Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

Solvation dynamics in liquid water. A novel interplay between librational and diffusive modes

A microscopic calculation of the solvation dynamics of an ion in liquid water is presented. The calculated solvation time correlation function shows an ultrafast Gaussian decay which carries about 70%–90% of the strength followed by a biexponential decay with time constants equal to 250 fs and 1 ps. These results are in excellent agreement with the computer simulations of Maroncelli and Fleming and also with the experimental findings of Barbara and Jarzeba. In addition, we find that both the rotational librations and the intermolecular translational vibrational modes of water contribute significantly to the initial Gaussian decay.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Can one electrochemically measure the statistical morphology of a rough electrode

We have developed a theory for an electrochemical way of measuring the statistical properties of a nonfractally rough electrode. We obtained the expression for the current transient on a rough electrode which shows three times regions: short and long time limits and the transition region between them. The expressions for these time ranges are exploited to extract morphological information about the surface roughness. In the short and long time regimes, we extract information regarding various morphological features like the roughness factor, average roughness, curvature, correlation length, dimensionality of roughness, and polynomial approximation for the correlation function. The formulas for the surface structure factors (the measure of surface roughness) of rough surfaces in terms of measured reversible and diffusion-limited current transients are also obtained. Finally, we explore the feasibility of making such measurements.

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Ionic and dipolar solvation dynamics in liquid water

The solvation time correlation function for solvation in liquid water was measured recently. The solvation was found to be very fast, with a time constant equal to 55 fs. In this article we present theoretical studies on solvation dynamics of ionic and dipolar solutes in liquid water, based on the molecular hydrodynamic approach developed earlier. The molecular hydrodynamic theory can successfully predict the ultrafast dynamics of solvation in liquid water as observed from recent experiments. The present study also reveals some interesting aspects of dipolar solvation dynamics, which differs significantly from that of ionic solvation.

Perturbative growth of cosmological clustering. I: Formalism

Here we rederive the hierarchy of equations for the evolution of distribution functions of various orders using a convenient parameterization. We use this to obtain equations for two- and three-point correlation functions in powers of a small parameter, viz., the initial density contrast. The correspondence of the lowest order solutions of these equations to the results from the linear theory of density perturbations is shown for an OMEGA = 1 universe. These equations are then used to calculate, to the lowest order, the induced three-point correlation function that arises from Gaussian initial conditions in an OMEGA = 1 universe. We obtain an expression which explicitly exhibits the spatial structure of the induced three-point correlation function. It is seen that the spatial structure of this quantity is independent of the value of OMEGA. We also calculate the triplet momentum. We find that the induced three-point correlation function does not have the ''hierarchical'' form often assumed. We discuss possibilities of using the induced three-point correlation to interpret observational data. The formalism developed here can also be used to test a validity of different schemes to close the

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Collective Effects on Single Particle Orientational Relaxation in Slow Dipolar Liquids

Theoretical and computer simulation studies of orientational relaxation in dense molecular liquids are presented. The emphasis of the study is to understand the effects of collective orientational relaxation on the single-particle orientational dynamics. The theoretical analysis is based on a recently developed molecular hydrodynamic theory which allows a self-consistent description of both the collective and the single-particle orientational relaxation. The molecular hydrodynamic theory can be used to derive a relation between the memory function for the collective orientational correlation function and the frequency-dependent dielectric function. A novel feature of the present work is the demonstration that this collective memory function is significantly different from the single-particle rotational friction. However, a microscopic expression for the single-particle rotational friction can be derived from the molecular hydrodynamic theory where the collective memory function can be used to obtain the single-particle orientational friction. This procedure allows, us to calculate the single-particle orientational correlation function near the alpha-beta transition in the supercooled liquid. The calculated correlation function shows an interesting bimodal decay below the bifurcation temperature as the glass transition is approached from above. Brownian dynamics simulations have been carried out to check the validity of the above procedure of translating the memory function from the dielectric relaxation data. We have also investigated the following two issues important in understanding the orientational relaxation in slow liquids. First, we present an analysis of the ''orientational caging'' of translational motion. The value of the translational friction is found to be altered significantly by the orientational caging. Second, we address the question of the rank dependence of the dielectric friction using both simulation and the molecular hydrodynamic theory.

Sponge phase transitions from a lattice model

We use Monte Carlo simulations to obtain thermodynamic functions and correlation functions in a lattice model we propose for sponge phases. We demonstrate that the surface-density correlation function dominates the scattering only along the symmetric-sponge (SS) to asymmetric-sponge (AS) phase boundary but not the boundary between the sponge-with-free-edges (SFE) and symmetric-sponge phases. At this second thermodynamic transition the scattering is dominated instead by an edge-density (or seam-density) correlation function. This prediction provides an unambiguous diagnostic for experiments in search of the SS-SFE transition.

Orientational relaxation in dipolar systems: How much do we understand the role of correlations

Dipolar systems, both liquids and solids, constitute a class of naturally abundant systems that are important in all branches of natural science. The study of orientational relaxation provides a powerful method to understand the microscopic properties of these systems and, fortunately, there are many experimental tools to study orientational relaxation in the condensed phases. However, even after many years of intense research, our understanding of orientational relaxation in dipolar systems has remained largely imperfect. A major hurdle towards achieving a comprehensive understanding is the long range and complex nature of dipolar interactions which also made reliable theoretical study extremely difficult. These difficulties have led to the development of continuum model based theories, which although they provide simple, elegant expressions for quantities of interest, are mostly unsatisfactory as they totally neglect the molecularity of inter-molecular interactions. The situation has improved in recent years because of renewed studies, led by computer simulations. In this review, we shall address some of the recent advances, with emphasis on the work done in our laboratory at Bangalore. The reasons for the failure of the continuum model, as revealed by the recent Brownian dynamics simulations of the dipolar lattice, are discussed. The main reason is that the continuum model predicts too fast a decay of the torque-torque correlation function. On the other hand, a perturbative calculation, based on Zwanzig's projection operator technique, provides a fairly satisfactory description of the single particle orientational dynamics for not too strongly polar dipolar systems. A recently developed molecular hydrodynamic theory that properly includes the effects of intermolecular orientational pair correlations provides an even better description of the single-particle orientational dynamics. We also discuss the rank dependence of the dielectric friction. The other topics reviewed here includes dielectric relaxation and solvation dynamics, as they are intimately connected with orientational relaxation. Recent molecular dynamics simulations of the dipolar lattice are also discussed. The main theme of the present review is to understand the effects of intermolecular interactions on orientational relaxation. The presence of strong orientational pair correlation leads to a strong coupling between the single particle and the collective dynamics. This coupling can lead to rich dynamical properties, some of which are detailed here, while a major part remains yet unexplored.

Ultrafast solvation dynamics in water: Isotope effects and comparison with experimental results

A detailed theoretical study of solvation dynamics in water is presented. The motivation of the present study comes from the recent experimental observation that the dynamics of solvation of an ion in water is ultrafast and the solvation time correlation function decays with a time constant of about 55 fs. The slower decay in the long time can be described by a sum of two exponentials with time constants equal to 126 and 880 fs. The molecular theory (developed earlier) predicts a time constant equal to 52 fs for the initial Gaussian decay and time constants equal to 134 and 886 fs for the two exponential components at the long time. This nearly perfect agreement is obtained by using the most detailed dynamical information available in the literature. The present study emphasizes the importance of the intermolecular vibrational band originating from the O...O stretching mode of the O�H...O units in the initial dynamics and raises several interesting questions regarding the nature of the decay of this mode. We have also studied the effects of isotope substitution on solvation dynamics. It is predicted that a significant isotope effect may be observed in the long time. The experimental results have also been compared with the prediction of the dynamic mean spherical approximation (DMSA); the agreement is not satisfactory at the long time. It is further found that the molecular theory and the DMSA lead to virtually identical results if the translational modes of the solvent molecules are neglected in the former. DMSA has also been used to investigate the dynamics of solvation of a dipolar solute in water. It is found that the dynamics of dipolar solvation exhibit features rather different from those of ion solvation. © 1995 American Institute of Physics.

Ultrafast Solvation Dynamics Of An Ion In A Restricted Environment

The solvation dynamics of an excited coumarin dye molecule (C-480) enclosed within a restricted space have been studied using molecular hydrodynamic theory (MHT) and compared with the recent experimental findings. The solvation dynamics of the dye molecule within the cavity of a toroidal gamma-cyclodextrin molecule have been shown to be explained only in terms of the freezing of the solvent translational modes using MHT. The results of the theoretical calculation are in good agreement with the experimental results. The inertial components of the solvation time correlation function remain the same in both the restricted environment and in the free space. These results are interesting in the light of the simulation studies of Maroncelli and Fleming [J chem Phys, 89 (1988) 5044] which concludes that the participation of the different solvation shells in controlling the dynamics are much different. The earlier studies have been reviewed and the recent findings are discussed.

Solvation dynamics of a charge bubble in water

A microscopic theory is used to calculate the solvation-time correlation function, (S(t)), of a light, non-stationary charge bubble in water. The calculated correlation function is found to be similar to the energy-time correlation function of a solvated electron. The ionic mobility of a charge bubble of the size of the hydrated electron is also calculated. It is found that the mobility of the charge plays a very important role in its own solvation.