Solvation Time Correlation Function Research Articles

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics.

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.

Non-equilibrium solvation dynamics: results beyond linear response theory

Optically controlled non-equilibrium solvation dynamics in condensed phase have been studied extensively both experimentally and theoretically. The main drawback of linear response theory (LRT) and other existing theories is that they are unable to elucidate the dependence of non-equilibrium solvation time correlation function, S(t), on the excitation wavelength, as observed in the experiment. In order to explain the experimental observation, we first develop a kinetic equation in 1D solvation coordinate (SC) space and then we propose a new perturbative method to derive an analytical expression for S(t) for an anharmonic potential in SC space. We observe from the result of S(t) that the calculated results of the same depend strongly on the innumerable optical states through excitation wavelength, when the potential is anharmonic in SC space, indicating the breakdown of LRT. We have shown that both excitation wavelength and rotational relaxation time carry the information of micro-heterogeneity. Another significant aspect of our work is that the analytical expression obtained for S(t) corresponding to the anharmonic potential decays multi-exponentially, whereas S(t) decays single exponentially for a harmonic potential. More significantly, the calculated results for S(t) are found to be in excellent agreement with the available experimental results for the heterogeneous system.

How different are the dynamics of nanoconfined water?

We unravel the combined effects of confinement and surface interactions by studying the position dependent, time-resolved dynamic response functions in nano-containers of different shapes. Spectroscopic signatures are additionally studied through solvation dynamics by placing ionic and dipolar probes at varying distances from the enclosing surface. We find that the confined water molecules exhibit exotic dynamical features and stark differences from that in the bulk liquid. We employ atomistic molecular dynamics simulation to obtain the solvation time correlation function, non-Gaussian parameter, and non-linear response function that reveal the existence of heterogeneous and non-exponential dynamics with a strong sensitivity to both the size and the shape of the enclosure. Importantly, the slower long-time decay constant exhibits a non-monotonic spatial dependence. The initial ultrafast component is reminiscent of the same in the bulk, but it is found to have a different origin in the present systems. We perform shell-wise analyses to understand the microscopic origin of these observations and the range of the propagation of the surface induced effects.

Concept of reaction coordinate for dynamics of optically controlled non-equilibrium processes in condensed phase

Optically controlled non-equilibrium processes in condensed phase, such as solvation of ions and electron transfer reactions, have been widely studied both experimentally and theoretically. The dynamics of these processes is investigated through the experimentally observable quantities, like non-equilibrium solvation time correlation function $$ S\left( t \right) $$ and the time-dependent survival probability $$ P\left( t \right) $$ of the reactant, respectively. On the theoretical side, although the linear response theory and Marcus theory have been widely used to predict $$ S\left( t \right) $$ and $$ P\left( t \right) $$, respectively, their main drawback is that their prediction of $$ S\left( t \right) $$ and $$ P\left( t \right) $$ does not show dependence on the initial preparation of the system, while experimental observations suggest that both these quantities depend on the initial preparation through dependence on the excitation wavelength. In this work, we address this issue and introduce the concept of a new reaction coordinate, which can take into account the effect of initial optically prepared innumerable phase space coordinates through a single parameter, viz. the optical excitation wavelength. We first project the dynamics in multi-dimensional Liouville space onto a one-dimensional reaction coordinate (RC) space, obtaining thereby a new kinetic equation for the RC. We have calculated both $$ S\left( t \right) $$ and $$ P\left( t \right) $$ by numerically solving this new equation in one-dimensional RC space for harmonic as well as anharmonic potentials and studied the effect of the initial preparation of the system by considering the excitation wavelength dependence. It is found that for solvation process, the calculated $$ S\left( t \right) $$ depends strongly on the initial preparation of the system (i.e. the excitation wavelength) only for anharmonic effective potentials. For electron transfer reaction, however, $$ P\left( t \right) $$ depends on the excitation wavelength for both harmonic and anharmonic potentials, which cannot be predicted by the Marcus theory.

Origin of Slow Solvation Dynamics in DNA: DAPI in Minor Groove of Dickerson-Drew DNA.

The measurement and understanding of collective solvation dynamics in DNA have vital biological implications, as protein and ligand binding to DNA can be directly controlled by complex electrostatic interactions of anionic DNA and surrounding dipolar water, and ions. Time-resolved fluorescence Stokes shift (TRFSS) experiments revealed anomalously slow solvation dynamics in DNA much beyond 100 ps that follow either power-law or slow multiexponential decay over several nanoseconds. The origin of such dispersed dynamics remains difficult to understand. Here we compare results of TRFSS experiments to molecular dynamics (MD) simulations of well-known 4',6-diamidino-2-phenylindole (DAPI)/Dickerson-Drew DNA complex over five decades of time from 100 fs to 10 ns to understand the origin of such dispersed dynamics. We show that the solvation time-correlation function (TCF) calculated from 200 ns simulation trajectory (total 800 ns) captures most features of slow dynamics as measured in TRFSS experiments. Decomposition of TCF into individual components unravels that slow dynamics originating from dynamically coupled DNA-water motion, although contribution from coupled water-Na+ motion is non-negligible. The analysis of residence time of water molecules around the probe (DAPI) reveals broad distribution from ∼6 ps to ∼3.5 ns: Several (49 nos.) water molecules show residences time greater than 500 ps, of which at least 14 water molecules show residence times of more than 1 ns in the first solvation shell of DAPI. Most of these slow water molecules are found to occupy two hydration sites in the minor groove near DAPI binding site. The residence time of Na+, however, is found to vary within ∼17-120 ps. Remarkably, we find that freezing the DNA fluctuations in simulation eliminates slower dynamics beyond ∼100 ps, where water and Na+ dynamics become faster, although strong anticorrelation exists between them. These results indicate that primary origin of slow dynamics lies within the slow fluctuations of DNA parts that couple with nearby slow water and ions to control the dispersed collective solvation dynamics in DNA minor groove.

Optical controlled non-equilibrium processes: effect of excitation wavelength

Experimental results on optically controlled non-equilibrium solvation dynamics show their dependence on excitation wavelength, However, the renowned Onsager regression hypothesis and Smoluchowski equation-based approach fail to explain such dependance. Failure of this theory prompted us to develop a novel theory by projecting the dynamics in a higher-dimensional space onto a one-dimensional energy gap space, where the effect of is included explicitly. We have then derived hierarchical equations of moments in time domain for an anharmonic potential based on the new kinetic equation derived here in the energy gap space to evaluate the non-equilibrium solvation time correlation function (NSTCF). The new methodlogy presented here also removes the difficulties in perturbative approaches to evaluate the NSTCF in a condensed phase. We have also shown that the NSTCF is independent of excitation wavelength for harmonic potential but dependent on the same for anharmonic potential, which is in accord with experimental observation. However, Onsager’s regression hypothesis-based prediction for the NSTCF is independent of excitation wavelength for all kinds of potentials. More importantly, the calculated results of NSTCF is in excellent agreement with the experimental results where the Onsager regression hypothesis-based prediction fails.

The Time-Resolved Fluorescence Stokes Shift of Cucurbit[6]Uril Complexes with a Pyridinium Styryl Dye.

The time-resolved Stokes shift of fluorescence of styryl dye, trans-4-[4-(dimethylamino)-styryl]-1-methylpyridinium iodide (DASPI), and its host-guest complexes with cucurbit[6]uril (CB[6]) was studied by up-conversion technique on a 5ps time scale. In all cases, the solvation time correlation function - that describes relaxation of the fluorescent state - contains two components. The time constant of the first component, which is related to the vibrational relaxation of the dye cation, increases from 118fs without CB[6] to 224fs in the presence CB[6]. It suggests the production of CB[6] complexes to disturb the hydrogen-bond net in the vicinity of DASPI cation. The time constant of the second component, which is associated with solvation, changes from 0.81ps without CB[6] to 1.15ps in the presence of the cavitand. The observed increase can be related to the displacement of the dye cation deeper into CB[6] that allows considering DASPI-CB[6] complexes as a light-controlled molecular machine with a response time on the picosecond scale.

Broad-Band Pump-Probe Spectroscopy Quantifies Ultrafast Solvation Dynamics of Proteins and Molecules.

In this work, we demonstrate the use of broad-band pump-probe spectroscopy to measure femtosecond solvation dynamics. We report studies of a rhodamine dye in methanol and cryptophyte algae light-harvesting proteins in aqueous suspension. Broad-band impulsive excitation generates a vibrational wavepacket that oscillates on the excited-state potential energy surface, destructively interfering with itself at the minimum of the surface. This destructive interference gives rise to a node at a certain probe wavelength that varies with time. This reveals the Gibbs free-energy changes of the excited-state potential energy surface, which equates to the solvation time correlation function. This method captures the inertial solvent response of water (∼40 fs) and the bimodal inertial response of methanol (∼40 and ∼150 fs) and reveals how protein-buried chromophores are sensitive to the solvent dynamics inside and outside of the protein environment.

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe–ion direct correlation function and ion–ion dynamic structure factor. Although the power law decay is reminiscent of Debye–Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.

Solvation dynamics of tryptophan in water-dimethyl sulfoxide binary mixture: In search of molecular origin of composition dependent multiple anomalies

Experimental and simulation studies have uncovered at least two anomalous concentration regimes in water-dimethyl sulfoxide (DMSO) binary mixture whose precise origin has remained a subject of debate. In order to facilitate time domain experimental investigation of the dynamics of such binary mixtures, we explore strength or extent of influence of these anomalies in dipolar solvation dynamics by carrying out long molecular dynamics simulations over a wide range of DMSO concentration. The solvation time correlation function so calculated indeed displays strong composition dependent anomalies, reflected in pronounced non-exponential kinetics and non-monotonous composition dependence of the average solvation time constant. In particular, we find remarkable slow-down in the solvation dynamics around 10%-20% and 35%-50% mole percentage. We investigate microscopic origin of these two anomalies. The population distribution analyses of different structural morphology elucidate that these two slowing down are reflections of intriguing structural transformations in water-DMSO mixture. The structural transformations themselves can be explained in terms of a change in the relative coordination number of DMSO and water molecules, from 1DMSO:2H2O to 1H2O:1DMSO and 1H2O:2DMSO complex formation. Thus, while the emergence of first slow down (at 15% DMSO mole percentage) is due to the percolation among DMSO molecules supported by the water molecules (whose percolating network remains largely unaffected), the 2nd anomaly (centered on 40%-50%) is due to the formation of the network structure where the unit of 1DMSO:1H2O and 2DMSO:1H2O dominates to give rise to rich dynamical features. Through an analysis of partial solvation dynamics an interesting negative cross-correlation between water and DMSO is observed that makes an important contribution to relaxation at intermediate to longer times.

Simulations of Solvation and Solvation Dynamics in an Idealized Ionic Liquid Model

Equilibrium and nonequilibrium molecular dynamics simulations of solvation and solvation dynamics of a variety of solutes have been performed in the coarse-grained ionic liquid model ILM2 (Roy, D.; Maroncelli, M. J. Phys. Chem. B 2010, 114, 12629). Some comparisons are made between ionic and dipolar solvation using parallel simulations in CH(3)CN. Despite the fact that the multipolar character of electrostatic interactions and their spatial extent differ in the two solvents, solvation energies are equal to within about 10% in ILM2 and CH(3)CN. This near equality also holds with reduced accuracy in the case of reorganization energies. Solvation energies of spherical solutes in ILM2 and its variants can be correlated as a function of solute and solvent size using a Born-type expression with an effective cavity size. Solvation time correlation functions in ILM2 exhibit a subpicosecond inertial component followed by a broadly distributed component related to solvent viscosity, comparable to what has been observed in experiment. Direct comparison of simulation to experiment using the solute coumarin 153 (C153) shows general agreement on the time scales and character of the fast and slow components, but the amplitude of the fast component is overestimated by the simulations. Solute motion can significantly increase the speed of solvation, even in the case of large solutes such as C153. Good agreement is found between linear response estimates and the nonequilibrium dynamics associated with electronic excitation of C153. In contrast, perturbations involving changes of a full electron charge in atomic solutes lead to local heating which greatly hastens solvation compared to linear response predictions. The mechanism of charge solvation in atomic solutes is examined in some detail. It is found that ion translation dominates the inertial dynamics. The rotational contribution only becomes comparable to the translation contribution in the tail of the response. Adjustments of ion positions over distances of ~30% of their diameters are all that is required to relax the solvation energy in these systems.

Polar solvation dynamics of lysozyme from molecular dynamics studies

The solvation dynamics of a protein are believed to be sensitive to its secondary structures. We have explored such sensitivity in this article by performing room temperature molecular dynamics simulation of an aqueous solution of lysozyme. Nonuniform long-time relaxation patterns of the solvation time correlation function for different segments of the protein have been observed. It is found that relatively slower long-time solvation components of the α-helices and β-sheets of the protein are correlated with lower exposure of their polar probe residues to bulk solvent and hence stronger interactions with the dynamically restricted surface water molecules. These findings can be verified by appropriate experimental studies.

ChemInform Abstract: Solvation Dynamics in Dipolar Liquids

AbstractReview: 124 refs.

Solvation dynamics in dipolar liquids

The time dependent response of a polar solvent to a changing charge distribution is studied in solvation dynamics. The change in the energy of the solute is measured by a time domain Stokes shift in the fluorescence spectrum of the solute. Alternatively, one can use sophisticated non-linear optical spectroscopic techniques to measure the energy fluctuation of the solute at equilibrium. In both methods, the measured dynamic response is expressed by the normalized solvation time correlation function, S(t). The latter is found to exhibit unique features reflecting both the static and dynamic characteristics of each solvent. For water, S(t) consists of a dominant sub-50 fs ultrafast component, followed by a multi-exponential decay. Acetonitrile exhibits a sub-100 fs ultrafast component, followed by an exponential decay. Alcohols and amides show features unique to each solvent and solvent series. However, understanding and interpretation of these results have proven to be difficult, and often controversial. Theoretical studies and computer simulations have greatly facilitated the understanding of S(t) in simple systems. Recently solvation dynamics has been used extensively to explore dynamics of complex systems, like micelles and reverse micelles, protein and DNA hydration layers, sol-gel mixtures and polymers. In each case one observes rich dynamical features, characterized again by multi-exponential decays but the initial and final time constants are now widely separated. In this tutorial review, we discuss the difficulties in interpreting the origin of the observed behaviour in complex systems.

Exploration of the Secondary Structure Specific Differential Solvation Dynamics between the Native and Molten Globule States of the Protein HP-36

Recent experiments have shown that the time dependence of fluorescence Stokes shift of a chromophore is substantially different when the chromophore is located in a molten globule (MG) state and in the native state of the same protein. To understand the origin of this difference, particularly the role of water in the differential solvation of the protein in the native and the MG states, we have carried out fully atomistic molecular dynamics simulations with explicit water of a partially unfolded MG state of the protein HP-36 and compared the results with the solvation dynamics of the protein in the folded native state. It is observed that the polar solvation dynamics of the three helical segments of the protein is influenced in a nonuniform heterogeneous manner in the MG state. While the equilibrium solvation time correlation function for helix-3 has been found to relax faster in the MG state as compared to that in the native state, the decay of the corresponding function for the other two helices slows down in the MG state. A careful analysis shows that the origin of such heterogeneous relative solvation behavior lies in the differential location of the polar probe residues and their exposure to bulk solvent. We find a significant negative cross-correlation between the contribution (to the solvation energy of a tagged amino acid residue) of water and the other groups of the protein, indicating a competing role in solvation. The sensitivity of solvation dynamics to the secondary structure and the immediate environment can be used to discriminate the partially unfolded and folded states. These results therefore should be useful in explaining recent solvation dynamics experiments on native and MG states of proteins.

Dynamics in a room-temperature ionic liquid: A computer simulation study of 1,3-dimethylimidazolium chloride

The transport properties and solvation dynamics of model 1,3-dialkylimidazolium chloride melt at 425 K is studied using molecular-dynamics simulations. Long trajectories of a large system have been generated and quantities such as the self-diffusion coefficient of ions, shear viscosity, and ionic conductivity have been calculated. Interestingly, the diffusion of the heavier cation is found to be faster than the anion, in agreement with experiment. The interaction model is found to predict a higher viscosity and lower electrical conductivity compared to experimental estimates. Analysis of the latter calculations points to correlated ion motions in this melt. The solvation time correlation function for dipolar and ionic probes studied using equilibrium simulations exhibits three time components, which include an ultrafast (subpicosecond) part as well as one with a time constant of around 150 ps. The ultrafast solvent relaxation is ascribed to the rattling of anions in their cage, while the slow component could be related to the reorientation of the cations as well as to ion diffusion.

Hydration Layer of a Cationic Micelle, C10TAB: Structure, Rigidity, Slow Reorientation, Hydrogen Bond Lifetime, and Solvation Dynamics

We report a theoretical study of the structure and dynamics of the water layer (the hydration layer) present at the surface of the cationic micelle decyltrimethylammonium bromide (DeTAB) by using atomistic molecular dynamics simulations. The simulated micelle consisted of 47 surfactant molecules (and an equal number of bromide ions), in good agreement with the pioneering light scattering experiments by Debye which found an aggregation number of 50. In this micelle, three partially positively charged methyl groups of each surfactant headgroup face the surrounding water. The nature of the cationic micellar surface is found to play an important role in determining the arrangement of water which is quite different from that in the bulk or on the surface of an anionic micelle, like cesium perfluorooctanoate. Water molecules present in the hydration layer are found to be preferentially distributed in the region between the three partially charged methyl headgroups. It is found that both the translational and rotational motions of water exhibit appreciably slower dynamics in the layer than those in the bulk. The solvation time correlation function (TCF) of bromide ions exhibits a long time component which is found to originate primarily from the interaction of the probe with the micellar headgroups. Thus, the decay of the solvation TCF is controlled largely by the residence time of the probe in the surface. The residence time distribution of the water molecules also exhibits a slow time component. We also calculate the collective number density fluctuation in the layer and find a prominent slow component compared to the similar quantity in the bulk. This slow component demonstrates that water structure in the hydration layer is more rigid than that in the bulk. These results demonstrate that the slow dynamics of hydration layer water is generic to macromolecular surfaces of either polarity.

Sensitivity of Polar Solvation Dynamics to the Secondary Structures of Aqueous Proteins and the Role of Surface Exposure of the Probe

The structure and dynamics of water around a protein is expected to be sensitive to the details of the adjacent secondary structure of the protein. In this article, we explore this sensitivity by calculating both the orientational dynamics of the surface water molecules and the equilibrium solvation time correlation function of the polar amino acid residues in each of the three helical segments of the protein HP-36, using atomistic molecular dynamics simulations. The solvation dynamics of polar amino acid residues in helix-2 is found to be faster than that of the other two helices (the average time constant is smaller by a factor of 2), although the interfacial water molecules around helix-2 exhibit much slower orientational dynamics than that around the other two helices. A careful analysis shows that the origin of such a counterintuitive behavior lies in the dependence of the solvation time correlation function on the surface exposure of the probe-the more exposed is the probe, the faster the solvation dynamics. We discuss that these results are useful in explaining recent solvation dynamics experiments.

Time-dependent friction and solvation time correlation function

We have derived a new relation between the time-dependent friction and solvation time correlation function (STCF) for non-polar fluids. The friction values calculated using this relation and simulation results on STCF for a Lennard–Jones fluid are shown to have excellent agreement with the same obtained through mode-coupling theory. Also derived is a relation between the time-dependent dielectric friction and STCF for polar fluids. Routes are thus provided to obtain the time-dependent friction (non-polar as well as dielectric) from an experimentally measured quantity like STCF, even if the interparticle interaction potential is not known.

Polar solvation dynamics in supercritical fluids: A mode-coupling treatment

A mode-coupling treatment of polar solvation dynamics in supercritical fluids is presented. The equilibrium solvation time correlation function for the solute fluctuating transition frequency is obtained from the mode-coupling theory method and from molecular-dynamics simulations. The theory is shown to be in good agreement with the simulation. The solvation time correlation function exhibits three distinct time scales, with rapid initial decay, followed by a recurrence at intermediate times, and a slowly decaying long-time tail. Our theoretical analysis shows that the short-time decay arises from the coupling of the solute energy gap to the solvent polarization modes, the recurrence at intermediate times is due to the energy modes, while the slow long-time decay reflects the coupling to the number density modes.