predict T1 times. We use this observation to probe the dependence of these relaxation rates on thermodynamic conditions and to look at the molecular mechanisms underlying the process. We find that raising the temperature at any given density or raising the density at any given temperature will invariably increase the rate of energy relaxation. However, since these two trends may be in conflict in a typical constant-pressure laboratory experiment, we also find that it is possible to make sense of the “anomalous” inverted temperature dependence recently seen experimentally. We find, as well, that the INM theory—which has no explicit collisions built into it—predicts exactly the same density dependence as the venerable independent-binary-collision (IBC) theory (an intriguing result in view of recent claims that experimental observations of this kind of dependence provide support for the IBC theory). The actual mechanisms behind vibrational population relaxation are revealed by looking in detail at the vibrational friction “influence spectrum”—the spectrum of INMs weighted by how efficiently each mode acts to promote the relaxation. Through suitable projections we show that the average influence spectrum is dominated by longitudinal motion of the solvent atoms in the first solvation shell. We go further, however, and examine the nature of the instantaneous relaxation promoted by individual liquid configurations. The number of instantaneous modes that contribute significantly fluctuates strongly from configuration to configuration, and the number of solvent atoms strongly coupled to the solute has a certain amount of variation as well, but invariably each significant mode ends up promoting the relaxation by moving just one or two significant solvent atoms—a feature we explore in a companion paper.

Swelling Kinetics of Polymer Gels

The kinetics of gel swelling is theoretically analyzed by considering coupled motions of both the solvent and the polymer network. This model avoids the two process approach of Li and Tanaka, in which the solvent motion is indirectly considered. Analytical solutions of solvent and network movement are found from the collective diffusion equations for a long cylindrical and a large disk gel. For a cylindrical gel, the speed of solvent motion is proportional to −r/(2a) along the radial direction and z/a along the axial direction, respectively. Here r and z represent radial and axial coordinates, respectively, and a is the radius of the cylinder. The flow diagram of the solvent is obtained. It is also found that the solvent motion can be independently derived from Li−Tanaka's isotropy and continuity conditions without solving the collective diffusion equations. The swelling behavior is obtained at the gel boundary and also in the interior of the gel.

The influence of the alkaline earth cations, magnesium, calcium, and barium on the dissolution kinetics of quartz

This study quantifies the influence of the four major dissolved solutes found in terrestrial and marine environments on the dissolution kinetics of quartz. Dissolution rates are dependent upon the concentration and identity of alkali and alkaline earth cations in near-neutral pH solutions. We determine the effect of alkaline earth cations upon quartz reactivity by measuring dissolution rates in 0.0001–0.2 molal solutions of MgCl 2, CaCl 2, BaCl 2, LiCl, KCI, and NaCl at near-neutral pH and 200°C. The results fit a first order rate law, where dissolution rates are slowest in pure water and increase with the introduction of salts in the order: Mgt+ < Ca 2+ ≈ Li + ≈ Na + ≈ K+ < Ba 2+. The trend is consistent with previously reported lower temperature measurements of dissolution rate for amorphous silica and sources of quartz. This suggests cation-specific effects hold for multiple silica polymorphs over temperatures of 25–200°C. Combining evidence from the literature and the kinetic data presented in this study, we propose a simple model: The dissolution rate of quartz. Alkali and alkaline earth cations indirectly enhance dissolution by] modifying rates of solvent motion, exchange, or orientation at the mineral-solution interface. Rate enhancement is proportional to the concentration of ions at the surface and their solvation character. The resulting model predicts (1) the dissolution rate of quartz for a suite of cations with weak surface interactions, (2) the influence of ion concentration, (3) that the catalyzing effect of salts diminish as the concentration of silicic acid in solution increases (decreasing reaction affinity) by increasing the amount of H 4SiO 4 at the interface, (4) that electrolytes have little rate-enhancing effect on the dissolution kinetics of silicate minerals, and (5) that dissolution rates of other oxide materials containing constituents with sluggish solvent interactions are also enhanced by introduction of alkali or alkali cations. Our findings reiterate the need to understand relationships between near-surface solute/solvent properties and mineral reactivity.