Heat capacity effects associated with the hydrophobic hydration and interaction of simple solutes: a detailed structural and energetical analysis based on molecular dynamics simulations

We examine the SPCE [H. J. C. Berendsen et al., J. Chem. Phys. 91, 6269 (1987)] and TIP5P [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys 112, 8910 (2000)] water models using a temperature series of molecular-dynamics simulations in order to study heat-capacity effects associated with the hydrophobic hydration and interaction of xenon particles. The temperature interval between 275 and 375 K along the 0.1-MPa isobar is studied. For all investigated models and state points we calculate the excess chemical potential for xenon employing the Widom particle insertion technique. The solvation enthalpy and excess heat capacity is obtained from the temperature dependence of the chemical potentials and, alternatively, directly by Ewald summation, as well as a reaction field based method. All three methods provide consistent results. In addition, the reaction field technique allows a separation of the solvation enthalpy into solute/solvent and solvent/solvent parts. We find that the solvent/solvent contribution to the excess heat capacity is dominating, being about one order of magnitude larger than the solute/solvent part. This observation is attributed to the enlarged heat capacity of the water molecules in the hydration shell. A detailed spatial analysis of the heat capacity of the water molecules around a pair of xenon particles at different separations reveals that even more enhanced heat capacity of the water located in the bisector plane between two adjacent xenon atoms is responsible for the maximum of the heat capacity found for the desolvation barrier distance, recently reported by Shimizu and Chan [J. Am. Chem. Soc. 123, 2083 (2001)]. The about 60% enlarged heat capacity of water in the concave part of the joint xenon-xenon hydration shell is the result of a counterplay of strengthened hydrogen bonds and an enhanced breaking of hydrogen bonds with increasing temperature. Differences between the two models with respect to the heat capacity in the xenon-xenon contact state are attributed to the different water model bulk heat capacities, and to the different spatial extension of the structure effect introduced by the hydrophobic particles. Similarities between the different states of water in the joint xenon-xenon hydration shell and the properties of stretched water are discussed.     

Entropy and dynamics of water in hydration layers of a bilayer

We compute the entropy and transport properties of water in the hydration layer of dipalmitoylphosphatidylcholine bilayer by using a recently developed theoretical scheme [two-phase thermodynamic model, termed as 2PT method; S.-T. Lin et al., J. Chem. Phys. 119, 11792 (2003)] based on the translational and rotational velocity autocorrelation functions and their power spectra. The weights of translational and rotational power spectra shift from higher to lower frequency as one goes from the bilayer interface to the bulk. Water molecules near the bilayer head groups have substantially lower entropy (48.36 J/mol/K) than water molecules in the intermediate region (51.36 J/mol/K), which have again lower entropy than the molecules (60.52 J/mol/K) in bulk. Thus, the entropic contribution to the free energy change (TΔS) of transferring an interface water molecule to the bulk is 3.65 kJ/mol and of transferring intermediate water to the bulk is 2.75 kJ/mol at 300 K, which is to be compared with 6.03 kJ/mol for melting of ice at 273 K. The translational diffusion of water in the vicinity of the head groups is found to be in a subdiffusive regime and the rotational diffusion constant increases going away from the interface. This behavior is supported by the slower reorientational relaxation of the dipole vector and OH bond vector of interfacial water. The ratio of reorientational relaxation time for Legendre polynomials of order 1 and 2 is approximately 2 for interface, intermediate, and bulk water, indicating the presence of jump dynamics in these water molecules.     

High-resolution neutron-scattering study of slow dynamics of surface water molecules in zirconium oxide

We have performed a quasielastic neutron-scattering experiment on backscattering spectrometer with sub-mueV resolution to investigate the slow dynamics of surface water in zirconium oxide using the sample studied previously with a time-of-flight neutron spectrometer [E. Mamontov, J. Chem. Phys. 121, 9087 (2004)]. The backscattering measurements in the temperature range of 240-300 K have revealed a translational dynamics slower by another order of magnitude compared to the translational dynamics of the outer hydration layer observed in the time-of-flight experiment. The relaxation function of this slow motion is described by a stretched exponential with the stretch factors between 0.8 and 0.9, indicating a distribution of the relaxation times. The temperature dependence of the average residence time is non-Arrhenius, suggesting that the translational motion studied in this work is more complex than surface jump diffusion previously observed for the molecules of the outer hydration layer. The observed slow dynamics is ascribed to the molecules of the inner hydration layer that form more hydrogen bonds compared to the molecules of the outer hydration layer. Despite being slower by two orders of magnitude, the translational motion of the molecules of the inner hydration layer may have more in common with bulk water compared to the outer hydration layer, the dynamics of which is slower than that of bulk water by just one order of magnitude.     

Solvation shell dynamics studied by molecular dynamics simulation in relation to the translational and rotational dynamics of supercritical water and benzene

The solvation shell dynamics of supercritical water is analyzed by molecular dynamics simulation with emphasis on its relationship to the translational and rotational dynamics. The relaxation times of the solvation number (tau S), the velocity autocorrelation function (tau D), the angular momentum correlation function (tau J), and the second-order reorientational correlation function (tau 2R) are studied at a supercritical temperature of 400 degrees C over a wide density region of 0.01-1.5 g cm(-3). The relaxation times are decomposed into those conditioned by the solvation number n, and the effect of the short-ranged structure is examined in terms of its probability Pn of occurrence. In the low to medium-density range of 0.01-0.4 g cm(-3), the time scales of water dynamics are in the following sequence: tau D>tau S approximately or > tau J approximately or > tau 2R. This means that the rotation in supercritical water is of the "in-shell" type while the translational diffusion is not. The comparison to supercritical benzene is also performed and the effect of hydrogen bonding is examined. The water diffusion is not of the in-shell type up to the ambient density of 1.0 g cm(-3), which corresponds to the absence of the transition from the collision to the Brownian picture, whereas such transition is present in the case of benzene. The absence of the transition in water comes from the fast reorganization of the hydrogen bonds and the enhanced mobility of the solvation shell in supercritical conditions.     

A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. II. Noncollisional mechanism for the relaxation of a polar solute in supercritical water

Mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of a hydrophilic model NO in supercritical water at various densities along an isotherm above the critical temperature. The relaxation rate was determined based on Fermi's golden rule at each state point and showed an inverse S-shaped curve as a function of bulk density. The hydration number was also calculated as a function of bulk density based on the calculated radial distribution function, which showed a good correlation with the relaxation rate. Change of the survival probability of the solute vibrational state was analyzed as a function of time together with the trajectory of the solvent water and the interaction with it. We will show that the solvent molecule resides near the solute molecule for a while and the solvent contributes to the relaxation by the random-noiselike Coulombic interaction only when it stays near the solute. After the solvent leaves the solute, it shows no contribution to the relaxation. The relaxation mechanism for this system is significantly different from the collisional one found for a nonpolar solute in nonpolar solvent in Paper I. Then, the relaxation rate is determined, on average, by the hydration number or local density of the solvent. Thus, the density dependence of the relaxation rate for the polar solute in supercritical water is apparently similar to that found for the nonpolar solute in nonpolar solvent, although the molecular process is quite different from each other.     

On the heat-capacity change of pairwise hydrophobic interactions

Computer simulations [S. Shimizu and H. S. Chan, J. Am. Chem. Soc. 123, 2083 (2001); D. Paschek, J. Chem. Phys. 120, 10605 (2004)] have demonstrated that the heat-capacity change associated with the interaction of two nonpolar spherical particles, at room temperature, shows a complex behavior with a significant maximum at the distance corresponding to the desolvation barrier configuration and a small minimum at the distance corresponding to the contact configuration. Taking advantage of the detailed analysis performed by Paschek, the two-state model of Muller is applied to estimate the energetic strength and the intactness of the H bonds in the hydration shell of a xenon atom and in the concave part of the joint Xe-Xe hydration shell. In both hydration shell regions the H bonds are energetically stronger but more broken than those in bulk water. In addition, those in the concave part of the joint Xe-Xe hydration shell are, in absolute, stronger and more broken. These thermodynamic features coupled to simple geometric arguments allow the calculation of heat-capacity values that are in agreement with those provided by computer simulations for the pairwise Xe-Xe interaction.     

Water rotational relaxation and diffusion in hydrated lysozyme

This paper is concerned with the dynamics of water around a small globular protein. Dipolar second-rank relaxation time and diffusion properties of surface water were computed by extensive molecular dynamics simulations of lysozyme in water which lasted a total of 28 ns. Our results indicate that the rotational relaxation of water in the vicinity of lysozyme is 3-7 times slower than that in the bulk depending on how the hydration shell is defined in the calculation. We have also verified that the dynamics of water translational diffusion in the vicinity of lysozyme have retardations similar to rotational relaxation. This is a common assumption in nuclear magnetic relaxation dispersion (NMRD) studies to derive residence times. In contrast to bulk water dynamics, surface water is in a dispersive diffusion regime or subdiffusion. Very good agreement of dipolar second-rank relaxation time with NMRD estimates is obtained by using appropriate dimensions of the hydration shell. Although our computed second-rank dipolar retardations are independent of the water model, SPC/E describes more realistically the time scale of the water dynamics around lysozyme than does TIP3P.     

Water structure about the dimer and hexamer repeat units of amylose from molecular dynamics computer simulations

We have analyzed a set of molecular dynamics (MD) trajectories of maltose in vacuum and water for solute imposed structuring on the solvent. To do this, we used a novel technique to calculate water probability densities to locate the areas in which the solvent is most populated in the maltose solution. We found that only the layer of water within the first maltose hydration shell has a probability density 50% and greater than that of bulk water. On investigating this water layer using Voronoi polyhedra (VP) analysis it was seen that only the waters adjacent to the hydrophobic (CH and CH₂) groups are more structured than bulk water. We found that in a maltose solution of approximately 1.0 g/cm³ the solute does not disrupt the structure of the surrounding water beyond the first hydration shell. Next we performed a 700‐ps MD simulation of a maltohexaose strand in a box of 4096 SPC/E waters. The water probability density calculations and the VP analysis of the maltohexaose solution show that the larger amylose repeat unit decreases the solvent configurational entropy of the water beyond the first hydration shell. Analysis of this trajectory reveals that the helical conformation of the maltohexaose strand is preserved via bridging intermolecular water hydrogen bonds, indicating that a single amylose helical turn in water is preserved by hydrophilic and not hydrophobic interactions. Using VP analysis we present a method to accurately determine the number of water molecules in the first hydration shell of dissolved solutes. In the case of maltose, there are 40 water molecules in this shell, while for maltohexaose the number is 98. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 445–456, 2001     

An investigation of water dynamics in binary mixtures of water and dimethyl sulfoxide

The motion of water molecules in mixtures of water and d6-dimethyl sulfoxide (DMSO) has been explored through molecular dynamics (MD) simulations using the SPC/E water model (J. Chem. Phys. 1987, 91, 6269) and the P2 DMSO model (J. Chem. Phys. 1993, 98, 8160). We evaluate the self-intermediate scattering functions, FS(Q,t), which are related by a Fourier transform to the incoherent structure factors, S(Q,omega), measured in quasielastic neutron scattering (QNS) experiments. We compare our results to recent QNS experiments on these mixtures reported by Bordallo et al. (J. Chem. Phys. 2004, 121, 12457). In addition to comparing the MD data to the experimental signals, which correspond to a convolution of S(Q,omega) with a resolution function, we examine the rotational and translational components of FS(Q,t) and investigate to what extent simulation results for the single-molecule dynamics follow the dynamical models that are used in the analysis of the experimental data. We find that the agreement between the experimental signal and the MD data is quite good and that the portion of FS(Q,t) due to translational dynamics is well represented by the jump-diffusion model. The model parameters and their composition dependence are in reasonable agreement with experiment, exhibiting similar trends in water mobility with composition. Specifically, we find that water motion is less hindered in water-rich and water-poor mixtures than it is near equimolar composition. We find that the extent of coupling between rotational and translational motion contributing to FS(Q,t) increases as the equimolar composition of the mixture is approached. Thus, the decoupling approximation, which is used to extract information on rotational relaxation from QNS spectra at higher momentum transfer (Q) values, becomes less accurate than that in water-rich or DMSO-rich mixtures. We also find that rotational relaxation deviates quite strongly from the isotropic rotational diffusion model. We explore this issue further by investigating the behavior of orientational time correlations for different unit vectors and corresponding to Legendre polynomials of orders 1-4. We find that the rotational time correlations of water molecules behave in a way that is more consistent with the extended jump rotation model recently proposed by Laage and Hynes (Science 2006, 311, 832).     

The importance of the shape of the protein-water interface of a kinesin motor domain for dynamics of the surface atoms of the protein

A single kinesin motor domain immersed in water has been investigated using molecular dynamics. It has been found that local properties of water in the solvation shell change along with the nature of the neighboring protein surface. However, a detailed analysis leads to the conclusion that the geometrical features of hydrogen bonds and overall structure of kinesin hydration water are not very different from bulk water. The local values of diffusion coefficients (translational and rotational) of water adjacent to specific patches on the protein surface seem not to be correlated to the orientational ordering of hydration water, but instead they depend on spatial roughness and degree of exposure of the patch to the solvent. Finally, a relationship between the mobility of various surface atoms of the protein and the mean values of the diffusion coefficient of the adjacent water molecules has been observed. The latter finding suggests a close relationship between the dynamics of the inner kinesin movements and the behavior of solvation water which is in turn determined by the topography of the contact surface between the protein and the surrounding water molecules.     

Thermal signature of hydrophobic hydration dynamics

Hydrophobic hydration, the perturbation of the aqueous solvent near an apolar solute or interface, is a fundamental ingredient in many chemical and biological processes. Both bulk water and aqueous solutions of apolar solutes behave anomalously at low temperatures for reasons that are not fully understood. Here, we use (2)H NMR relaxation to characterize the rotational dynamics in hydrophobic hydration shells over a wide temperature range, extending down to 243 K. We examine four partly hydrophobic solutes: the peptides N-acetyl-glycine-N'-methylamide and N-acetyl-leucine-N'-methylamide, and the osmolytes trimethylamine N-oxide and tetramethylurea. For all four solutes, we find that water rotates with lower activation energy in the hydration shell than in bulk water below 255 +/- 2 K. At still lower temperatures, water rotation is predicted to be faster in the shell than in bulk. We rationalize this behavior in terms of the geometric constraints imposed by the solute. These findings reverse the classical "iceberg" view of hydrophobic hydration by indicating that hydrophobic hydration water is less ice-like than bulk water. Our results also challenge the "structural temperature" concept. The two investigated osmolytes have opposite effects on protein stability but have virtually the same effect on water dynamics, suggesting that they do not act indirectly via solvent perturbations. The NMR-derived picture of hydrophobic hydration dynamics differs substantially from views emerging from recent quasielastic neutron scattering and pump-probe infrared spectroscopy studies of the same solutes. We discuss the possible reasons for these discrepancies.     

A molecular dynamics study of the dielectric properties of aqueous solutions of alanine and alanine dipeptide

Molecular dynamics simulations were used to compute the frequency-dependent dielectric susceptibility of aqueous solutions of alanine and alanine dipeptide. We studied four alanine solutions, ranging in concentration from 0.13-0.55 mol/liter, and two solutions of alanine dipeptide (0.13 and 0.27 mol/liter). In accord with experiment we find a strong dielectric increment for both solutes, whose molecular origin is shown to be the zwitterionic nature of the solutes. The dynamic properties were analyzed based on a dielectric component analysis into solute, a first hydration shell, and all remaining (bulk) waters. The results of this three component decomposition were interpreted directly, as well as by uniting the solute and hydration shell component to a "suprasolute" component. In both approaches three contributions to the frequency-dependent dielectric properties can be discerned. The quantitatively largest and fastest component arises from bulk water [i.e., water not influenced by the solute(s)]. The interaction between waters surrounding the solute(s) (the hydration shell) and bulk water molecules leads to a relaxation process occurring on an intermediate time scale. The slowest relaxation process originates from the solute(s) and the interaction of the solute(s) with the first hydration shell and bulk water. The primary importance of the hydration shell is the exchange of shell and bulk waters; the self-contribution from bound water molecules is comparatively small. While in the alanine solutions the solute-water cross-terms are more important than the solute self-term, the solute contribution is larger in the dipeptide solutions. In the latter systems a much clearer separation of time scales between water and alanine dipeptide related properties is observed. The similarities and differences of the dielectric properties of the amino acid/peptide solutions studied in this work and of solutions of mono- and disaccharides and of the protein ubiquitin are discussed.     

Mobility of CD4 molecules in nanoscale cages of zeolites as studied by deuteron NMR relaxation

Deuteron spin–lattice relaxation was applied to study mobility of CD₄ molecules trapped in the cages of zeolite NaY. There are two, interconnected sets of cages: α-cages and β-cages with 1.16 and 0.74 nm diameter, respectively. The relaxation temperature dependence, measured between 4 and 300 K, can be divided into four ranges with characteristic motional parameters. At higher temperatures exchange between cages dominates. Increasing rate of translational motion leads to a significant reduction of the relaxation rate. Features typical for quantum rotors were observed at low temperatures. Molecules in the α-cages exhibit reorientational freedom, while motion of these in β-cages is significantly restricted. Increasing abundance of molecules in β-cages indicates slow diffusion down to low temperatures.     

Single particle and pair dynamics in water-formic acid mixtures containing ionic and neutral solutes: nonideality in dynamical properties

A series of molecular dynamics simulations of water-formic acid mixtures containing either an ionic solute or a neutral hydrophobic solute has been performed to study the extent of nonideality in the dynamics of these solutes for varying composition of the mixtures. The diffusion coefficients of the charged solutes, both cationic and anionic, are found to show nonideal behavior with variation of composition, and similar nonideality is also observed for the diffusion and orientational relaxation of solvent molecules in these mixtures. The diffusion coefficient of a neutral hydrophobic solute, however, decreases monotonically with increase in water concentration. We have also investigated some of the pair dynamical properties such as water-water and water-formic acid hydrogen bond relaxation and residence dynamics of water molecules in water and formic acid hydration shells. The lifetimes of water-water hydrogen bonds are found to be longer than those between formic acid carbonyl oxygen-water hydrogen bonds, whereas the lifetimes of formic acid hydroxyl hydrogen-water hydrogen bonds are longer than those of water-water hydrogen bonds. In general, the hydrogen bond lifetimes for both water-water and water-formic acid hydrogen bonds are found to decrease with increase in water concentration. Residence times of water molecules also show the same trend with increase in formic acid concentration. Interestingly, these pair dynamical properties show a monotonic dependence on composition without any maximum or minimum and behave almost ideally with respect to changes in the composition of the mixtures. The present calculations are performed with fixed-charge nonpolarizable models of the solvent and solute molecules without taking into account many-body polarization effects in an explicit manner.     

The effect of the counterion on water mobility in reverse micelles studied by molecular dynamics simulations

In this study, mobility and structure of water molecules in Aerosol OT (bis(2-ethylhexyl) sulfosuccinate, AOT) reverse micelles with water content w0 = 5 and Na+, K+, Cs+ counterions have been explored with molecular dynamics (MD) simulations. Using the Faeder/Ladanyi model (J. Phys. Chem. B, 2000, 104, 1033) of the reverse micelle interior, MD simulations were performed to calculate the self-intermediate scattering function, FS(Q,t), for water hydrogen atoms that could be measured in a quasielastic neutron scattering experiment. Separate intermediate scattering functions FRS(Q,t) and FCMS(Q,t) were determined for rotational and translational motion. We find that the decay of FCMS(Q,t) is nonexponential and our analysis of the MD data indicates that this behavior arises from decreased water mobility for molecules close to the interface and from confinement-induced restrictions on the range of translational displacements. Rotational relaxation also exhibits nonexponential decay, which is consistent with relatively rapid restricted rotation and slower rotational relaxation over the full angular range. Rotational relaxation is anisotropic, with the O-H bond short-time rotational mobility considerably higher than that of the molecular dipole. This behavior is related to the decreased density of water-water hydrogen bonds in the vicinity of the interface compared to core or bulk water. We find that the interfacial mobility of water molecules is quite different for the three counterion types, but that the core mobility exhibits weak counterion dependence. Differences in interfacial mobility are strongly correlated with structural features, especially ion-water coordination, and the extent of disruption by the counterions of the water hydrogen bond network.     

Expressions for the Activity Coefficients and Osmotic Coefficients of Solutions of Electrolytes and Nonelectrolytes Based on the Hydration Model of Zavitsas

In two papers Zavitsas described a model for the thermodynamic properties of aqueous solutions of a single electrolyte or nonelectrolyte (Zavitsas, J Phys Chem B 105:7805–7817, 2001; J Solution Chem 39:301–317, 2010) in which he assumed that part of the water is so strongly bound to the solute that it can be considered as part of it, and thus only the remaining unbound water is considered to be the solvent. He showed that when the usual water mole fraction was replaced by the resulting mole fraction of unbound water, obtained by optimizing an effective hydration number, basically linear relations were obtained to fairly high molalities for the freezing temperature lowering, boiling temperature elevation, and the water activity/vapor pressure of water. However, Zavitsas only considered the properties of the solvent, not the solute. In this paper we derive the corresponding expressions for the activity coefficient of the solute for the usual molality scale based on 1 kg of water, for the modified molality scale based on 1 kg of unbound water, for the mole fraction scale based on the total number of moles of water, and for the modified mole fraction scale based on the number of moles of unbound water. These equations show that if the hydration number is larger than the stoichiometric ionization number of the electrolyte, then all four types of mean activity coefficients are predicted to always be >1 (nearly all hydration numbers reported by Zavitsas for electrolyte solutions are greater than the corresponding ionization numbers), which directly conflicts with extensive experimental and theoretical evidence that the mean activity coefficients of electrolytes in aqueous solutions always initially decrease below unity. In contrast, for nonelectrolyte solutions, the hydration model of Zavitsas gives more realistic values of the activity coefficients.     

Computational investigation of order, structure, and dynamics in modified water models

Model liquids have been constructed to study the role of local structure in the anomalous properties of liquid water. The intermolecular potentials were modified by increasing the weight of the Lennard-Jones term relative to the electrostatic term in the SPC/E model for water. The resulting family of liquids varies from SPC/E water to a Lennard-Jones-like liquid. Properties were measured as a function of density and temperature. The local structure was described by two order parameters, one measuring the tetrahedral order and the other measuring the translational order. The translational order parameter was found to be large for both tetrahedral and Lennard-Jones liquids, but to go through a minimum as the potentials were modified, demonstrating that the two types of structure are incompatible. Just as in water several properties (e.g., the translational diffusion coefficient, entropy) exhibit anomalous density dependence as a result of the breakdown of local tetrahedrality, we observed nonmonotonic behavior of the translational diffusion constant and reorientational relaxation rate as the fluids were transformed from tetrahedral to Lennard-Jones-like. This is also an indication of the incompatibility between Lennard-Jones and water-like structure.     

Sound velocity dispersion in room temperature ionic liquids studied using the transient grating method

Sound velocity is determined by the transient grating method in a range from 10(6) to 10(10) Hz in three room temperature ionic liquids, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide, 1-butyl-3-methylimidazolium hexafluorophosphate, and N,N,N-trimethyl-N-propylammonium bis(trifluoromethanesulfonyl)imide. In all room temperature ionic liquids studied, the sound velocity increased with increasing frequency. The cause of this change is posited to be structural relaxation in the room temperature ionic liquids. Frequency dependence of the sound velocity is not reproduced by a simple Debye relaxation model. The sound velocity dispersion relation in 1-butyl-3-methylimidazolium hexafluorophosphate matches a Cole-Davidson function with parameters determined by a dielectric relaxation [C. Daguenet et al., J. Phys. Chem. B 110, 12682 (2006)], indicating that structural and reorientational relaxations are strongly coupled. Conversely, the sound velocity dispersions of the other two ionic liquids measured do not match those measured for dielectric relaxation, implying that structural relaxation is much faster than the reorientational relaxation. This difference is discussed in relation to the motilities of anions and cations.