Orientation of Water Molecules around Small Polar and Nonpolar

Neutron diffraction data on the aqueous system dimethyl sulfoxide (DMSO) in water at a concentration of 2 water molecules to 1 DMSO molecule are prese...
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J. Phys. Chem. 1996, 100, 1357-1367

1357

Orientation of Water Molecules around Small Polar and Nonpolar Groups in Solution: A Neutron Diffraction and Computer Simulation Study A. K. Soper* ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, U.K.

Alenka Luzar Department of Chemistry, UniVersity of California at Berkeley, Berkeley, California 94720-1460 ReceiVed: June 27, 1995; In Final Form: July 31, 1995X

Neutron diffraction data on the aqueous system dimethyl sulfoxide (DMSO) in water at a concentration of 2 water molecules to 1 DMSO molecule are presented. The hydrogen/deuterium substitution technique is used to extract the HH (water-H to water-H) pair correlation function, gHH(r), the MM (methyl-H to methyl-H) correlation function, gMM(r), and the MH (methyl-H to water-H) correlation function, gMH(r). In addition, three composite pair correlation functions are extracted from the data: XH, which represents the correlation of water hydrogens with nonsubstituted atoms (dominated by the hydrogen bond correlation); XM, which represents the correlation of methyl hydrogens to nonsubstituted atoms (and, therefore, gives information on nonpolar group hydration); and XX, which represents a weighted sum of nonsubstituted atom correlations. The results, together with assumed molecular geometries and expected constraints on atomic overlap, are used to perform a computer simulation of the structure of the solution. This simulated structure is compared, via the site-site pair correlation functions, with the predictions of a recent molecular dynamics simulation of the same system. The results show the pronounced contrast in structure of the water of hydration around DMSO, with the oxygen atom strongly hydrogen-bonded, but the methyl groups surrounded by a loose, hydrogen-bonded cage of water molecules. There is no evidence for the hydrophobic association of DMSO molecules that has been suggested to occur in this system. The data indicate that while the degree of hydrogen bond bending is greater in the solution compared to pure water, the water structure, as measured by the heights of peaks in the pair correlation functions, is more pronounced than in the pure liquid. This enhanced water structure is associated with the strong hydrogen bonding of water to the DMSO oxygen atom, rather than with the hydrophobic hydration of water molecules with the methyl groups.

1. Introduction One approach to understanding the competing effects of hydrophobic and hydrophilic groups in aqueous solution is to study at a microscopic level the effect of these groups on water structure in solution, comparing it to the structure of bulk water and at the same time examining the nature of water coordination and orientation around those groups. In a recent neutron diffraction experiment1 and molecular dynamics simulation,2 the small-scale structure in a hydrogen-bonded system which has competing hydrophobic/hydrophilic interactions has been explored. The system chosen for those studies was the waterdimethyl sulfoxide (DMSO) system because DMSO is miscible with water in all proportions and forms pronounced hydrogen bonds with water at the oxygen site on the DMSO molecule. It also has two methyl groups which probably have no strong interaction, either with themselves or with water, other than the usual atomic overlap restrictions. At the same time, DMSO can only act as a proton acceptor, but not as proton donor, in the process of hydrogen bond formation. This makes interpretation of the neutron diffraction data less ambiguous than in the analogous case of, for example, alcohols in water.3 In the present paper, the earlier neutron diffraction measurements1 have been extended to a measurement of all the possible correlations that can be extracted from this system using hydrogen/deuterium substitution, and the results have been used as the starting point * Also affiliated with the Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K. X Abstract published in AdVance ACS Abstracts, December 15, 1995.

0022-3654/96/20100-1357$12.00/0

for building a comprehensive computer model of the solution, in a manner which has not been achieved previously from diffraction data on solutions. Interest in the DMSO-water system and its role in biochemical processes has spurred the measurements of many of its thermodynamic properties,4-10 measurements of its excitation spectra via infrared absorption,11,12 Raman scattering,11 and NMR.13-15 Inelastic neutron scattering and X-ray diffraction on this system have also been reported.16 The interpretation of those data in terms of water structure tends to be qualitative: the results for the dilute aqueous solutions of DMSO have been interpreted10,16 as indicating that the presence of DMSO enhances the water hydrogen bond network, due to the hydrophobic hydration of the methyl groups. The data from the concentrated aqueous solution10,16 suggested that DMSO molecules form clusters which protect water molecules from exposure to the nonpolar methyl groups of DMSO, apparently indicating a strong hydrophobic association between DMSO molecules in water. However, both of these conclusions were obtained only after a great deal of speculative interpretation of the available data, and neither has, in fact, been tested against a microscopic structure experiment. In a recent computer simulation study of DMSO-water mixtures2 no preferential association of methyl groups on DMSO was detected. Neutron diffraction with isotope substitution is well suited in principle to obtain structural data on these solutions in a direct way, by determining specific atom-atom distribution functions.17 In the case of aqueous solutions of DMSO, however, © 1996 American Chemical Society

1358 J. Phys. Chem., Vol. 100, No. 4, 1996 it is not possible to obtain a complete separation by isotopic contrast of the 21 partial pair correlation functions which are needed to define the structure, because the scattering lengths of 2 of the components, oxygen and carbon, do not change appreciably with isotope, while sulfur has only a weak isotopic contrast and the higher cost of this substitution inhibits its use. On the other hand, hydrogen and its isotope deuterium have a dramatic contrast, and deuterated DMSO and deuterated water are readily available. As will be seen below, the various hydrogen isotope combinations that are possible allow a total of six composite partial correlation functions to be extracted. In the previous neutron experiment,1 the structure of water in concentrated aqueous solutions of DMSO was investigated, using neutron diffraction and H/D isotope substitution on the water hydrogens alone to separate out the water-H to water-H correlation function. Two concentrations were investigated, namely, one at roughly 1DMSO:2H2O, corresponding to minima or maxima in several thermodynamic properties,4,5,7,8 and the other at 1DMSO:4H2O, in order to investigate the trend with dilution. These concentrations also straddle the composition at which DMSO forms a stable hydrate in the crystalline state, 1DMSO:3H2O.18 At these high concentrations, all the water molecules are in close proximity to a DMSO molecule, and any significant effect on the water structure should have been readily observable. In fact, the neutron data indicated that the local water structure is not strongly affected by the presence of DMSO, in the sense that the peak locations in gHH(r) of the first molecular coordination shell were still preserved at both concentrations studied, compared to pure water. As expected, on simple geometrical arguments,19-21 a reduction in the H-H coordination number with increasing concentration of DMSO was observed, and the percentage of water molecules that hyrogen bond to themselves was substantially reduced compared to pure water. This can be understood by assuming that an increasing fraction of water molecules are bonded to DMSO as the concentration rises, while at the same time the likelihood that water molecules can interact with each other becomes smaller. The trend in coordination number with concentration in fact agreed with that predicted by a simple hydrogen-bonding model of DMSO-water solutions.19-21 In parallel with the neutron study, two molecular dynamics (MD) computer simulations of pure liquid DMSO and concentrated DMSO-water mixtures have been performed.2,22 These studies are complementary to a recently reported molecular dynamics simulation of DMSO-water mixtures at low concentrations.23 The simulation of pure DMSO,22 which was also compared with neutron diffraction data on the same system, was performed to establish the interaction potential for pairs of DMSO molecules in the liquid state and, hence, to enable a model to be set up for the DMSO-water potential. Various interaction site potentials for DMSO, which we2,22 and others24 have developed, were tested against the neutron diffraction data of the pure liquid. In fact, it was found that the neutron data from the pure liquid are not particularly sensitive to the detailed form of the potential, showing a broad agreement with the computer simulation for at least two of the potentials that were tried. However, only one of these potentials (we will call it the P2 potential to be consistent with the previous work) reproduced both the thermodynamic properties of liquid DMSO and the pair distribution functions, as deduced by neutron diffraction. The results from that potential, when used in the simulation of DMSO-water solutions,2 have already been compared with the earlier neutron data.1 With the increased

Soper and Luzar number of pair correlation functions that are available from the present experiment, this comparison can be made more definitive. Analysis of the simulated water-water radial distribution functions (OH and OO functions) not accessible to the previous experiment1 revealed a significant enhancement of peak heights for the first-neighbor coordination shell, compared to the equivalent radial distribution functions in pure water.2 These increased peak heights were accompanied by a reduction, by about a factor of 2, in the number of hydrogen bonds per water molecule, compared to bulk water, with water-water hydrogen bonds being replaced by water-DMSO hydrogen bonds. Thus, it was concluded that the hydrogen bond network of water had been disrupted in the presence of DMSO, and this is no doubt a contributory factor to the significant reduction in freezing point of the solution with increased concentration. However, this factor of 2 is smaller than might be expected. The average density of water oxygens in the concentrated mixture is about a factor of 3 smaller than the same density in pure water (0.011 oxygen/Å3 at the 2:1 concentration compared to 0.033 oxygen/ Å3 in pure water). If it is assumed on the basis of a random mixture that the likelihood of two molecules interacting is proportional to their densities, then this reduction of the hydrogen bond coordination number would be around 3. Hence, it can be argued that the hydrogen bond interaction between water molecules has in some sense been enhanced in the presence of concentrated DMSO compared to what it might have been if the molecules simply formed a random mixture. Note that the same behavior of the water radial distribution functions as a function of the solute concentration has been observed from MD simulation studies of binary aqueous mixtures of methanol,25 acetone,25 ammonia,25 and acetonitrile.26 The previous neutron experiment on DMSO in solution1 verified the apparent hydrogen bond enhancement predicted by the computer simulation. However, several questions remain unanswered: it is not clear, for example, whether this enhanced hydrogen bonding compared to bulk water is a result of the formation of a hydrogen-bonded cage around the methyl groups in solution or is due to the presence of a strong hydrogenbonding site on the DMSO oxygen. Furthermore, a more complete description of the hydration structure of DMSO requires knowledge of the orientation of water molecules in the hydration shell around DMSO. The extent of hydrophobic hydration can be visualized most accurately by estimating the extent of orientational pair correlations between the methyl groups on DMSO and the surrounding water molecules, while the extent of hydrophobic association is determined via the methyl-methyl orientational pair correlations. The present experiment is devised to investigate the nature of DMSO hydration in more detail. In particular, by combining hydrogen/deuterium isotope substitution experiments on both the water and the methyl groups of DMSO, it is possible to obtain, in addition to the water hydrogen to water hydrogen correlation function of water (HH) already measured,1 the methyl hydrogen to methyl hydrogen correlation function for DMSO (MM), as well as the cross-correlation function between methyl hydrogen atoms and water hydrogen atoms (MH). Three other composite correlation functions can also be obtained by this procedure, namely, XH, XM, and XX, where X represents a neutron weighted sum of correlations with the unlabeled atoms, sulfur, oxygen (both DMSO and water oxygens), and carbon. The MH function provides useful information about the way water molecules coordinate the hydrophobic methyl groups, while the MM correlation function indicates the extent to which the hydrophobic methyl groups on different molecules cluster together in solution, as has been proposed elsewhere.10,16 The

Orientation of H2O around Polar and Nonpolar Groups XH correlation is dominated by the hydrogen bonding of water molecules to DMSO and to themselves, while the XM correlation represents the correlations of methyl hydrogens to nonsubstituted atoms and, therefore, gives information on nonpolar group hydration. On their own, these six correlation functions do not lead directly to a picture of the hydration around DMSO, since they are averaged over molecular orientations. To proceed further, it is necessary to undertake some form of molecular modeling of the diffraction data, and the use of the spherical harmonic expansion of the orientational correlation function, as was done for pure water,27 is one possible route to developing a clearer picture of the local molecular coordination. In fact, a preliminary spherical harmonic study of pure DMSO has been reported,28 and the method has been successfully applied to methanol3 and tetramethylammonium ion (TMA) in water.29 However, there are difficulties with applying the spherical harmonic method3,27-29 to DMSO and its solutions. These are associated with the fact that DMSO has a much more complicated molecular geometry compared to a more spherically symmetric molecule such as the TMA ion, for which the spherical harmonic method has proved to be successful. This more complex geometry is reflected in a large number of spherical harmonic expansion coefficients being required and a high likelihood that the reconstructed orientational correlation function will go unphysically negative for some molecular orientations, due to the premature truncation of the series. At the same time, for DMSO solutions, the analysis would require setting up three sets of coefficients, one set for each of the correlations DMSO-DMSO, water-water, and DMSO-water, making for an unwieldy set of coefficients to try to estimate. Nonetheless, the great power of spherical harmonic analysis is that, once the coefficients are established, they can be used to explore the correlation functions for any specified set of orientations without the need to run a new simulation. They store all the orientational information that is needed to define the structure. Because of these difficulties for DMSO and its solutions, an alternative tack has been adopted here. Based on the ideas of reverse Monte Carlo (RMC) simulation,30 a computer model of the diffraction data has been set up, using an empirical potential energy function. The idea behind this empirical potential Monte Carlo simulation, EPMC,31 is that, starting from an assumed set of site-site reference potentials and a corresponding equilibrated distribution of molecules, a relative perturbation to those potentials is determined which, when used in the computer simulation, reproduces the set of experimentally determined pair correlation functions, while at the same time preserving the known or expected molecular geometries without violating atomic overlap constraints. It does this by comparing the potential of mean force for each measured and simulated pair correlation function repeatedly during the simulation: when they are the same, the two sets of correlation functions must be similar. Note that because the perturbation to the reference potential can only be determined up to the maximum radius value for which the pair correlation function can be calculated (normally half the box size of the simulation), this perturbation will generally be short-ranged, even though the reference potential may itself have long-range contributions. The benefit of this kind of analysis, compared to standard RMC simulation, is that the structure is based on a potential energy function of the system: this potential energy can, through the reference potential on which the structure is based, include known long-range interactions such as charge-charge, chargedipole, and dipole-dipole interactions, etc., as well as realistic forms for the hard-core repulsion and intramolecular interactions.

J. Phys. Chem., Vol. 100, No. 4, 1996 1359 By constrast, RMC simulation assumes a hard-sphere repulsion between atomic sites on different molecules and very simple constraints on molecular geometry. It uses a simple χ2 statistic to determine the quality-to-fit to the data, and as has been argued elsewhere,31 this may lead to the simulated system becoming trapped in local minima. On the other hand, the EPMC simulation readily samples a broad range of phase space, as would occur in any Monte Carlo simulation of a fluid with an assumed intermolecular potential, and because the perturbation to the reference potential is continually being adjusted, it is unlikely to find local minima. For the purposes of discussing the local structure in a liquid, all the tests carried out so far indicate that the EPMC simulation method works well. In a test in which the site-site correlations, as derived from a previous Monte Carlo simulation using the SPC/E32 potential for pure water, were used as the input data for an EPMC simulation, the EPMC simulation sampled a similar range of structures to those in the original simulation with the SPC/E potential.31 Note that because the perturbation to the site-site potentials is only short ranged in the EPMC simulation, there has so far been no attempt to constrain the total potential energy of the simulation. Thus, the derived empirical potentials are only good for determining the local structure in the liquid and will not necessarily obtain the correct thermodynamics properties, which are also affected by longrange interactions. In the next section, the neutron diffraction experiment is described. Section 3 deals with the empirical potential Monte Carlo simulation for the water-DMSO system. Local orientational structures are analyzed in section 4, and the conclusions are given in section 5. 2. Neutron Diffraction Experiment Neutron diffraction measurements were made on a total of seven aqueous solutions of DMSO, at a concentration of 1DMSO:2.00H2O. This concentration is close to that used in our previous analysis (1DMSO:1.86H2O1). The compositions of these seven samples were (i) (CD3)2SO in D2O, (ii) (CD3)2SO in H2O, (iii) (CD3)2SO in H2O:D2O (1:1), (iv) (CH3)2SO in D2O, (v) (CH3)2SO:(CD3)2SO (1:1) in D2O:H2O (1:1), (vi) (CH3)2SO in H2O, and (vii) (CH3)2SO:(CD3)2SO (1:1) in D2O: H2O (1:1). By labeling the water protons H, the DMSO methyl protons M, and all the other atoms, including the water oxygens, OW, and the remaining atoms of the DMSO molecule (S,C,OD), X, the combination of data from solutions (i), (ii), and (iii) yields the HH correlation directly. Combining the data from (i), (iv), and (v) yields the MM correlation directly, while the combination (i), (vi), and (vii) produces a sum of HH, MM, and MH correlations, from which the MH correlation can be isolated. Further combinations of the same seven sets of diffraction data yield the composite XH, XM, and XX correlation functions referred to above. The relative weights on the correlation functions in these composite correlation functions are as follows:

gXH ) 0.085gSH + 0.173gODH + 0.396gCH + 0.346gOWH (1) gXM ) 0.085gSM + 0.173gODM + 0.396gCM + 0.346gOWM (2) and

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gXX ) 0.007gSS + 0.029gSOD + 0.067gSC + 0.059gSOW + 0.030gODOD + 0.137gODC + 0.120gODOW + 0.157gCC + 0.274gCOW + 0.120gOWOW (3) Note that the XH function is different from the XH function defined in ref 1 in that the MH contribution is subtracted and appears as a separate correlation function. Similarly, the XX correlation is different from that in ref 1 because the MM and MX correlations to not contribute but are isolated separately. The diffraction measurements were carried out on the SANDALS time-of-flight neutron diffractometer for liquid and amorphous samples at ISIS. At the time of the experiment, the instrument covered a range in scattering angles from 3 to 21°. The samples were contained in flat-plate cells made from an alloy of zirconium and titanium which scatters neutrons almost incoherently and so does not make any tangible contribution to the structural features in the diffraction pattern. The data were corrected for attenuation, multiple scattering, and container scattering and normalized to the scattering from a standard vanadium plate, in the usual way.33 Further analysis to remove the single atom scattering from the diffraction patterns followed the same method as described previously.1,22 Of course, the interference differential cross sections obtained in this way included contributions from intramolecular correlations, and since these are not useful for understanding the intermolecular structure, they were estimated on the basis of the molecular geometry of DMSO and water molecules in the pure liquids,22,34 with some refinement of the intramolecular parameters to obtain the most satisfactory subtraction. These refined parameters were not significantly different from those obtained in the pure liquids. Finally, once all the corrections were completed, the diffraction data were separated into the six partial structure factors discussed above, i.e., HH, MM, MH, XH, XM, and XX, and transformed to real space, using the minimum noise convention27,35 to achieve the smoothest possible set of intermolecular pair correlation functions consistent with the diffraction data. This set of six pair correlation functions is shown in Figures 1 and 2, and for the rest of this paper, they will be referred to as the “data”, even though, strictly speaking, they are quantities derived from the true diffraction data. Of these correlation functions, the HH correlation is very similar in form to what was measured previously:1 the positions of the first two peaks are very similar to the positions of the corresponding peaks in pure water, indicating as before that the local hydrogen-bonding structure is retained in the concentrated DMSO solution. The amplitude of the peaks is, however, significantly greater compared to the amplitude of the peaks in pure water, a point which had already been alluded to when discussing the results of the MD simulation2 in the Introduction. Also, it will be noted that in the region 3-5 Å, the MH correlation function is above unity, while the MM correlation is below unity for the same region. There will be further discussion of this point later, but the contrast between these two correlation functions already suggests that there is only a weak degree of methyl-methyl association present in this mixture. For the correlations in Figure 2, it is not easy to make a direct interpretation of the structure, because of the lack of spherical symmetry around the DMSO molecule and the many contributions to these composite correlation functions. In this instance, it is more instructive to proceed directly to a simulation of these data and then use the simulation to evaluate the local structure.

Figure 1. Measured site-site correlation functions (circles) for the HH, MH, and HH correlations. The lines show the empirical potential Monte Carlo (EPMC) fit to these data. The MH and MM functions have been shifted up by 1.5 and 2.5, respectively.

Figure 2. Same as Figure 1 but for the XX, XH, and XM correlations. The XH and XM correlation functions have been shifted up by 1.25 and 2.5, respectively.

3. Empirical Potential Monte Carlo (EPMC) Simulation of DMSO-Water Solutions To proceed further with the analysis of the data of Figures 1 and 2, a computer model of DMSO-water was set up, in which 48 DMSO and 96 water molecules were contained in a cubic box of dimension 20.29 Å. Although a relatively small system by modern standards, there was little to be achieved by simulating a larger system since the maximum radius value for which the pair correlation functions could be reliably derived from the diffraction data was of the order of 10 Å. The

Orientation of H2O around Polar and Nonpolar Groups molecules themselves were not rigid but were held together by assumed harmonic potentials which were large enough to maintain the underlying correct molecular geometry during the course of the simulation, while allowing some individual atomic freedom. This was an attempt to let the simulation mimic the experimental situation as realistically as possible. The reference potential used in this case was chosen to be identical, including individual site charges, to that used in the previous simulation of DMSO-water,2 with the P2 potential22 used to control the atomic overlap between all sulfur, carbon, and oxygen atoms on DMSO molecules and the SPC potential36 used to control overlap between all oxygen atoms on water molecules (see Table I of ref 2). The DMSO-water LennardJones parameters were derived using the standard LorentzBerthelot mixing rules.2 There were no restrictions on how closely methyl and water hydrogen atoms could approach other atoms or one another, although, of course, this would be controlled by the oxygen and carbon hard-core potentials combined with the harmonic forces holding the molecules together. Periodic boundary conditions and the minimum image convention were employed in the usual way to take into account the finite size of the box. However, because perturbations to the reference potential cannot be estimated beyond half the box size, no correction was made to account for longer range interactions beyond this distance. The primary aim of the simulation was to estimate the local structures around the molecules, and the absence of long-range corrections was not expected to have any significant effect on calculated short-range correlations. It will be noted, of course, that the reference potential contains 15 separate contributions from all the possible pairs of sites, even though the diffraction experiment cannot separate out all the corresponding site-site correlation functions. In the simulation, the allowed moves were random displacements of individual atoms and random displacements and rotations of whole molecules. The methyl groups were not rotated on their own because the evidence from the pure liquid was that the methyl groups on DMSO do not rotate freely.22 At the outset, the reference potential was used on its own to bring the system of molecules into equilibrium. This produced a set of site-site g(r)’s which were closely similar to those already published,2 confirming that the simulation program used here gave similar results, within the approximation of ignoring longrange interactions, to those achieved in the independent MD simulation.2 Comparison of the results of this initial simulation (not shown here) with the data of Figures 1 and 2 showed general qualitative agreement with the experiment. However, there were quantitative discrepancies, particularly in the XX function, which were outside the range of possible experimental errors. In particular, the first peak in the XH function of this initial simulation was too high compared to the experiment, while the first peak in the XX function was too low compared to experiment, and the larger radius peaks in the XX function were reproduced only approximately. The first peak in the XX function coincides quite closely with some intramolecular distances in the DMSO molecule (C-C and O-C), but as these have already been subtracted in the data of Figure 2, it is hard to see how they can contribute to this discrepancy. Once equilibrium was reached in the initial simulation, the perturbation term was switched on and was updated regularly throughout the simulation, in order to drive the simulated pair correlation functions toward the diffraction results. For the HH, MH, and MM correlations, these perturbations were derived from the potential of mean force as follows (see ref 31 for full details):

J. Phys. Chem., Vol. 100, No. 4, 1996 1361 N O D O URβ (r) ) URβ (r) + (ψRβ (r) - ψRβ(r)) ) URβ (r) + D (r)}] (4) kT[ln{gRβ(r)/gRβ O N where URβ (r) and URβ (r) are the potential energy functions between sites R and β before and after the perturbation, respectively, and the potential of mean force for the data is D D (r) ) -kT ln(gRβ (r)),with a defined, for example, as ψRβ corresponding definition for the simulated pair correlation function, gRβ(r). For the composite functions, however, it is not possible to derive separate site-site perturbations for each of the contributions to eqs (1), (2), and (3). Instead, composite perturbations were derived, UXH, UXM, and UXX, respectively, by using eq (4) but with the individual site-site correlations replaced with the appropriate composite correlation functions, simulation, and data. Hence, in these composite potentials, all the unlabeled atoms X were treated as a single, average, atom when estimating the likelihood of a Monte Carlo move being accepted or rejected. After an equilibration period of about 1 million moves, the simulation was run for several more million moves while a number of quantities (described below) were accumulated. The lines in Figures 1 and 2 show that this process obtained an accurate representation of the measured pair correlation functions. In particular, it was found that the longer the simulation was run, the statistical uncertainty of the accumulated simulated correlation functions improved steadily, implying that the simulation was sampling a wide range of structures consistent with the data and proceeding on a true random walk through phase space. To guage the usefulness of this procedure, it should be emphasized that although three of the original six pair correlation functions extracted from the data are composite correlation functions, it is possible to calculate individual site-site correlation functions from the EPMC simulation, in the same way as is done in other computer simulations of fluids. A subset of some of the individual site-site correlations that were extracted from this simulation is shown in Figures 3-6, where they are compared to the corresponding correlation functions from the previous MD simulation.2 The oxyen atom on DMSO is here labeled OD to distinguish it from the water oxygen, OW. Figure 3 shows the EPMC water-water correlations, HH, OWH, and OWOW in the mixture, together with those obtained from the MD simulation2 and the corresponding functions for pure water.27 It is seen that the qualitative trend in peak height in the mixture compared to pure water is similar in both the EMPC and MD simulated functions. Table 1 lists the coordination numbers of the first peaks in the radial distribution functions estimated from EMPC simulation of the present data and from the previous MD simulation.2 In particular, it is to be noted that in both EPMC and MD simulations, the OW-OW correlation shows a significant second hump near r ) 4.5 Å, a position which has traditionally been assumed to indicate the tetrahedral nature of water hydrogen bonding. This is evidence that the tetrahedral nature of water-water cooordination is still present even at this high concentration of DMSO. Figures 4 and 5 show functions relating to DMSO-water correlations, in particular the OD-OW and OD-H correlations in Figure 4, and the C-OW and C-H correlations in Figure 5. Figure 4 shows clearly that OD is hydrogen bonded by water molecules. The integration of the OD-H function out to r ) 2.4 Å gives a coordination number of 0.9 (see Table 1), similar to the number of hydrogen bonds on the hydrogen-accepting site on a water molecule, i.e., about 1 hydrogen bond per molecule. This is notably smaller than the ∼1.5 H bonds per DMSO molecule found in the MD simulation and can be seen

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Figure 3. Water-water correlations in the 1DMSO:2H2O mixture, as represented by the OWOW, OWH, and HH correlation functions. The lines show the results from the EPMC simulation of the diffraction data, while the dashed lines and circles show the results from the previous MD simulation.2 Note that the MD pair correlation functions were obtained on a somewhat bigger system where long-range electrostatic interactions were treated using the Ewald summation technique. The crosses show the corresponding results for pure water. The OWH and HH correlation functions are shifted up by 6 and 9.5, respectively.

Soper and Luzar

Figure 5. DMSO-water correlations as represented by the COW and CH correlation functions. Notation is the same as in Figure 3. The CH correlation functions are shifted up by 1.2.

Figure 6. DMSO-DMSO correlations as represented by the SS, ODOD, ODC, and CC correlation functions. The notation is the same as in Figure 3. Each curve is shifted successively upward by 1.5.

Figure 4. DMSO-water correlations as represented by the ODOW and ODH correlation functions. Notation is the same as in Figure 3. The ODH correlation functions are shifted up by 5.

as the big change in the low r peak heights between MD simulation and EPMC simulation in the OD-H functions of Figure 4, even though the larger radius structure looks very similar. Note also the nearest-neighbor OD-OW distance is shorter than the nearest-neighbor OW-OW distance by about 0.2 Å, a trend that is reproduced in the MD computer simulation.2

The C-H correlation, Figure 5, is qualitatively similar between MD and EPMC simulations, and the C-OW correlation is only slightly broader in the EPMC simulation compared to the MD simulation. This suggests that the P2 potential used in the MD simulation produces a more or less accurate view of the structure of the water shell around the methyl groups and gets the relative orientation of molecules in that shell correct. Both of the radial distribution functions also look qualitatively similar to corresponding functions estimated by integral equation theory for nonspherical apolar molecules in water.37 It is interesting to note, also, that the ratio of the two coordination numbers NCOW/NCC (where NRβ is the number of β atoms in the

Orientation of H2O around Polar and Nonpolar Groups

J. Phys. Chem., Vol. 100, No. 4, 1996 1363

TABLE 1: Coordination Numbers for Selected Site-Site Distributions, as Estimated from the Present Empirical Potential Monte Carlo Simulation of the Diffraction Data (This Work) and from the Previous MD Simulation2 a EPMC simulationb

MD simulationc d

gRβ(r)

integration range, Å

NRβ

integration range, Å

NRβ

H-H OW-H OD-H OW-OW OD-OW OD-OD C-C C-OW

0.0-3.1 0.0-2.4 0.0-2.4 0.0-3.3 0.0-3.2 0.0-3.1 0.0-4.3 0.0-4.2

2.7 1.1 0.9 2.1 0.9 0.4 2.3 3.2

0.0-3.2 0.0-2.4 0.0-2.4 0.0-3.6 0.0-3.3 0.0-4.7 0.0-5.0 0.0-4.7

3.3 1.1 1.5 2.7 1.6 1.5 4.5 4.9

a The coordination number for the g (r) site-site correlation Rβ function is the number of atoms of β atoms about an R atom in the solution, NRβ. The integration ranges shown correspond to the first minima in the corresponding pair correlation functions. b Neutron diffraction data. c P2 plus SPC potentials. d Coordination number.

first coordination shell around an R atom at the origin) is similar in both simulations; i.e., it is 1.1 in the MD simulation and 1.4 in the EMPC simulation (see Table 1). Since this ratio is not very different from the corresponding ratio of the atomic fractions in the solution (0.92 in MD and 1.0 in EMPC), it is evident that random distribution takes preference over hydrophobic association between DMSO molecules. The results of the MD and EMPC simulations show a general agreement on this point: it is difficult to find evidence for a significant degree of hydrophobic association between methyl groups on neighboring DMSO molecules on the basis of the present or previous2 analysis. If anything, because the ratio of coordination numbers in either simulation is greater than the ratio of atomic fractions, it suggests that the methyl groups actually prefer hydrating water molecules rather than other methyl groups to be nearby. Finally, Figure 6 shows some of the DMSO-DMSO correlations, specifically the S-S, OD-OD, OD-C, and C-C correlations. Here, the separation of the composite pair correlation functions into specific site-site distributions is more ambiguous because of the relatively large number of correlations included in a single function, eq 3, and the relatively small weighting of many of them. As a result, the overlap between EPMC and MD simulations is perhaps the poorest, particularly in the S-S and OD-OD terms. The OD-OD pair correlation is particularly intriguing since it appears to imply the DMSO oxygen atoms approach one another much more closely than would be allowed on the basis of the P2 potential used in the MD simulation,2 raising the possibility of DMSO-DMSO association through the oxygen atoms. This is reminiscent of what occurs in the crystalline state of pure DMSO,38 where the S-O bonds on neighboring molecules are aligned antiparallel to one another. The disparity between the EPMC simulation of the present diffraction data and the earlier MD simulation2 on this issue arises from the fact that the P2 plus SPC potential produces too small an intensity in the first peak of the XX function and too much intensity in the XH first peak compared to the diffraction data. Any attempt in the simulation to increase the XX peak by reinforcing the hydrogen bonding around DMSO (via the OD-OW correlation) would necessarily also increase the XH peak. Therefore, the EPMC simulation has to obtain the extra intensity in the XX function by enhancing a correlation which does not reinforce the XH term. It does this by enhancing the OD-OD correlation at short distances, which can be achieved without an unphysical molecular overlap and without enhancing the small radius XH function. This no doubt is the reason why the OW-H coordination number is about the same for both EPMC and MD simulations, Table 1, while the OD-H

Figure 7. Geometry used for calculating the bond angle distribution. A central atom, OW, in this example is joined to a neighboring water oxygen by the vector r. Angle θ corresponds to the angle the O-H vector makes with r. Thus, θ ) 0° corresponds to the O-H vector pointing directly away from the oxygen at the origin. Equivalent geometries apply to all the other angular distributions discussed in the text.

coordination number in the EPMC simulation is significantly less than the corresponding number in the MD simulation: ODto-OW hydrogen bonds in the MD simulation have been partly replaced by OD-to-OD associations in the EPMC simulation. Unfortunately, the smallness of the contribution that the ODOD pair correlation makes to the XX correlation renders this particular site-site correlation susceptible to artifacts in the EMPC simulation process, so confirmation of the effect will require further study: further neutron experiments with sulfur isotope contrast to highlight interactions around the S-O bond in the DMSO molecule, and X-ray diffraction experiments are probably needed. The evidence for DMSO-DMSO association via the DMSO oxygens comes in this case not from direct observation of the OD-OD pair correlation function but from the requirement for the EPMC simulation to fit all six experimental composite pair correlation functions simultaneously. While it may be difficult to understand this association in terms of the assumed form of the interaction potential (such as the P2 potential), the present data appear to imply such an association. Although EPMC simulation of the pure liquid data has not so far been attempted, a recent analysis of the pure liquid diffraction data,28 using spherical harmonic reconstruction, came to a similar conclusion about pure liquid DMSO. Therefore, the observed association is either real or must be an artifact of both experiments. 4. Analysis of Local Orientational Structures In discussing the local structure of the liquid, use can be made of the atom-atom distribution functions and the coordination numbers obtained by integration, as has been done in the previous section. However, these functions alone do not provide sufficient detail to interpret the molecular structure of the liquid completely. One way of establishing the nature of the correlations between water molecules and DMSO molecules in the solution is to estimate the so-called bond angle distributions between neighboring molecules. These quantities are defined here as the distribution of angles between a specific vector on one molecule and the line joining the two molecules, as shown in Figure 7. They do not provide us with as detailed information as the orientational correlation functions determined from spherical harmonic expansion analysis.39 However, they are easily calculated by a computer simulation and still give a good indication of the degree of alignment between neighboring molecules. A number of these bond angle distributions have been calculated from the empirical potential Monte Carlo simulation of the DMSO-water system described above: (a) OD to OW-H (Figure 8), (b) OW to OW-H (Figure 8), (c) C to OW-H (Figure 9), (d) S to OW-H (Figure 10), (e) S to OW-H (Figure 10), (f) OD to µW (Figure 11), (g) OW to µW (Figure 11), (h) C to µW (Figure 12), (i) S to µD (Figure 13), and (j) S

1364 J. Phys. Chem., Vol. 100, No. 4, 1996

Soper and Luzar

Figure 8. Angular distributions (a) OD to OW-H (2.0-3.2 Å, line) and (b) OW-H to OW-H (2.0-3.2 Å, dashed) compared to OW to OW-H in pure water (2.0-3.5 Å, circles). The curves have been normalized to have the same area when integrated over cos θ.

Figure 11. Angular distributions (f) OD to µW (2.0-3.2 Å, line) and (g) OW to µW (2.0-3.2 Å, dashed), compared to the OW to µW angular distribution for pure water (2.0-3.5 Å, circles). Here µW represents the water molecule’s dipole moment.

Figure 9. Angular distribution (c) C to OW-H (2.0-4.0 Å).

Figure 12. Angular distribution (h) C to µW (2.0-4.0 Å).

Figure 10. Angular distributions (d) S to OW-H (2.0-4.2 Å, line) and (e) S to OW-H (4.2-6.5 Å, dashed).

Figure 13. Angular distribution (i) S to µD (2.0-5.0 Å). Here µD represents a nominal dipole moment on the DMSO (not the real one) defined by the vector joining the sulfur atom and the midpoint of the line between the two carbon atoms.

to S-OD (Figure 14), where µW represents the water dipole moment vector and is defined as the line joining the OW and the bisector of the H-H distance in water, and µD represents a nominal dipole on the DMSO molecule given by the vector which goes from the sulfur atom to the midpoint of the line joining the two carbon atoms. The above angular distributions have been integrated over a distance range corresponding to the first coordination shell of the appropriate central atom. Also shown in these figures, where appropriate, are of the corresponding quantities for pure water, evaluated using the empirical potential Monte Carlo simulation described elsewhere.31 All the curves have been normalized so that they oscillate about unity. Considering angular distributions (a) and (b) (Figure 8), it is seen that the most probable orientation is with the O-H vector pointing directly toward OD and OW; i.e., DMSO oxygen and water oxygen form linear hydrogen bonds with the greatest

probability. However, there is a significant degree of hydrogen bond bending, as much as 50° in both cases, and the bond angle distribution is broader than in pure water, indicating that there is a higher proportion of bent hydrogen bonds in the mixture than in the pure liquid. Furthermore, distribution (a) produces a more pronounced peak at 180 compared to distribution (b), indicating that the DMSO-water hydrogen bond is more pronounced than the water-water bond in the mixture. The observation of stronger DMSO-water bonds than water-water bonds in the solution coincides with recent NMR measurements,40 as well as with the MD simulations.2 The broad hump at ∼75° in (a) and (b) comes in part from the second hydrogen on the same water molecule and, for OW, from hydrogens on water molecules at the hydrogen-donating sites. Between these two peaks, the probability density for pure water does not go to zero, as would be expected if the central

Orientation of H2O around Polar and Nonpolar Groups

Figure 14. Angular distribution (j) S to S-OD (2.0-4.0 Å).

molecule were only hydrogen bonded in tetrahedral positions. Instead, there is a broad hump at cos θ ∼ -0.5, suggesting there are a significant number of non-hydrogen-bonded molecules in the first coordination shell of pure water. This is consistent with the oxygen coordination number in pure water being greater than 4.34 In addition, all empirical pair potentials developed for water give that number greater than 4, when integrated out to the first minimum in gOO(r). It also fits with the angular distribution of water molecules around a central molecule as deduced by computer simulation.41 It is interesting to note, however, that this same feature is almost absent in the OD to OW-H and OW to OW-H probability densities, indicating that all the water molecules near the oxygen of DMSO or water in solution are hydrogen bonded to that oxygen, in accord with the results of the MD simulation of the mixture.2 According to that simulation, the solvated DMSO has two sites for hydrogen bonding, and the average angle between the two hydrogen bonds in the DMSO:H2O aggregate is nearly tetrahedral. This structure is consistent with a relatively unperturbed local tetrahedral structure of water in the presence of DMSO, as observed by our first neutron diffraction experiment on this mixture.1 Peaks in the C to OW-H angular distribution c (Figure 9) are much broader compared to the bond angle distribution in OD to OW-H, and the main peak has moved from 180 to 110°; i.e., methyl groups on DMSO prefer the OW-H angle to be at about 110° to the normal C to OW, with a very broad distribution. The qualitative difference between Figure 8 and Figure 9 illustrates the fundamental distinction between hydrogen bonding on the hydrophilic site of the DMSO molecule and hydrophobic hydration on the hydrophobic site of the DMSO molecule. The OW-H bonds near the methyl groups in solution prefer not to point directly toward the methyl group but have a large angular distribution, whereas around the oxygen atom they are strongly directed toward that oxygen. S to OW-H correlations (d) and (e) (Figure 10) are split into two radius values, because the S-OW correlations obtained by MD simulation show a double peak,2 split at r ∼ 4.2 Å, corresponding to water molecules hydrogen bonded to OD (shorter distance peak) and water molecules around the methyl groups (larger distance peak). The distinction between those two regions is entirely born out by the present simulation, because the two angle distributions are quite different. The S to OW-H distribution integrated over 2-4.2 Å looks qualitatively similar to the OD to OW-H or OW to OW-H angular distributions (Figure 8), while the S to OW-H distribution, integrated from 4.2 to 6.5 Å, looks qualitatively similar to the C to OW-H angular distribution. It is therefore established here again that the hydration around DMSO has two distinct regions: hydrogen bonded around oxygen and hydrophobic hydration around the methyl groups. In the latter case, water

J. Phys. Chem., Vol. 100, No. 4, 1996 1365 forms a lose hydrogen-bonded cage around the methyl groups, quite similar to what has been found in the case of methanol in water3 or the tetramethylammonium ion in water.29 Figure 11 shows the angular correlations in the mixture between OW or OD and µW, as defined previously. Both distributions are compared to the same distribution in pure water. In pure water, we notice quite a pronounced peak at about 130° and a very broad one near 0°. The 130° peak corresponds to hydrogen-acceptor sites (180-109/2)°, while the broad one at ∼0° corresponds to hydrogen-donor sites but indicates a wide range of angles are possible in this direction, as was deduced by spherical harmonic analysis of the same data.27 These two regions are not symmetric in this figure nor are they expected to be on the basis of the angular distribution functions of Svishchev and Kusalik.41 In the mixture, DMSO is a hydrogen acceptor but not a donor; therefore, the hydrogen-acceptor peak at ∼130° in pure water becomes much higher in the OD to µW angular distribution (f), and the hydrogen-donor peak vanishes completely. In distribution (g), there is a broader hydrogen-acceptor peak than in pure water, but the orientations in the hydrogen-donor position correspond to the water molecule’s dipole moment pointing directly away from the OW-OW axissa feature of trigonal bonding rather than tetrahedral hydrogen bonding. This confirms again the fact that although hydrogen bonding is still pronounced in the solution, the water network must be disrupted compared to the pure liquid. Figure 12 shows the C to µW angular distribution. As in the case of the C to OW-H, distribution (c), this is much broader than (f) or (g), indicating the much greater disorder of the water relative to the methyl groups compared to the oxygen atom. Note, however, that the distribution has a broad hump near θ ) 70°, corresponding to the broad hump in distribution (c). Thus, it appears that both the OW-H vector and the dipole moment prefer to lie roughly tangential to the methyl-water axis on average. Note also that there is a slight preference for the dipole moment to point away from the methyl group rather than away from it, a feature seen in concentrated methanol water solutions.3 Figure 13 shows the angular distribution of S to µD. Note that it increases almost monotonically with diminishing angle from near zero at cos θ ) -1, with the maximum near cos θ ) 0.5. In other words, the methyl groups have no strong propensity to orientate toward each other: if they did so, then the maximum in this distribution would have been expected to be nearer cos θ ) -1 instead. This is a further indication that there is no strong hydrophobic association in this system. Finally, Figure 14 shows the distribution of orientations S to S-OD and shows a pronounced peak at θ ) 140°. This would occur if the S-OD bonds on neighboring molecules were in roughly antiparallel association, an effect which has already been alluded to when discussing the pair correlation functions. There is an additional broad peak at cos θ ) 1, indicating some parallel arrangements as well. The overall picture from orientational distributions (i) and (j) is that orientations between neighboring DMSO molecules might be correlated around the S-OD bond, but there is no evidence for any hydrophobic association in the solution, in spite of a significant number of DMSO-DMSO contacts at the high concentration of the mixture we have studied. The earlier MD simulation2 did not find evidence for the DMSO-DMSO association reported here. It did conclude, however, that the hydrophobic association between methyl groups on DMSO does not occur in the mixture. The combined evidence from the neutron experiment given here and computer simulation described previously2 appears to rule out any possibility of

1366 J. Phys. Chem., Vol. 100, No. 4, 1996 hydrophobic association occurring in a manner that is often suggested by others.10,16 5. Conclusions The present empirical potential Monte Carlo analysis of the diffraction data from DMSO-water solutions has established how the molecules are organized with respect to one other in the hydrogen-bonded system with both hydrophobic and hydrophilic interactions present. The coordination and orientation of water molecules around DMSO in concentrated solutions, have been estimated from these diffraction data in a manner which has not been achieved before. In general, the picture obtained is closely analogous to that obtained by MD simulation using assumed molecular interaction potentials.2 Specifically, water-water correlations are enhanced in the presence of concentrated DMSO, when compared to what they might be in a random mixture of DMSO and water. The enhanced hydrogen bonding between water molecules in the mixture compared to bulk water is due to the presence of a strong hydrogen-bonding site on the DMSO oxygen and not to any special ordering around the methyl headgroups. The DMSO-water hydrogen bond is found to be more pronounced than the water-water hydrogen bond. In the mixing process, hydrogen bonding is simply transferred from water-water interactions to water-DMSO interactions, as was found in the previous MD simulation2 and in agreement with the qualitative ideas underyling the meanfield model of this system.19-21 In terms of orientational correlations, the picture is not complete because the full orientational pair correlation functions have so far not been estimated. These functions are most readily accessible from their spherical harmonic expansion coefficients, which store the orientational information and which can subsequently be used to explore the probability of particular orientations of pairs of molecules occurring without running the simulation again. However, as already pointed out in the Introduction, these coefficients cannot reliably be estimated directly from the diffraction data in this case. It would, however, be feasible to estimate the coefficients by using the empirical potential Monte Carlo simulation to generate the configurations of the molecules. Work on developing this approach is underway and if successful will be reported on separately. It would, for example, allow a 3D map of the distribution of water around DMSO to be plotted. Nonetheless, the orientational analysis given here in terms of bond angle distributions does show the very different nature of hydration around the DMSO oxygen and the DMSO methyl groups. On the one hand, the DMSO oxygen forms pronounced hydrogen bonds with water; on the other, the orientational correlations around the methyl headgroups are weakly defined, with a preference for O-H vectors to lie tangential to the methyl to water molecule axis, a picture consistent with other recent experiments.3,29 The EPMC analysis used here starts from an assumed set of interaction potentials, in this case those in a previous MD simulation of the same solution, and then modifies the shortrange part of these potentials in such a way that the experimental pair correlation functions are reproduced accurately. This procedure goes a lot further than most analyses of diffraction data from aqueous systems of this kind. It serves to show the very great deal of information that can be extracted from diffraction experiments with isotope contrast variation while highlighting the limitations that arise from not being able to separate all the site-site correlations needed to define the liquid structure. The results show clearly the distinctly different hydration around the oxygen atom and methyl groups in

Soper and Luzar solution. Questions about the relative orientation of neighboring solute molecules are still not completely resolved, due to the relatively weak contribution their correlation functions make to the measurable functions. All the evidence accumulated so far, however, is against the notion of a high degree of hydrophobic association in this system, at least at the high concentration of this experiment. It remains to be seen whether the lack of hydrophobic association observed here is a general characteristic of solutes with a simultaneous presence of hydrophobic and hydrophilic sites or is intimately dependent on the type of interaction made with the hydrogen-bonding site. DMSO has a large dipole moment, probably along the S-OD bond, which is roughly double that of water. Other equivalent molecules which have similar mixed sites often have smaller dipole moments. The analysis of bond angle distributions between methyl groups on DMSO and surrounding water confirms the previous direct experimental evidence3,29 that water molecules form a disordered hydrogen-bonded cage around small apolar groups. The hydrogen bond network deforms to avoid regions occupied by small hydrophobic species. The fairly broad angle distribution of water around methyl headgroups on DMSO confirms this deformation. As has been indicated in studies of related systems,2,29 direct observation of some of the microscopic correlation functions proves useful in understanding the physics of hydrophobic hydration: there is an entropic cost due to the deformation of hydrogen bond network around small apolar groups in water, but there are no significant energetic effects. These experimental findings are consistent with the theoretical predictions of the hydration and solvent-induced interactions between small hydrophobic species in water, developed by Pratt and Chandler almost 20 years ago.42 Further, from the water-water (HH) correlation in the mixture, as determined experimentally, it is obvious that this deformation of the hydrogen bond network is obtained without a significant degree of hydrogen bond breaking between water molecules. It is interesting to note that geometrical analysis through analytical models and computer simulations shows that water around small apolar entities tends to maintain all possible hydrogen bonds.43-45 Acknowledgment. It is a pleasure to dedicate this paper to Professor Harold L. Friedman, in honor of his seminal contributions to the statistical mechanics of solutions. Partial financial support from the Chemistry Division of ONR is gratefully acknowledged. References and Notes (1) Soper, A. K.; Luzar, A. J. Chem. Phys. 1992, 97, 1320. (2) Luzar, A.; Chandler, D. J. Chem. Phys. 1993, 98, 8160. (3) Soper, A.; Finney, J. L. Phys. ReV. Lett. 1993, 71, 4346. (4) Tommila, E.; Pajunen, A. Suom. Kemistil. 1969, B41, 172. (5) Cowie, J. M. G.; Toporowski, P. M. Can. J. Chem. 1964, 39, 2240. (6) Krishnan, C. V.; Friedman, H. L. J. Phys. Chem. 1969, 73, 1572; 1970, 74, 3900. (7) Fox, M. F.; Whittingham, K. P. J. Chem. Soc., Faraday Trans. 1974, 75, 1407. (8) Kenttammaa, J.; Lindberg, J. J. Suom. Kemistil, 1960, B33, 32. (9) Westh, P. J. Phys. Chem. 1994, 98, 3222. (10) Lai, J. T. W.; Lau, F. W.; Robb, D.; Westh, P.; Nielsen, G.; Tradum, C.; Hvidt, A.; Koga, Y. J. Solution Chem. 1995, 24, 89. (11) Bertulozza, A.; Bonora, S.; Battaglia, M. A.; Monti, P. J. Raman Spectrosc. 1979, 8, 231. (12) Falk, M.; Brink, G. J. Mol. Struc. 1970, 5, 27. (13) Gordalla, B. C.; Zeidler, M. D. Mol. Phys. 1986, 59, 817; 1991, 74, 975. (14) Tukouhiro, T.; Menafra, L.; Szmant, H. H. J. Chem. Phys. 1974, 61, 2275. (15) Barker, E. S.; Jonas, J. J. Phys. Chem. 1985, 89, 1730. (16) Safford, J. G.; Schaffer, P. C.; Leung, P. S.; Doebbler, G. F.; Brady, G. W.; Lyden, E. F. X. J. Chem. Phys. 1969, 50, 2140.

Orientation of H2O around Polar and Nonpolar Groups (17) Soper, A. K.; Turner, J. Int. J. Mod. Phys. B. 1992, 7, 3049 and references therein. (18) Rasmussen, D. H.; Mackenzie, A. P. Nature 1968, 220, 1315. (19) Luzar, A. In Interactions of Water in Ionic and Nonionic Hydrates; Kleeberg, H., Ed.; Springer: Berlin, 1987; p 125. (20) Luzar, A. J. Chem. Phys. 1989, 91, 3603. (21) Luzar, A. In Hydrogen-Bonded Liquids; Dore, J. C., Teixeira, J., Eds.; NATO ASI Series; Kluwer Academic: Dordrecht, 1993; Vol. 329, p 197. (22) Luzar, A.; Soper, A. K.; Chandler, D. J. Chem. Phys. 1993, 99, 6836. (23) Vaisman, I. I.; Berkowitz, M. L. J. Am. Chem. Soc. 1992, 114, 7889. (24) Rao, B. G.; Singh, U. C. J. Am. Chem. Soc. 1990, 112, 3803. (25) Ferrario, M.; Haughley, M.; McDonald, I. R.; Klein, M. L. J. Chem. Phys. 1990, 93, 5156. (26) Laaksonen, A.; Kovacs, H. J. Am. Chem. Soc. 1991, 113, 5596. (27) Soper, A. K. J. Chem. Phys. 1994, 101, 6888. (28) Soper, A. K. Physica B 1995, 213, 214, 448. (29) Turner, J. Z.; Soper, A. K.; Finney, J. L. J. Chem. Phys. 1995, 102, 5438. (30) McGreevy, R. L.; Pusztai, L. Mol. Sim. 1988, 1, 359. (31) Soper, A. K. Chem. Phys., in press. (32) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (33) Soper, A. K.; Howells, W. S.; Hannon, A. C. RAL Report No. 89-046, Rutherford Appleton Laboratory, Chilton, 1989.

J. Phys. Chem., Vol. 100, No. 4, 1996 1367 (34) Soper, A. K.; Phillips, M. G. Chem. Phys. 1986, 107, 47. (35) Soper, A. K.; Andreani, C.; Nardone, M. Phys. ReV. E 1993, 47, 2598. Also: Soper, A. K. In Neutron Scattering Data Analysis 1990; Johnson, M. W., Ed.; IOP Conference Series No. 107; IOP: Bristol, 1990; p 57. (36) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullmann, B., Ed.; Reidel: Drodrecht, 1981; p 331. (37) See Figures 2-4 in: Pratt, L. R.; Chandler, D. J. Chem. Phys. 1980, 73, 3430. And Figure 3 in: Pratt, L. R.; Chandler, D. Methods Enzymol. 1986, 127, 131. (38) Thomas, R.; Shoemaker, C. B.; Eriks, K. Acta Crystallogr. 1966, 21, 12. (39) Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids I; OUP: Oxford, 1984. (40) Ludwig, R.; Farrar, T. C.; Zeidler, M. D. J. Phys. Chem. 1994, 98, 6684. (41) Svishchev, I. M.; Kusalik, P. G. J. Chem. Phys. 1993, 99, 3049. (42) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1977, 67, 3683. (43) Stillinger, F. H. J. Solution Chem. 1973, 2, 141. Stillinger, F. H. Science 1980, 209, 451. (44) Postma, J. P.; Berendsen, H. J.; Haak, J. R. Faraday Symp. Chem. Soc. 1982, 17, 55. (45) Zichi, D. A.; Rossky, P. J. J. Chem. Phys. 1985, 83, 797.

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