DMSO Water Simulasi

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Structure and hydrogen bond dynamics of water-dimethyl sulfoxidemixtures by computer simulationsAlenka Luzara) and David ChandlerDepartment of Chemistry, University of California, Berkeley, Berkeley, California 94720(Received 21 December 1992; accepted 26 January 1993)We have used two different force field models to study concentrated dimethyl sulfoxide(DMSO)-water solutions by molecular dynamics. The results of these simulations are shownto compare well with recent neutron diffraction experiments using H/D isotopesubstitution [A. K. Soper and A. Luzar, J. Chem. Phys. 97, 1320 (1992)]. Even for thehighly concentrated 1 DMSO : 2 H,O solution, the water hydrogen-hydrogen radial distribu-tion function, g,,(r), exhibits the characteristic tetrahedral ordering of water-water hydro-gen bonds. Structural information is further obtained from various partial atom-atom distri-bution functions, not accessible experimentally. The behavior of water radial distributionfunctions, go0 (r) and gon (r) indicate that the nearest neighbor correlations among remain-ing water molecules in the mixture increase with increasing DMSO concentration. No prefer-ential association of methyl groups on DMSO is detected. The pattern of hydrogen bondingand the distribution of hydrogen bond lifetimes in the simulated mixtures is further investi-gated. Molecular dynamics results show that DMSO typically forms two hydrogen bondswith water molecules. Hydrogen bonds between DMSO and water molecules are longer livedthan water-water hydrogen bonds. The hydrogen bond lifetimes determined by reactive fluxcorrelation function approach are about 5 and 3 ps for water-DMSO and water-water pairs,respectively, in 1 DMSO : 2 H,O mixture. In contrast, for pure water, the hydrogen bondlifetime is about 1 ps. We discuss these times in light of experimentally determined rotationalrelaxation times. The relative values of the hydrogen bond lifetimes are consistent with a sta-tistical (i.e., transition state theory) interpretation.

I. INTRODUCTIONDimethyl sulfoxide (DMSO) , (CHs) $0, is an impor-tant industrial solvent as well as being used widely in bi-ology as a cryoprotector in the denaturation of proteins,and as a drug carrier across cell membranes. Unquestion-ably the broad range of properties are closely related to itsproperties in water solutions. The partial negative chargeon the oxygen atom of the DMSO molecule favors theformation of the hydrogen bonds with water molecules,giving rise to strongly nonideal behavior of the mixture. Asolution of 1 mol DMSO to -3 mol HZ0 has a freezingpoint of -70 C compared to + 18.6 and 0 C for the pureconstituents, respectively.2 The nonideality of the variation

of the dielectric constant with composition3t4 is paralleledby similar positive deviations of the viscosity and densityand negative deviations of heats of mixing.5-8 The maxi-mum deviations occur at 30-40 mol % of DMSO. Onemight expect that strong associates like DMSO-2 H,O ex-ist in the region of extrema of the excess quantities. Theexistence of well defined complexes of this compositionhas, however, not so far been proved.In earlier workg- an attempt was made to analyzethermodynamic properties of the mixture in a mean-fieldapproximation. A simple model for hydrogen bonded so-Also affiliated with Medi cal Facult y and Josef Stefan Institute, Univer-

sity of Ljubljana, Slovenia.

lution was shown to describe the experimental data for theexcess enthalpies and free energies of mixing, as well as theexcess surface free energies of mixing reasonably well overthe entire composition range. The model accounts for onlythe hydrogen bond interaction between molecules, suggest-ing a nearly tetrahedral hydrogen bonding complex involv-ing two or three water molecules per DMSO molecule. Thesame simplified description of the hydrogen bond interac-tion has also been capable of predicting the observed di-electric behavior. I2 While the success of the model wouldindicate the dominant role of hydrogen bond interaction inthis mixture, the model does not provide the answer towhat is the geometrical arrangement of water moleculesneighboring DMSO in the solution. Also, the degree towhich the coordination of DMSO by water can be regardedas a long lived complex is not known.Very little consensus among experimentalists ex-ists5p3-7 regarding these questions. Controversy arises pri-marily because the techniques that are used, such as mea-surements of thermodynamic quantities,4-8 measurementsof excitation spectra via IR absorption,7*8 Raman scatter-ing, l7 or NMR (nuclear magnetic resonance),g-21 as wellas inelastic neutron and x-ray scatteringI are either notsensitive to the detailed microscopic structure or else re-quire a considerable degree of interpretation to obtainstructural information. Recent advances in neutron diffrac-tion techniques22 allow the hydrogen bonding geometry tobe probed directly in the solution, through the use of iso-

8160 J. Chem. Phys. 98 (lo), 15 May 1993 0021-9606/93/108160-14$06.00 @ 1993 American institute of Physics


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TABLE I. Intermolecular potential parameters

OxygenHydrogen

Water(SPC, Ref. 29)adkJ mol- u/A

0.6502 3.15600.0 0.0

DMSOb

Q-0.82

0.41

&.I mol- o/B, q (Pl potential) q (P2 potential)Oxygen 0.29922 2.8 -0.54 -0.459Sulphur 0.99141 3.4 0.54 0.139Methyl group 1.230 3.8 0.0 0.160- _,=For the eeometrv of H,O, we have taken the O-H bond length as 1 b;and the HOH angle as-109.28.bFor the eometry of DMSO, from Ref. 36, we used the S-O bond lengthof 1.53i, -he S C bond length of 1.8 A, the OSC angle of 106.75; andthe CSC angle 97.4.

water potentials. No parameter optimization has beencarried out for mixtures, once the parameters for the purecompounds have been determined. This approach is a stan-dard first approximation. Klein and co-workers35 haveshown it to be reasonably accurate for simulating water-methanol, water-acetone, and water-ammonia mixtures.Both types of molecules in our simulation were mod-eled as completely rigid. The methyl groups on DMSOwere replaced by uni ted atoms of atomic mass 15. We havetaken the intramolecular structure of DMSO from thecrystallographic data.36 The Lennard-Jones interaction co-efficients and charges were chosen on the basis of experi-mentation with -50 simulation runs, using as criteria ac-curate values for the heat of vaporization, vanishingpressure, and a molecular dipole moment at least as largeas that of the gas phase molecule (-4 D).37 The twomodel potentials, Pl and P2, used further in the simulationof the mixture, were chosen according to the best agree-ment with recent neutron diffraction data on pure DMSO(Ref. 38) and at the same time giving reasonably accuratevalues for the mean potential energy and pressure. In bothmodels, the Lennard-Jones parameters for 0 , S, and CH,in DMSO are those of the isoelectronic Ne, Ar, and CH4,respectively. In one of the models, P 1, there are no chargeson methyl groups. In the other model, P2, we used thepartial point charges for DMSO obtained by fitting theelectrostatic potential around this molecule.3g A detaileddiscussion on the parameterization of the DMSO potentialwill be presented elsewhere.38 All Lennard-Jones parame-ters and the fractional charges for water and DMSO arelisted in Table I.The number of particles in the simulation box was 250for pure water, and for pure DMSO with the P2 potential.There were 432 particles in the simulations of pure DMSOwith the P 1 potential. Along with the pure liquids, we havestudied two systems coinciding with the 1:1.85 and 1:3.7DMSO-water mixtures. The first includes 162 water mol-ecules and 88 DMSO molecules (corresponding to thehigher concentration of the mixture measured with neu-tron diffractionz4); the second includes 197 water mole-

8162 A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMS O mixturesTABLE II. Molecular dynamics results for DMSO aqueous mixtures;mean potential energy per mole, (u), and pressurep, using Pl potential orP2 potential for DMSO. Numbers in parentheses are the experimentalestimates of the mean potential energy per mole (Ref. 33 ) .

With Pl potential With P2 potentialMole fraction --(WIof DMSO - (U)/kJ mol- P/kbars kJ mol- P/kbars

0.21 47.9OhO.4 (45.25) 0.39kO.5 47.9OhO.4 0.41AO.50.35 50.87kO.5 (47.18) 0.3OhO.5 49.90h0.4 0.41+0.5

cules and 53 DMSO molecules (corresponding to thelower experimental concentration). In many cases we havecarried out simulations first with the DMSO potentialmodel Pl, and second with the DMSO potential model P2.The calculation began with the molecules in a body cen-tered cubic lattice, with a lattice constant of 24.564 A (for1:2 mixture) or 22.784 A (for 1:4 mixture), which is con-sistent with the experimental room temperature densities.5The molecular dynamics calculations were carried out inN, V, T ensemble, and the Nose-Hoover thermostat404*was used to control the temperature at 298 K. The ther-mostat was switched off when calculating dynamic prop-erties. The equations of motions were integrated using thevelocity predictor-corrector method usually with a timestep of 1.0 or 1 .5 fs. Energy drift was 0.0023 kJ/mol per ps,which represents only 0.005% of the total energy. The longrange electrostatic interactions were treated using Ewaldsummation technique.42 Periodic boundary conditionswere used together with the minimum image conventionfor non-Coulombic interactions.42 All the simulations wereextended up to 160 ps, where the first 50 ps were consid-ered as equilibration. The runs were performed on a CrayXMP/416 and/or IBM/RS 6000. Results of the mean po-tential energy per mole, ( U), and pressure P, together withthe experimental estimates of ( U),33T43p44re given inTable II.III. STRUCTURAL RESULTSA. Partial correlation functions

Atom-atom distribution functions gafl( r) provide agood method to discuss the structure. In Figs. l-5 we dis-play all partial correlation functions for two potential mod-els for DMSO used in the simulation of the mixture at theconcentration 2 H,O :l DMSO. The largest differences be-tween the two models are observed in the three out of sixcorrelation functions involving 0, S, and C of the DMSOmolecule (Fig. 1) . In contrast, the change from Pl to P2produces no significant differences in the radial distributionfunctions for water molecules in the mixture (Fig. 2).Maxima of the first molecular coordination shell peaks forthe radial distributions illustrated in Fig. 3 indicate thatthe nearest water molecules are hydrogen bonded to theoxygen in DMSO molecule.DMSO is a suitable solvent to study small l ength scalemanifestations of hydrophobicity as it has methyl groupswhich bear no strong interaction with water. The uppertwo curves in Fig. 4 show the distribution functions that

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A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMSO mixtures 8163

: 0.6cn

1.4

1.0

0.6/I

0.6

0.2t.0

A/r3 i-tl2m

->

1

1i

H-H

OH20 - OHzO-

H-OH,0 16.0 8.0 2.0 4.0 6.0 8.0 10.0

FIG. 1. Atom-atom distribution functions between pairs of DMSO mol-ecules for water-DMSO mixture with DMSO mole fraction x,=0.35.Full lines correspond to calculations using the Pl potential for DMSOand dotted lines correspond to calculations using P2 potential for DMSO.Capital letters indicate which pairs of atoms coincide with CY nd y. Allg,,(r)s are asymptoti c to 1 at large Y.

characterize the radial hydration of methyl groups onDMSO. The lower two curves on Fig. 4 show the carbon-carbon distribution describing hydrophobi c pair correla-tions of DMSO in the mixture. The first of them indicatethat there are on the average 6.2 water oxygens aroundcarbon within a 5.1 A radius, the carbon-carbon functionindicates that the carbon in the methyl group is sur-roundedby -4.8 other carbonatomswithin the samedis-

FIG. 2. Atom-atom pair distribution functions between pairs of watermolecules for water-DMSO mixture with x,=0.35. Lines and lettering asin Fig. 1. Note change of scale in middle panel.

tance range. As the ratio of those two coordination num-bers is, not very different from the ratio of correspondingatomic fractions in the solution, hydrophobic association,if it exists among the methyl groups, does not seem to havea significant effect upon the structure of the mixture. It isinteresting to note that these pair correlations involving thehydrophobic methyl group are similar to the correspond-ing distributions computed by Pratt and Chandler for non-spherical apolar molecules in water (see Figs. 2, 3, and 4 ofRef. 45 and Fig. 3 of Ref. 46). For completeness,he re-J. Chem. Phys., Vol. 98, No. 10, 15 May 1993


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8164 A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMSO mixtures

4-

3-

m2-Lii--1-

W2

1

0

OH20 - ODMSO i

3

I I I I2.0 4.0 6.0 8.0 10.0

FIG. 3. Atom-atom pair distribution functions for water-DMSO mixturewith x2=0.35. Lines and lettering as in Fig. 1.

maining radial distribution functions are provided in Fig.5. There, it is interesting to compare the C-H radial dis-tribution in Fig. 5 with the corresponding C-OH20 functionplotted in Fig. 4. The sharpness and location of the mainpeak and cusped shoulder in the C-H function manifeststhe presence of orientational correlations in the hydropho-bic solvation.In Fig. 6, we present running coordination numbers

1.5

1.0- L

cQ) 0.5

0.:

0

IIIiL.I \ lP\/II

- I c-c- 1/ I I I I

2.0 4.0 6.0 8.0 10.0flA

FIG. 4. Atom-atom pair distribution functions for water-DMSO mixturewith x,=0.35. Lines and lettering as in Fig. 1.

where pP is the bulk number density of atom fi. The hy-dration number could be defined as the plateau value of therunning coordination number of the water oxygen. Forboth potential models, nap(y) increases continuously withdistance. Hence, there is no well defined hydration shell ofwater around the sulfur atom of DMSO. This result is due,at least in part, to the steric hindrance of the methyl groupwhich causes water molecules to associate with DMSOover a range of distances.Consider now how the radial distribution functions ofwater molecules change with concentration of DMSO. Fig-



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H-S

11:III s-sI

t J t I I I

2.0 4.0 6.0 8.0 lo.04

2.0

1.5

1.0

, 0.5

r/

0.5

0

I- I--I H-C2.0 4.0 6.0 8.0 10.0

r/A

- 0/

FIG. 5. Atom-atom pair distribution functions for water-DMSO mixture with x,=0.35. Lines and lettering as in Fig. 1.

ure 7 shows the pair-distribution functions for water mol- compositions of the mixture. The same behavior of waterecule oxygen atoms in 1:4 and 1:2 mixtures, as well as for radial distribution functions as a function of the solutepure SPC water. In this case we present results for P2 concentration has been observed from MD simulationpotential only. Both mixtures have their main O-O peaks studies of water-methanol ,35 water-acetone,35 water-at the same distance, but the peak intensities increase on ammonia,35 and water-acetonitri14 mixtures. It is evidentgoing from pure water to 1:4 and 1:2 mixture. The same from Figs. 7 and 8 that the nearest neighbor tetrahedralfeatures are seen also in O-H distribution functions (Fig. structure of water in the mixture is preserved. However,S), indicating the persistence of the hydrogen bonds, but the decrease in net water density with increasing DMSOalso an increased first coordination shell structure at both concentration causes the coordination numbers to decreaseJ. Chem. Phys., Vol. 98, No. 10, 15 May 1993


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A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMSO mixtures166

3.53.02.5

%0(T) 2.01.51.00.5

F 310

1 -+Ltx j. 1 I2.5 3.0 3.5 .~ 4.0 4.5 ~~~ 5.0

FIG. 6. Running coordination number, nso ( Y) [Eq. (3)] for water oxygenatoms around DMSO sulfur atoms calculated using Pl (solid line) or P2(dashed line) potentials for pure DMSO.

with increasing mole fraction of DMSO in the system (Ta-ble III). Further, it is worth noting that the remainingwater molecules are more strongly correlated with eachother, therefore higher peaks in the radial distributionfunctions for water in the mixture (Figs. 7 and 8) areobserved compared to pure water.B. Comparison with neutron diffraction experiment24and mean-field model (MFM)

In the case of aqueous solutions of DMSO, it is notpossible to obtain a complete separation of all the partialcorrelation functions by isotropic contrast, because two ofthe scattering lengths of two of the components, oxygenand carbon, change little with isotope. Sulfur could be sub-stituted, a lthough a very weak contrast and also high cost

6.0 1 I 1I.iiI\

4.0 - , I,uv

d I I I_.. *2.0 4.0 6.0 8.0

4FIG. 7. Molecular dynamics results for the oxygen-oxygen radial distri-bution function of water in pure SPC (solid line), water in 1:4 mixture(dashed line) and water in 1:2 mixture (dashed-dotted line).

2.50x 2.0T=b

3 1.5g

1.00.5

; 1 I 1 1iiiiii

2.0 4.0 6.0 8.06

FIG. 8. Molecular dynamics results for oxygen-hydrogen radial distri-bution function of water. Lines as in Fig. 7.

inhibits its use. On the other hand, hydrogen and its iso-tope deuterium have a significant contrast. Because deute-rium has a markedly different neutron scattering cross sec-tion from hydrogen, we can explore the distribution ofhydrogen bonds in water and water mixtures by isotopiclabeling of the protons involved in hydrogen bonding. Aswith most isotope difference techniques the H/D substitu-tion yields partial structure factors to absolute accuraciesof -10%. Within that accuracy, important trends withdilution and in comparison with pure water are detectable.In all the experiments, DMSO was fully deuterated to re-duce the incoherent scattering as much as possible. In an-alyzing simulation data we will focus on the manifestationof DMSO induced changes in water-water interactions, asmeasured by neutron diffraction.241. H-H dorrelations

r- In Figs. 9 and 10, molecular dynamics results are pre-sented at two concentrations of the mixture and comparedwith neutron diffraction data.24 Results for pure SPC arealso included for comparison. There is no significant dif-ference in hydrogen-hydrogen radial distribution function,gHH( r), calculated by the two po tentials for DMSO.Therefore we cannot give preference to either of the twomodels on the basis of water pair correlation functions in

TABLEIIII Coordination numbers, ha0 (r) [Eq. (3)] in pure water andaqueous solutions of DMSO determined by molecular dynamics simula-tion; xi denotes mole fraction of water...U.--Z ~~__ :. _ ___II-.~.:...x1=1 x, =0.79 x, =0.65

Oxygen aroundoxygenHydrogen aroundoxygen

5.92 3.35 2.601.84 1.42 1.16



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A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMS O mixtures 81672.5

2.0

1.5

1.00.5

FIG. 9. H-H correlations in water-DMSO mixture at x,=0.21. Solid linerepresents gun(r) +s&T) as determined by the neutron experiment(Ref. 24) where rnn(r) denotes intramolecular H-H distribution func-tion. Dashed line is gnu(r) from molecular dyn amics simulation (MD).On the scale of the graph, the distribution between MD calculations withpotential model Pl are indistinguishable from those with P2. Dash-dotline represents molecular dynamics calculation of pure SPC water.

the mixture. The HH function in pure water is dominatedby three peaks at 1 .5, 2.3, and 3.8 A. The latter two cor-respond to a mostly tetrahedral coordination of the watermolecules. The peak at 1.5 A corresponds to the intramo-lecular bond distance and is not interesting from the pointof view of orientational correlations. If the positions of theintermolecular peaks change, or even merge into a singlebroad peak in the mixture, this would be an indication of asignificantly distorted first molecular coordination shell

3.0 -2.5

s2.0

2 1.51.00.5 I

.0 4.0 6.0 6.0f I%+FIG. 10. H-H correlations in DMSG-water mixture at xoMSO=0.35.Lines as in Fig. 9. Experimental uncertainties in the height of the firstintermolecular peak, based upon two independent measu rements (Refs.24 and 58) are &13%.

1 oxygen of Hz0or DMSO

FIG. 11. Geometric definition of the hydrogen b ond, used in moleculardynamics simulation.

structure in the mixture. This type of behavior is observedin concentrated ionic solutions of LiCI, for example,48 butnot in DMSO-water mixtures.The 2.3 %, peak in pure water is shifted to slightlylarger Y values at the highest concentration of DMSO inthe neutron diffraction experiment ( Ar-0.15 A). No suchshift has been detected in methanol-water mixtures orCSCl, water mixtures, however, a similar shift has beenrecently seen in pure water at elevated temperatures alongthe coexisting curve.49 Molecular dynamics of the systemwe examined gives a negligible shift. The experimental shiftof 0.15 A is small enough to be due to quantum effects.50 nmaking this comparison, note that the SPC model gi ves agHH( y) for pure water whose phase is -0.06 A larger thanthat of experiment.51 As seen from Figs. 9 and 10 there isno significant change in the general pattern in &H(Y) evenat the highest concentration of DMSO. The H-H distribu-tions obtained from simulations show more structure com-pared to neutron data. Notice, however, that the experi-mental intramolecular peak is somewhat broader thanmight seem physically reasonable thus indicating possibleexperimental uncertainties. Since the neutron data under-estimates intramolecular correlations, it may also underes-timate the intermolecular structure. This point is the focusof future experimental work.--In general, the qualitative trends seen in the experi-ment are also seen with the simulation: for the DMSOsolutions the same sequence of peaks is observed, indicat-ing that the most probable nearest neighbor tetrahedralcoordination of water has not been significantly changed bythe presence of concentrated DMSO. At those high con-centrations of DMSO a significant fraction of water mole-cules will take part in the hydration shell of DMSO mol-ecule. The first coordination shells exhibit progressivelypronounced structure with increasing DMSO concentra-tion. Correspondingly, the non nearest neighbor structure(i.e., the tetrahedral network of liquid water) must be di-minished with increasing DMSO concentration.2. Hydrogen bond structurea. Hydrogen bond deJnition. To extend this analysis ofthe effect of DMSO on water structure, we use moleculardynamics to look at the hydrogen bond statistics as a func-tion of mole fraction. The definition of a hydrogen bond issomewhat arbitrary. Different definitions have been used to

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8168 A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMS O mixturesTABLE IV. Values of the parameters in Fig. 11. Their determination isexplained in the text.Mole fraction of DMSO RgJ (A, gtc)/deg

0.00 2.45 3.60 300.21 2.40 3.20 300.35 2.40 3.20 30

estimate the number of hydrogen bonds of a given type onthe basis of various energetic and structural criteria.52 Wehave here adopted a geometric criterion similar to thatused by Klein and co-workers regarding water-methanoland water-acetone mixtures.35 We say that a hydrogenbond exists between a pair of molecules if the coordinatesdefined in Fig. 11 are smaller than some specified cutoffdistance R$& R&, and angle 4 (). We define the hydrogenbond occupation number for the ath pair of molecules tobeh,=l, for Roo


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A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMS O mixtures 8169

TABLE V. Average fraction of water and DMSO molecules (%) with N hydrogen bonds at mole fractionof water, xt; statistics is obtained from two independent 2.5 ps runs. Numbers in parentheses were computedat xt =0.65 with the SPC and Pl potentials; all others were evaluated with the SPC and P2 potentials.x,=1 x, =0.79 x, =0.65

N Hz0 Hz0 DMSO H2O DMSO0 0.07 *0.01 0.41 *o.os 0.38*0.05 2.20a0.02 (4.03) 0.7 kO.02 (1.43)1 2.12=+=0.08 7.6 ho.6 24.6 kO.9 19.0 *2.0 (22.9) 58.2hO.5 (44.1)2 14.11*0.30 30.6 rtO.2 69.3 *0.6 42.0 *2.5 (42.6) 39.7*0.5 (54.4)3 38.12bO.45 41.7 rto.2 5.7 rto.3 30.0 f 1.0 (26.5) 1.4hO.7 (0.05)4 40.58*0.50 18.7 kO.5 0.04*0.04 7.0 f 1.7 (4.0) 0.05 4.93*0.15 1.0 *0.1 0.0 0.2 *to.1 (0.0) 0.06 0.06*0.01 0.0 0.0 0.0 (0.0) 0.0

where p-r is temperature times Boltzmanns constant, and&4 is the free energy change due to the formation of lipair, able to form a bond, as defined in Ref. 10. The num-ber density of water-DMSO pairs, n12 s obtained fromO=Bll ln(l-n&72112) -& ln(nlz/2nl), (6)where n2 is the number density of DMSO molecules.The phase space of li pairs is formally divided into twosubvolumes: Yi for hydrogen bonded and Vf for nonhy-drogen bonded pairs, with only two energy levels, E (i= 1,2)


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collected in Table V show that the Pl potential favors-9% more hydrogen bonds between DMSO-water mole-cules compared to the P2 potential, and -9% less hydro-gen bonds between water-water molecules in 1:2 mixture.These differences between the two potentials are consid-ered only partly to be due to statistical uncertainty. Hence,we have to bear in mind, that the population of hydrogenbonds between water-DMSO molecules in 1:2 mixture de-pends to some extent on the potential of DMSO used insimulations. Notice, for example, that the probability fortwo hydrogen bonds with DMSO is larger for the Pl po-tential model than that for the P2 potential model. Thisfeature is understandable. The charge on the DMSO oxy-gen is smaller in the P2 potential than it is in the Pl po-tential. As a result, the DMSO-H,O hydrogen bond isslightly weaker in the former case.We now consider the structure of the DMSO-waterhydrogen bonded aggregates. By molecular dynamics, wecalculated the H* * -0-S angle. Its average value is 126 2for either of the two potentials. The assumption of a planarcoordination of the DMSO oxygen atom therefore coin-cides with a tetrahedral angle between hydrogen bonds inthe DMSO : 2H,O aggregate. This structure is consistentwith a relatively unperturbed local tetrahedral structure ofwater in the presence of DMSO, as observed by neutrondiffraction.24

molecular dynamics and the neutron diffraction experi-ment. It is therefore evident that DMSO hydrogen bondsto water in preference to the water itself. Compari ng thecoordination numbers from H-( O,,,, + ODMSO ) correla-tions, the experiment, simulation and mean-field model allgive almost the same number at the lower concentration ofDMSO; however, at the highest concentration studied,neutron diffraction gives a questionably low value. Thisexperiment has since been repeated and shows a slightlybetter agreement with our simulations and the mean fieldmodel, the revised coordination number being 1.7h0.2.58The neutron diffraction results for coordination numbersare difficult to obtain in part because they are subject toseemingly small errors in the background subtraction.Also, neutron diffraction has not distinguished between thetwo types of OH correlations. To obtain these coordinationnumbers from neutron diffraction, it was assumed that Hswere equally distributed between DMSO and HzO. How-ever, the general trend is visible in the experiment: Thewater-water bonds are depleted as the increasing concen-tration of DMSO absorbs the water hydrogens.

IV. HYDROGEN BOND DYNAMICSTable VI compares coordination numbers for selectedpeaks in HH and H (0~~~+Oo~~o) correlation functions,

obtained from our molecular dynamics and from neutrondiffraction experiments. These values are results of inte-grating the first intermolecular peak of the correspondingradial distribution functions. Table VI also gives O-H co-ordination numbers estimated from the mole fractionweighted averages of (n&) predicted by the mean-fieldmodel of Ref. 9. Comparing the coordination numbersfrom H-H correlations, we see a diminishment of hydro-gen bonds with increasing DMSO concentration, indicat-ing that the water hydrogen bonding sites are becomingincreasingly less hydrogen bonded with increasing concen-tration of DMSO. We observe the same phenomena in

The preceding section discussed the equilibrium prop-erties of the hydrogen bonds in the mixture. Equally inter-esting is the question of the time-dependent behavior of thebonds, one measure of which is the hydrogen bond li fetime.There have been some efforts at using simulation re-sults to study lifetimes in a way proposed by Stillingernearly 20 years ago for water, however, in only a few stud-ies reported, time dependent hydrogen bond autocorrela-tion functions were actually computed.60a3 In systemswhere we expect relatively long lifetimes, as in the case ofDMSO-water mixtures, the direct determination of the hy-drogen bond autocorrelation function seems less efficientthan the reactive flux method often used in the context ofisomerization dynamics.2b127 he reactive flux method pro-vides information about the short time dynamics, i.e., tran-sient relaxation, as well as the lifetime. It is this approachthat we adopt here.

TABLE VI. H-H and H-(0,,,,, +Oo,so) coordination numbers inDMSO-water mixtures; comparison between neutron diffraction (ND)(Ref. 24) molecular dynamics (MD) (this work), and mean field model(MFM) (Ref. 9). The integration ranges for the calculation of coordi-nation numbers are in parentheses. Distances are in Angstroms.

Let us define a hydrogen bond correlation functionclj(t) as

CljW& ( c [RAo)~~,(t))nsjHH correlationsMole fraction of DMSO ND MD0.21 1.3AO.l (1.9-2.40) 1.63 (1.88-2.423)4.2*0.1 (1.9-3.10) 4.2 (1.88-3.10)0.35 0.9*0.1 (2.00-2.45) 1.22 (2.01-2.44)

2.6kO.l (2.OS3.10) 3.00 (2.01-3.09)

where j =l for water and j = 2 for DMSO and the dynam-ical variable h,(t) =Sh,( t) + (h,) is defined in Eq. (4).The sum in Eq. (8) is taken over all pairs consistent withthe index j and (* ..) represents the average over initialtimes. Note that cii( t) as defined in Eq. (8) has the initial,t=O, value of unity. By assuming exponential relaxationbeyond a transient time, we would writeMole fraction H-(OwaterOo~so) correlationsof DMSO ND MD MFM0.21 1.4hO.l (1.4-2.20) 1.41 (1.40-2.20) 1.450.35 0.7hO.2 (1.40-2.30) 1.21 (1.40-2.3) 1.15


Clj (t) = e-tr, for t > Ittransient , (9)where r is the relaxation time for times longer than that ofthe transient. Taking the time derivatives of Eqs. (8) and(9), we obtain

8170 A. Luzar and D. Chandler: Hydrogen bond dynamics of water D MSO mixtures

(8)


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A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMSO. mixtures 8171

0 50 100 150t/fs

FIG. 14. Hydrogen bond autocorrelation function derivative -c,(t),calculated by molecular dynamics; solid line denotes -i,,(t) for water-water pairs in pure water; dashed line and dash-dot line denote -C,,(i)and --f,,(t), respectively, for water-water and water-DMSO pairs in themixture with mole fraction of DMSO, x,=0.35.

1-Clj(t)=(Nlj) - ( zj l&OVz,(t) ) =i e-/I: (10)

where the dot denotes the time derivative. By employingthe reactive flux method, we can inspect the consistency ofthis exponential model for long time relaxation.For short times we expect transient behavior thatshould not correspond to the exponential macroscopic de-cay. The initial value of -clj(t> determines the transitionstate theory relaxation time, rTsr. After a relatively shorttransient time, --iij( t) shoul d relax to a plateau valuecorresponding to a long time behavior, determining thehydrogen bond lifetime, rns. Short time behavior providesinformation about the mechanism for hydrogen bondbreaking. But its particular functional form is sensitive tothe particular (and somewhat arbitrary) choice that wemake for the hydrogen bond. Exponential relaxation on alonger time scale, however, should be invariant to the def-inition of the hydrogen bond, provided a reasonable choicefor that bond has been made.In Fig. 14, -Cij(t) is presented for water-water pair(j = 1) and water-DMSO pair (j =2) in a 2 Hz0 :1 DMSO mixture and compared with pure water atT=289 K. The analysis in the mixture was carried out for0.2 ps covering di fferent portions of the simulations, andthe results averaged over 50 runs, with time step of 1.0 fsand using P2 potential for DMSO. The analysis in purewater, using SPC potential, was carried out for 0.4 ps(time step = 0.05 fs), and the results averaged over 25 runs.The derivatives of the autocorrelation functions were cal-culated every time step. Our calculations of --dij( t) areconsistent with a rapid transient relaxation. The simulationruns were, however, not long enough to show clearlywhether the plateau has been reached, and if it existed, todetermine an accurate plateau value of -eii( t). This is left

for future work. Present calculations (Fig. 14) indicate

TABLE-k. Hydrogen bond lifetimes, r ns, and the transition state the-ory estimate of that time r rSr, for water-water pairs in pure water, water-water pairs in 1:2 mixture, and water-DMSO pairs in I:2 mixture, ex-tracted from Fig. 14, considering Eq. (IO). For DMSO, the P2 potentialwas used. Calculations were done at T=298 K.

Water-water pairin pure SPCWater-water pairin I:2 DMSO-watermixtureWater-DMSO pairin 1:2 DMSO-watermixture

TTSThs0.20*0.010.45 hO.03

0.80*0.06

THLIhS1.2OrtO.083.3 +0.3

4.8 *0.9

that the recrossings lead to relaxation times which are al-most an order of magnitude longer than those obtainedfrom the transition state theory. Further, oscillations in-c,(t) show that the recrossing frequency is of the orderof (0.1 PS) - . We use the value of -ij( t) after the end ofthe first recrossing period to estimate the transmission co-efficient,26 rTsr/rnn, and therefore the hydrogen bond life-time, ruB. The hydrogen bond lifetimes, extracted from theresults depicted in Fig. 14 and considering Eq. (10) arecollected in Table VII. Both the initial transition state the-ory as well as the dynamical values obtained from -C,(t)at t= 0.1 ps are given. Our result for run in pure water isreasonably consistent with those found by others perform-ing molecular dynamics with different potentials and tech-niques: 1 4;64 1.6;62 0.9,35 and 2.0 PS.~~Experimental esti-mates of hydrogen bond lifetimes made from interpretingdepolarized Rayleigh light scattering and inelastic neutronscattering give -0.8 ps at room temperature.64-6g Recallthat it is only the complete breaking and making of hydro-gen bonds that is analyzed with the plateau value of-cij( t) . On the other hand, the line widths of the scatter-ing experiments probably possess contributions from thedephasing of small amplitude librations in addition to thelarger amplitude hydrogen bond fluctuations. As such, weexpect the scattering experiments should yield a somewhatlarger relaxation rate or a smaller relaxation time than therun we have computed.One interesting feature of the entries to Table VII isthat the transmission coefficient is approximately l/6 forall three cases investigated. Our preliminary study wouldtherefore indicate that the dynamical corrections to thestatistical transition state theory are not strongly depen-dent upon either the type of hydrogen bond nor the con-centration of DMSO. The larger value of rnn for thewater-DMSO bond than for the water-water bond in themixture is therefore understood as a simple statistical con-sequence of the formers hydrogen bond being strongerthan the latter. Similarly, the increase of the water-waterrun through the addition of DMSO is understood statisti-cally as the potential of mean force for water-water hydro-gen bonding grows with increasing DMSO concentration(see Figs. 7, 8, and 10).

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8172 A. Luzar and D. Chandler: Hydrogen bond dynamics of water DMS O mixtureswith the increase in DMSO concentration is consistentwith Baker and Jonas NMR observations of both self-diffusion constant and the single molecule reorientationalrelaxation time, re, for water molecules in water-DMSOmixtures.21 According to their data, rez3 ps for pure wa-ter and rez 11.7 ps for the 2:l water-DMSO mixture.(These numbers are extrapolated and interpolated fromTable II in Ref. 21. ) Our corresponding computed valuesof ?-us are 1.2 and 3.3 ps, respectively. Consistency there-fore implies that the reorientation of a water molecule byan angle -r/2 occurs in about three to four hydrogenbond lifetimes. Wang and co-workers have used depolar-ized light scattering to estimate ~~ for the DMSO mole-cules in water-DMSO mixture. At conditions coincidingwith our simulation, they find re to be between 12 and 14ps, again approximately three times the corresponding THBwhich we have computed, 4.8aO.9 ps. A recent NMRmeasurement to estimate re for water in the 2:l water-DMSO mixture by Gordalla and Zeidler9(b) gives a valueof 16.8 ps, about 30% larger than that of Barker and Jo-nas.21The trends are consistent, though a precise connec-tion between re and rHa has yet to be analyzed. Moleculardynamics calculations of re would be worthwhile and in-structive in this regard.

would decrease even faster than they do with increasingDMSO concentration.The DMSO molecules create these structural effects inpart because DMSO is a hydrogen bond acceptor but notdonor, and in part because DMSO bonds with water morestrongly than water bonds to water. According to the sim-ulations, the solvated DMSO is likely bonded to two wa-ters, and the average angle between the two hydrogenbonds in the DMSO :2H20 aggregate is nearly tetrahedral.A water is hydrogen bonded to water but near the oxygenof a DMSO molecule can simultaneously bond withDMSO or readily switch its bonding from water to DMSO.On the other hand, if that water was instead near the me-thyl groups of the DMSO, no such alternative bondingwould be possible. It is the occurrence of this latter casethat strengthens the attractive potential of mean force be-tween pairs of waters in the presence of DMSO.

V. CONCLUSIONSWith either potential model Pl or P2, our moleculardynamics results draw a consistent microscopic picture ofwater-DMSO mixtures. This robust picture, seemingly in-variant to reasonable changes to the intermolecular poten-tial, is in accord wi th the qualitative ideas underlying themean-field model of those systems.- In particular, in themixing process, hydrogen bonding is simply transferredfrom water-water interactions to water-DMSO interac-tions.

Our analysis of hydrogen bond lifetimes suggests thatthe slowing of water motions in the presence of DMSO canbe understood as a consequence of these structural effects.Much more could be done to extend our preliminary workon the dynamics. First, more accurate estimates of the hy-drogen bond lifetimes are needed. Runs with longer trajec-tories should provide quantitative plateau values of the re-active flux correlation functions have been reached.Further, the connections we have begun to make here be-tween orientational correlation times and hydrogen bondlifetimes deserve quantitative elaboration. Analysis of thetransient relaxations we have reported in Fig. 14 may beuseful in furthering our understanding of water motion andthe dynamics of solvation. Here we have in mind the pos-sible development of analytical models that could be testedthrough comparison wi th the simulation results for-&( t>.

The radial distribution functions we have computedare in reasonable agreement with those observed with neu-tron diffraction.24 Certain radial distribution functions,such as the water-water g&Y), provide a signature ofhydrogen bonding. We find that the peak locations ingmr(r) are hardly affected by DMSO. However, the peakamplitudes are altered significantly as the concentration ofDMSO changes. Specifically, we find that the first molec-ular coordination shells become more structured with theincrease of DMSO. At the same time, the average numberof water-water hydrogen bonds diminish with increasingDMSO concentration thus signaling a disruption of thehydrogen bond network beyond the range of nearest mo-lecular neighbors.

Concerning equilibrium structural aspects of this sys-tem, DMSO can serve as a prototypical amphiphilic mol-ecule from which much may yet be learned about hydro-phobic effects. Indeed, at lower DMSO concentrations thatwe have studied, Vaisman and Berkowitz2 have contrastedthe hydration of the hydrophilic S-O group from that ofthe hydrophobic CH, groups. Not all of the atom-atomdistribution functions we have computed are accessible ex-perimentally. However, through H/D substitution of themethyl hydrogens, it should be possible to use neutrondiffraction to test our results involving the hydrophobicmethyl groups. We hope that such experiments will beperformed.*ACKNOWLEDGMENTS

In a fluid mixture, average populations depend uponboth the relative concentrations of the components as wellas the pair correlations. The latter, of course, are describedby the potentials of mean force, or equivalently the devia-tions of the radial distributions from unity. Hence, oursimultaneous observations of diminishing number ofwater-water hydrogen bonds and increasing water-watercorrelations are not inconsistent. Indeed, without the in-creased correlations, the water-water bonding populations

We thank Joel Bader, Massimo Marchi, and BerendSmit for their help and advice. The authors acknowledgevaluable discussions with Alan Soper and Jose Teixeira.We thank Max Berkowitz for sending us the preprint ofRef. 25. This work was supported by NIH Grant No. ROlGM 37307 and ONR Grant No. N00014-92-J-136.

D. Martin and H. G. Hauthal, DimethylSulphoxide (Wiley, New York,1975).J. Chem. Phys., Vol. 98, No. 10, 15 May 1993


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