Rotational dielectric friction and dipole solvation: Tests of theory based on simulations of simple model solutions

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents

NMR-based measurements of the diffusion coefficients and rotation times of solitary water and benzene at 300 K are reported in a diverse collection of 13 conventional organic solvents and 10 imidazolium ionic liquids. Proton chemical shifts of water are found to be correlated to water OH-stretching frequencies, confirming the importance of electrostatic interactions in these shifts. However, the influence of magnetic interactions in aromatic solvents renders chemical shifts a less reliable indicator of electrostatics. Diffusion coefficients (DB) and rotational correlation times (τB) of benzene in the solvents examined are accurately described as functions of viscosity (η) by DB ∝ η-0.81 and τB ∝ η0.64. Literature values of DB and τB in alkane and normal alcohols, which were not included among the solvents studied here, are systematically faster than predicted by these correlations, indicating that factors beyond solvent viscosity play a role in determining the friction on benzene. In contrast to benzene, water diffusion and rotation are poorly described in terms of viscosity alone, even in the dipolar and ionic solvents measured here. The present data and the substantial literature data already available on dilute water diffusion show a systematic dependence of DW on solvent polarity among isoviscous solvents. The aspect of solvent polarity most relevant to water dynamics is the ability of a solvent to accept hydrogen bonds from water, as conveniently quantified by the frequency of water's OH stretching band, ΔνOH. The friction on translation, ζtr = kBT/DW, and rotation, ζrot = kBTτW, are both well correlated by functions of the form ζ(η, ΔνOH) = a1ηa2 exp (a3ΔνOH), where the ai are adjustable parameters. Molecular dynamics simulations reveal a strong coupling between electrostatic and nonelectrostatic water-solvent interactions, which makes it impossible to dissect the friction on water into additive dielectric and hydrodynamic components. Simulations also provide a tentative explanation for the unusual form of the correlating function ζ(η, ΔνOH), at least in the case of ζrot.

Rotational dynamics of polyatomic ions in aqueous solutions: From continuum model to mode-coupling theory, aided by computer simulations

Due to the presence of the rotational mode and the distributed surface charges, the dynamical behavior of polyatomic ions in water differs considerably from those of the monatomic ions. However, their fascinating dynamical properties have drawn scant attention. We carry out theoretical and computational studies of a series of well-known polyatomic ions, namely, sulfate, nitrate, and acetate ions. All three ions exhibit different rotational diffusivity, with that of the nitrate ion being considerably larger than the other two. They all defy the hydrodynamic laws of size dependence. Study of the local structure around the ions provides valuable insight into the origin of these differences. We carry out a detailed study of the rotational diffusion of these ions by extensive computer simulation and by using the theoretical approaches of the dielectric friction developed by Fatuzzo-Mason (FM) and Nee-Zwanzig (NZ), and subsequently generalized by Alavi and Waldeck. A critical element of the FM-NZ theory is the decomposition of the total rotational friction, ζ_Rot, into Stokes and dielectric parts. The study shows a dominant role of dielectric friction in the sense that if the ions are made neutral, the nature of diffusion changes and the values become much larger. Our analyses further reveal that the decomposition of total friction into the Stokes and dielectric friction breaks down for sulfate ions but remains semi-quantitatively valid for nitrate and acetate ions. We discuss the relationship between translational and rotational dielectric friction on rigid spherical ions. We develop a self-consistent mode-coupling theory (SC-MCT) formalism that could provide a unified view of rotational friction of polyatomic ions in polar medium. Our SC-MCT shows that the breakdown can be attributed to the change in the microscopic structural features. The mode-coupling theory helps in elucidating the role of coupling between translational and rotational motion of these ions. In fact, these two motions self-consistently determine the value of each other. The reference interaction site model-based MCT suggests an interesting relation between the torque-torque and the force-force time correlation function with the proportionality constant being determined by the geometry and the charge distribution of the polyatomic molecule. We point out several parallelisms between the theories of translational and rotation friction calculations of ions in polar liquids.

Free energy landscapes of electron transfer system in dipolar environment below and above the rotational freezing temperature

Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape.

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.

Protein hydration dynamics in solution: a critical survey

The properties of water in biological systems have been studied for well over a century by a wide range of physical techniques, but progress has been slow and erratic. Protein hydration--the perturbation of water structure and dynamics by the protein surface--has been a particularly rich source of controversy and confusion. Our aim here is to critically examine central concepts in the description of protein hydration, and to assess the experimental basis for the current view of protein hydration, with the focus on dynamic aspects. Recent oxygen-17 magnetic relaxation dispersion (MRD) experiments have shown that the vast majority of water molecules in the protein hydration layer suffer a mere twofold dynamic retardation compared with bulk water. The high mobility of hydration water ensures that all thermally activated processes at the protein-water interface, such as binding, recognition and catalysis, can proceed at high rates. The MRD-derived picture of a highly mobile hydration layer is consistent with recent molecular dynamics simulations, but is incompatible with results deduced from intermolecular nuclear Overhauser effect spectroscopy, dielectric relaxation and fluorescence spectroscopy. It is also inconsistent with the common view of hydration effects on protein hydrodynamics. Here, we show how these discrepancies can be resolved.

Rotational diffusion of the 7-diethylamino-4-methylcoumarin C1 dye molecule in polar protic and aprotic solvents

Fluorescence anisotropy decays of the 7-diethylamino-4-methylcoumarin C1 in various polar solvents of different viscosities and hydrogen bond donor/acceptor character have been recorded by means of the fluorescence upconversion and time-correlated single photon counting techniques. The resulting characteristic times for the rotational diffusion fall into two classes with regards to the viscosity-dependency: n-alcohols and "other" solvents. This deviation from the simple Stokes-Einstein-Debye model may be interpreted in terms of rotation of the coumarin molecule under two different hydrodynamic boundary-conditions ("stick" or "slip") in the two solvent classes. Possible explanations for this behaviour are discussed, and in particular solvent attachment and additional dielectric friction. Both these phenomena may in fact, under certain conditions, explain our findings. Our opinion, however, is that the dielectric friction model offers a more realistic picture of the additional rotational friction experienced by C1 in n-alcohols.

Heterogeneous relaxation patterns in supercooled liquids studied by solvation dynamics

We have measured the solvation dynamics of a dipolar supercooled liquid near its glass transition in a temperature range in which the average structural relaxation time varies more than four orders of magnitude. The analysis of the time dependent average emission energy and the inhomogeneous linewidth of the S0<--T1(0-0) transition reveals that the orientation correlation decay pattern intrinsic in each relaxing unit is associated with a stretching exponent beta(intr)=1.00+/-0.08 in the entire range T(g)</=T</=T(g)+6 K. Our analysis also allows one to detect fluctuations in terms of the resulting apparent homogeneity within the long time tail of the decay. Even at times significantly exceeding the average structural relaxation time, no sign of a transition towards purely exponential or otherwise homogeneous behavior could be observed. This implies that even at t approximately 50<tau>(KWW) the individual time constants remain correlated to their initial values at t=0.