Two-particle entropy and structural ordering in liquid water

Entropies of simple point charge (SPC) water were calculated over the temperature range 278-363 K using the two-particle correlation function approximation. Then, the total two-particle contribution to the entropy of the system was divided into three parts, which we call translational, configurational, and orientational. The configurational term describes the contribution to entropy, which originates from spatial distribution of surrounding water molecules (treated as points, represented by the center of mass) around the central one. It has been shown that this term can serve as the metric of the overall orientational ordering in liquid water. Analyzing each of these three terms as a function of intermolecular distance, r, we also find a rational definition of the hydration shell around the water molecule; the estimated radii of the first and second hydration shells are 0.35 nm and 0.58 nm, respectively. We find, moreover, that the first hydration shell around the water molecule participates roughly in 70% of the total orientational entropy of water, and this rate is roughly temperature independent.     

Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.     

Density dependence of hydrogen bonding and the translational-orientational structural order in supercritical water: a molecular dynamics study

Molecular dynamics simulation have been performed with a wide range of densities along a near critical isotherm of supercritical water (SCW) in order to study the density dependence of the structure order and hydrogen bonding (HB). It is revealed that the translational structure order is nearly invariant while the orientational tetrahedral structure order is very sensitive to the bulk density under supercritical conditions. Meanwhile, some energetically unfavorable intermediate water dimer structures are found to appear under supercritical conditions due to the reduced energy difference and the enhanced energy fluctuation. As a consequence, a general geometrical criterion or the inclusion of a energy-based criterion instead of currently widely adopted pure r(OH)-based geometric criterion is suggested to be used in the HB statistics under supercritical conditions. It is found that the average HB number per H(2)O molecule (n(HB)) reduces with the decreasing SCW bulk density although a given pair of H(2)O molecules are shown to have a stronger ability to form a hydrogen bond under lower SCW bulk densities. Accordingly, the orientational tetrahedral structure order q decreases with the reducing bulk density under supercritical conditions. However, when the fluid is dilute with ρ ≤ 0.19ρ(c) (ρ(c) = 0.322 g/cm(3)), the energy fluctuation increases sharply and the short-range order is destroyed, signifying the supercritical fluid (SCF)-gas state transition. Accordingly, the orientational tetrahedral structure order q gets reversal around ρ = 0.19ρ(c) and approaches zero under very dilute conditions. The sensitivity of the orientational order to the density implies the microscopic origin of the significant dependence of SCF's physicochemical properties on the pressure.     

Structural and dynamic properties of water within the solvation layer around various conformations of the glycine-based polypeptide

Several conformations of the solvated glycine-based polypeptides were investigated using molecular dynamics simulations. Some properties of water in the neighboring space around these molecules were investigated. It was found that water forms a well-defined layer-the first solvation shell-around the peptide molecule, and thickness of this layer is independent of the peptide structure and is equal to approximately 0.28 nm. Within this layer, water molecules show marked orientations relative to a peptide surface. Using the two-particle contribution to entropy as a measure of structural ordering of water, we found that the first solvation shell contributes 95% or more to the total water ordering around the peptide molecule. In investigating the dynamic properties of water, diffusion coefficients and lifetime of the hydrogen bond, clear differences between solvation layer and the bulk water were observed. It was found that the translational diffusion coefficient, D(T), decreases by 30% or more compared to bulk water; also, the lifetime of the water-water hydrogen bond clearly increases. The rotational diffusion coefficient, however, decreases only slightly, no more than approximately 10%. These differences correspond to the slightly higher energy of the hydrogen bond, and to its slightly distorted geometry. Analyzing the translational dynamics of water in the vicinity of the peptide molecule, it was deduced that the structure of the first solvation shell becomes more rigid than the structure of the bulk water. Investigation of a "pure hydrophobic" form of the polypeptide shows that the structure and the properties of water within the solvation shell are predominantly determined by the hydrophobic effect. The specific interactions between water molecules and various charge groups of the peptide molecule modifies this effect only slightly.     

Is ammonia a better solvent than water for contact ion pairs?

The existence of a charge-transfer-to-solvent process when a KI contact ion pair (CIP) dissolved in supercritical water (SCW) is excited by UV light was confirmed by use of electronic structure calculations applied to molecular dynamics trajectories. We observed similar behavior with fluid density as that found for the KI-CIP in supercritical ammonia (SCA); nevertheless, there are some distinct features in the two supercritical solvents. First, the effect of the solvent field due to the molecules lying beyond the first solvation shell is very different in SCW compared with that observed in SCA; in SCW it actually has a destabilizing effect over the ground and excited states. Second, our results for the thermodynamic behavior of the CIP indicate that SCA is better solvent than SCW for this species. The differences found can be attributed to the solvent molecules surrounding the CIP and bridging the two ions; they shield more efficiently the ion pair from long-range solvent effects in SCA. The different behavior is partially attributed to a stronger solvent-solvent interaction in SCW than in SCA.     

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.     

Hybrid QM/MM molecular dynamics simulations for an ionic SN2 reaction in the supercritical water: OH- + CH3Cl --> CH3OH + Cl-

A hybrid real space quantum mechanical/molecular mechanical (RS-QM/MM) method has been applied to an ionic S(N)2 reaction (OH- + CH3Cl --> CH3OH + Cl-) in water solution to investigate dynamic solvation effects of the supercritical water (SCW) on the reaction. It has been demonstrated that the approaching process of OH- to methyl group is prevented by water molecules in the ambient water (AW), while the reaction takes place easily in the gas phase. Almost the same solvation effect on the dynamics of OH- is observed in the SCW, though the bulk density of water is substantially reduced compared with that of the AW. It has been shown that the solvation of the SCW around the OH anion is locally identical to that of the AW due to the strong ion-dipole interactions between OH- and water molecules. At the transition state, the QM/MM simulations have revealed that the excess electron is quite flexible, and the charge volume, as well as the fractional charges on atoms, vary seriously depending on the instantaneous solvent configurations. However, it has been found that the solvation energy in the SCW can be qualitatively related to the HOMO volume of the system by Born's equation.     

Waterlike structural and excess entropy anomalies in liquid beryllium fluoride

The relationship between structural order metrics and the excess entropy is studied using the transferable rigid ion model (TRIM) of beryllium fluoride melt, which is known to display waterlike thermodynamic anomalies. The order map for liquid BeF2, plotted between translational and tetrahedral order metrics, shows a structurally anomalous regime, similar to that seen in water and silica melt, corresponding to a band of state points for which average tetrahedral (q(tet)) and translational (tau) order are strongly correlated. The tetrahedral order parameter distributions further substantiate the analogous structural properties of BeF2, SiO2, and H2O. A region of excess entropy anomaly can be defined within which the pair correlation contribution to the excess entropy (S2) shows an anomalous rise with isothermal compression. Within this region of anomalous entropy behavior, q(tet) and S2 display a strong negative correlation, indicating the connection between the thermodynamic and the structural anomalies. The existence of this region of excess entropy anomaly must play an important role in determining the existence of diffusional and mobility anomalies, given the excess entropy scaling of transport properties observed in many liquids.     

Water inside a hydrophobic cavitand molecule

The structure and dynamics of water inside a water-soluble, bowl-shaped cavitand molecule with a hydrophobic interior are studied using molecular dynamics computer simulations. The simulations find that the number of inside water molecules is about 4.5, but it fluctuates from being completely empty to full on a time scale of tens of nanoseconds. The transition from empty to full is energetically favorable and entropically unfavorable. The water molecules inside have fewer hydrogen bonds than the bulk and in general weaker interactions; the lower energy results from the nearest-neighbor interactions with the cavitand atoms and the water molecules at the entrance of the cavitand, interactions that are lost upon dewetting. An analysis of translational and rotational motion suggests that the lower entropy of the inside water molecules is due to decreased translational entropy, which outweighs an increased orientational entropy. The cavitand molecule acts as a host binding hydrophobic guests, and dewetting can be induced by the presence of a hydrophobic guest molecule about 3 A above the entrance. At this position, the guest displaces the water molecules which stabilize the inside water molecules and the empty cavitand becomes more stable than the full.     

Structural properties of water: comparison of the SPC, SPCE, TIP4P, and TIP5P models of water

Molecular-dynamics simulations were carried out for the SPC, SPCE, TIP4P, and TIP5P models of water at 298 K. From these results we determine the following quantities: the absolute entropy using the two-particle approximation, the mean lifetime of the hydrogen bond, the mean number of hydrogen bonds per molecule, and the mean energy of the hydrogen bond. From the entropy calculations we find that nearly all contributions to the total entropy originates from the orientation effects. Moreover, we determine the contributions to the total entropy which originate from the first, second, and higher solvation shells. It is interesting that the limits between solvation shells are clearly visible. The first solvation shell (0.22 < r < 0.36 nm) contributes approximately 43 J mol K to the total entropy; the second solvation shell (0.36 < r < 0.60 nm) contributes approximately 12 J mol K, while contributions from the third and other solvation shells are very small, approximately 2 J mol K in summary. This indicates that water molecules are strongly ordered up to 0.55-0.6 nm around the central water molecule, and beyond this limit the ordering diminishes. The results of calculations (entropy and hydrogen bonds) are compared with the experimental data for the choosing of the best water model. We find that the SPC and TIP4P models reproduce the best experimental values, and we recommend these models for computer simulations of the aqueous solution of biomolecules.     

Water's hydrogen bonds in the hydrophobic effect: a simple model

We propose a simple analytical model to account for water's hydrogen bonds in the hydrophobic effect. It is based on computing a mean-field partition function for a water molecule in the first solvation shell around a solute molecule. The model treats the orientational restrictions from hydrogen bonding, and utilizes quantities that can be obtained from bulk water simulations. We illustrate the principles in a 2-dimensional Mercedes-Benz-like model. Our model gives good predictions for the heat capacity of hydrophobic solvation, reproduces the solvation energies and entropies at different temperatures with only one fitting parameter, and accounts for the solute size dependence of the hydrophobic effect. Our model supports the view that water's hydrogen bonding propensity determines the temperature dependence of the hydrophobic effect. It explains the puzzling experimental observation that dissolving a nonpolar solute in hot water has positive entropy.     

Nature of hydration shells of a polyoxy‐anion with a large cationic centre: The case of iodate ion in water

The structural nature of the solvation shells of an iodate ion, which is known to be a polyoxy‐anion with a large cationic centre, is investigated by means of Born–Oppenheimer molecular dynamics (BOMD) simulations using BLYP and the dispersion corrected BLYP‐D3 functionals. The iodate ion is found to have two distinct solvation regions around the positively charged iodine (iodine solvation shell or ISS) and the negatively charged oxygens (oxygen solvation shell or OSS). We have looked at the spatial, orientational, and hydrogen bond distributions of water in the two solvation regions. It is found that the water orientational profile in the ISS is typical of a cation hydration shell. The hydrogen bonded structure of water in the OSS is found to be very similar to that of the bulk water structure. Thus, the iodate ion essentially behaves like a positively charged iodine ion in water as if there is no anionic part. This explains why the cationic character of the iodate ion was prominently seen in earlier studies. The arrangement of water molecules in the two solvation shells and in the intervening regions around the iodate ion is further resolved by looking at structural cross‐correlations. The electronic properties of the solvation shells are also looked at by calculating the solute–solvent orbital overlap and dipole moments of the solute and solvation shell water. We have also performed BOMD simulations of iodate ion‐water clusters at experimentally relevant conditions. The simulation results are found to be in agreement with experimental results. © 2018 Wiley Periodicals, Inc.     

Computer simulation of the supercritical carbon dioxide fluid (II) internal energy and structure of carbon dioxide system containing one benzene molecule

Using potential models based on ab initio quantum chemical calculations, we study a supercritical CO₂ fluid containing one benzene molecule using Monte Carlo simulations. First, molecular average internal energy is calculated for the whole system and for the first solvation shell of the benzene molecule. This analysis shows that the CO₂ molecules in the first solvation shell have a large energetic stabilization owing to the shape of the solute. In addition to the stabilization, the solute-solvent interactions in the first solvation shell show large fluctuations for both the in-plane and out-of-plane parts. Secondly, an orientational distribution function is defined to investigate the CO₂ fluid structure. This function indicates that the CO₂---CO₂ intermolecular configuration has a large dependence on the temperature of the system for both the whole system, and for the first solvation shell of the solute. Moreover, the benzene molecule is confirmed to control the mutual arrangement between neighboring CO₂ molecules.     

Characterizing hydrophobicity at the nanoscale: a molecular dynamics simulation study

We use molecular dynamics (MD) simulations of water near nanoscopic surfaces to characterize hydrophobic solute-water interfaces. By using nanoscopic paraffin like plates as model solutes, MD simulations in isothermal-isobaric ensemble have been employed to identify characteristic features of such an interface. Enhanced water correlation, density fluctuations, and position dependent compressibility apart from surface specific hydrogen bond distribution and molecular orientations have been identified as characteristic features of such interfaces. Tetrahedral order parameter that quantifies the degree of tetrahedrality in the water structure and an orientational order parameter, which quantifies the orientational preferences of the second solvation shell water around a central water molecule, have also been calculated as a function of distance from the plate surface. In the vicinity of the surface these two order parameters too show considerable sensitivity to the surface hydrophobicity. The potential of mean force (PMF) between water and the surface as a function of the distance from the surface has also been analyzed in terms of direct interaction and induced contribution, which shows unusual effect of plate hydrophobicity on the solvent induced PMF. In order to investigate hydrophobic nature of these plates, we have also investigated interplate dewetting when two such plates are immersed in water.     

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.     

Entropy, diffusivity, and structural order in liquids with waterlike anomalies

The excess entropy, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is studied as a function of density and temperature for liquid silica and a two-scale ramp potential, both of which are known to possess waterlike liquid state anomalies. The excess entropy for both systems is evaluated using a fairly accurate pair correlation approximation. The connection between the excess entropy and the density and diffusional anomalies is demonstrated. Using the pair correlation approximation to the excess entropy, it can be shown that if the energetically favorable local geometries in the low and high density limits have different symmetries, then a structurally anomalous regime can be defined in terms of orientational and translational order parameters, as in the case of silica and the two-scale ramp system but not for the one-scale ramp liquid. Within the category of liquids with waterlike anomalies, we show that the relationship between the macroscopic entropy and internal energy is sufficient to distinguish between those with local anisotropy and consequent open packings at low densities and those with isotropic interactions but multiple length scales. Since it is straightforward to evaluate the pair correlation entropy and internal energy from simulations or experimental data, such plots should provide a convenient means to diagnose the existence as well as type of anomalous behavior in a range of liquids, including ionic and intermetallic melts and complex fluids with ultrasoft repulsions.     

Temperature dependence of dimerization and dewetting of large-scale hydrophobes: a molecular dynamics study

We studied by molecular dynamics simulations the temperature dependence of hydrophobic association and drying transition of large-scale solutes. Similar to the behavior of small solutes, we found the association process to be characterized by a large negative heat capacity change. The origin of this large change in heat capacity is the high fragility of hydrogen bonds between water molecules at the interface with hydrophobic solutes; an increase in temperature breaks more hydrogen bonds at the interface than in the bulk. With increasing temperature, both entropy and enthalpy changes for association strongly decrease, while the change in free energy weakly varies, exhibiting a small minimum at high temperatures. At around T=Ts=360 K, the change in entropy is zero, a behavior similar to the solvation of small nonpolar solutes. Unexpectedly, we find that at Ts, there is still a substantial orientational ordering of the interfacial water molecules relative to the bulk. Nevertheless, at this point, the change in entropy vanishes due to a compensating contribution of translational entropy. Thus, at Ts, there is rotational order and translational disorder of the interfacial water relative to bulk water. In addition, we studied the temperature dependence of the drying-wetting transition. By calculating the contact angle of water on the hydrophobic surface at different temperatures, we compared the critical distance observed in the simulations with the critical distance predicted by macroscopic theory. Although the deviations of the predicted from the observed values are very small (8-23%), there seems to be an increase in the deviations with an increase in temperature. We suggest that these deviations emerge due to increased fluctuations, characterizing finite systems, as the temperature increases.     

Enthalpies of aqueous solution of noble gases at 25°C

The standard enthalpies of solution of rare gases (helium, neon, argon, krypton, and xenon) in water at 25°C have been measured by a high precision steady-state calorimetric method. The aqueous solvation process is energetically favorable at 25°C for the gases studied. Values of the standard free energy, enthalpy, and entropy changes are found to be well correlated with cavity surface areas and the number of water molecules in the first solvation shell. Also, the values of the standard enthalpy and entropy of solution for the rare gases are found to have the same dependence on the number of solvation shell water molecules as inorganic and hydrocarbon gases. These results imply that the dominant source of enthalpy and entropy change resides in the first solvation shell.     

Quantitative characterization of orientational order in liquid carbon tetrachloride

A simple geometrical construct is proposed for a clear-cut classification of the relative orientation between two tetrahedral molecules in terms of six orientational classes. When applied to sort out configurations from condensed phase simulations, it leads to a quantitative characterization of orientational order: A definite percentage for each class is obtained as a function of the distance between molecular centers. The basic picture that emerges, for liquid carbon tetrachloride, is that the dominant configuration for each distance is such that the number of chlorines in between both carbons diminishes with increasing separation, with a configuration here termed edge-to-face being the dominant one at contact. Regarding the range of orientational order, remnants are still noticeable at approximately 20 A, i.e., up to the fourth solvation shell. Beyond this distance the distributions are hardly distinguishable from the analytical predictions for random orientation. The analysis of the small fluctuations at such long distances shows that there are no significant differences between the ranges of positional and orientational order.     

Protons in non-ionic aqueous reverse micelles

Using molecular dynamics techniques, we investigate the solvation of an excess proton within an aqueous reverse micelle in vacuo, with the neutral surfactant diethylene glycol monodecyl ether [CH3(CH2)11(OC2H4)2OH]. The simulation experiments were performed using a multistate empirical valence bond Hamiltonian model. Our results show that the stable solvation environments for the excess proton are located in the water-surfactant interface and that its first solvation shell is composed exclusively by water molecules. The relative prevalence of Eigen- versus Zundel-like solvation structures is investigated; compared to bulk results, Zundel-like structures in micelles become somewhat more stable. Characteristic times for the proton translocation jumps have been computed using population relaxation time correlation functions. The micellar rate for proton transfer is approximately 40x smaller than that found in bulk water at ambient conditions. Differences in the computed rates are examined in terms of the hydrogen-bond connectivity involving the first solvation shell of the excess charge with the rest of the micellar environment. Simulation results would indicate that proton transfers are correlated with rare episodes during which the HB connectivity between the first and second solvation shells suffers profound modifications.