Published on Web 09/20/2002
`
`How Ions Affect the Structure of Water
`Barbara Hribar,† Noel T. Southall,‡ Vojko Vlachy,† and Ken A. Dill*,§
`Contribution from the Faculty of Chemistry and Chemical Technology, UniVersity of Ljubljana,
`AskercˇeVa 5, 1000 Ljubljana, SloVenia, Graduate Group in Biophysics, UniVersity of California,
`San Francisco, California 94143-1204, and Department of Pharmaceutical Chemistry and
`Graduate Group in Biophysics, UniVersity of California, San Francisco, California 94143-1204
`Received February 23, 2002
`
`Abstract:We model ion solvation in water. We use the MB model of water, a simple two-dimensional
`statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian
`hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo
`simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt
`solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity
`B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and
`Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of
`the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities
`govern the interactions of ions with water, and (2) that a balance of forces determines water structure:
`electrostatics (water’s dipole interacting with ions) and hydrogen bonding (water interacting with neighboring
`waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering
`of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities,
`and surrounding water molecules are largely hydrogen bonded.
`
`1. Introduction
`Ion-water interactions are important throughout biology and
`chemistry. Ions affect
`the conformations and activities of
`proteins and nucleic acids1-3 and the specificity of ion binding.
`Ion complexation in cells is crucial for the activities of
`biomolecules such as enzymes and drugs.4,5 Ions regulate the
`electrostatic potentials, conductances, and permeabilities of cell
`membranes,6,7 the structures of micelles, and the hydrophobic
`effect (called Hofmeister effects), which drives partitioning,
`permeation, and folding and binding processes.8,9 In chemistry,
`ions affect the rates of chemical reactions;10,11 rates of gelation,
`widely used in food applications;12 ion-exchange mechanisms,
`widely used for chemical separations;13 and the expansion and
`
`* To whom correspondence should be addressed. E-mail: dill@
`zimm.ucsf.edu.
`† University of Ljubljana.
`‡ Graduate Group in Biophysics, University of California.
`§ Department of Pharmaceutical Chemistry and Graduate Group in
`Biophysics, University of California.
`(1) Dill, K. A. Biochemistry 1990, 29, 7133-7155.
`(2) Rupley, J.; Careri, G. AdV. Protein Chem. 1991, 41, 37-172.
`(3) Chalikian, T. V.; Volker, J.; Plum, E.; Breslauer, K. Proc. Natl. Acad. Sci.
`U.S.A. 1999, 96, 7853-7858.
`(4) Sussman, F.; Weinstein, H. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 7880-
`7884.
`(5) Lybrand, T. P.; McCammon, A.; Wiff, G. Proc. Natl. Acad. Sci. U.S.A.
`1986, 83, 833-835.
`(6) Jordan, P. C. Biophys. J. 1990, 58, 1133-1156.
`(7) Katz, B. NerVe, Muscle, and Synapse; McGraw-Hill: London, 1966.
`(8) Collins, K. D.; Washabaugh, M. W. Q. ReV. Biophys. 1985, 18, 323-422.
`(9) Cacace, M. G.; Landau, E. M.; Ramsden, J. J. Q. ReV. Biophys. 1997, 30,
`241-277.
`(10) Maroncelli, M.; MacInnins, J.; Fleming, G. R. Science 1989, 243, 1674-
`1681.
`(11) Kropman, M. F.; Bakker, H. J. Science 2001, 291, 2118-2120.
`(12) Larwood, V. L.; Howlin, B. J.; Webb, G. A. J. Mol. Model. 1996, 2, 175-
`182.
`12302 9 J. AM. CHEM. SOC. 2002, 124, 12302-12311
`
`contraction of clays, responsible for environmental processes
`such as mudslides.14 Ion hydration has been studied extensively,
`both experimentally15-19 and theoretically.20-25
`Ions have long been classified as being either kosmotropes
`(structure makers) or chaotropes (structure breakers) according
`to their relative abilities to induce the structuring of water. The
`degree of water structuring is determined mainly by two types
`of quantities: the increase or decrease in viscosity in water due
`to added salt, and entropies of ion solvation. For example, the
`viscosity Ł of an aqueous salt solution typically has the
`following dependence on ion concentration c:18
`) 1 + Ac1/2 + Bc + ...
`
`Ł/Ł0
`where Ł0 is the viscosity of pure water at the same temperature.
`
`(1)
`
`(13) Habuchi, S.; Kim, H. B.; Kitamura, N. Anal. Chem. 2001, 73, 366-372.
`(14) Chavez-Paez, M.; Van Workum, K.; de Pablo, L.; de Pablo, L. L. J. Chem.
`Phys. 2001, 114, 1405-1413.
`(15) Samoilov, O. Y. Discuss. Faraday Soc. 1957, 24, 141-146.
`(16) Samoilov, O. Y. In Water and Aqueous Solution: Structure, Thermodynam-
`ics, and Transport Processes; Horne, R. A., Ed.; Wiley-Interscience: New
`York, 1972; pp 597-612.
`(17) Krestov, G. A. Thermodynamics of SolVation; Ellis Horwood: New York,
`1990.
`(18) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth Scientific
`Publications: London, 1959.
`(19) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515-548.
`(20) Marx, D.; Sprik, M.; Sprik, M.; Parinello, M. Chem. Phys. Lett. 1997, 273,
`360-366 and references therein.
`(21) Heinzinger, K.; Vogel, P. C. Z. Naturforsch. 1974, A29, 1164-1171.
`(22) Galli, G.; Parrinello, M. In Computer Simulations in Materials Science;
`Meyer, M., Pontikis, V., Eds.; Kluwer: Dordrecht, 1991.
`(23) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D.
`ReV. Mod. Phys. 1992, 64, 1045-1097.
`(24) Galli, G.; Pasquarello, A. In Computer Simulations in Chemical Physics;
`Allen, M. P., Tildesley, D. J., Eds.; Kluwer: Dordrecht, 1993.
`(25) Hummer, G.; Pratt, L. R.; Garcia, A. E. J. Phys. Chem. A 1998, 102, 7885-
`7895.
`
`10.1021/ja026014h CCC: $22.00 © 2002 American Chemical Society
`
`MYLAN INST. EXHIBIT 1121 PAGE 1
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`MYLAN INST. EXHIBIT 1121 PAGE 1
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`

`

`How Ions Affect the Structure of Water
`
`A R T I C L E S
`
`A is a constant independent of c; its corresponding term can be
`explained by Debye-Hu¨ckel theory as being due to counterion
`screening at low ion concentrations. The constant B, which is
`called the Jones-Dole B coefficient, is the quantity that defines
`the degree of water structuring of interest here.18 B is positive
`for kosmotropic ions and negative for chaotropic ions. One issue
`in interpreting experiments is how to separate the contributions
`of the anion from the cation. The standard assumption is that
`+ ) BCl
`-, because K+
`K+ has the same B coefficient as Cl-, BK
`and Cl- have approximately the same ionic conductances26 and
`because the value of B for KCl is approximately zero.
`Water structuring is also reflected in entropies of ion
`solvation. To obtain these entropies,
`two assumptions are
`commonly used. First, to separate the effects of the anion from
`the cation,
`it
`is assumed that
`the solvation entropies are
`additive.17 Second, an assumption is required to parse the ion
`solvation entropy into components due to the ion and due to
`water. By splitting the solvation entropy, ¢Shyd, into ion and
`hydration water contributions and subtracting the former, ¢SII
`is obtained, which describes the change in entropy of hydration
`water due to the presence of an ion.17 Ions which are kosmo-
`tropic in viscosity experiments tend to have a negative hydration
`component to their solvation entropy, implying that they order
`the nearby waters, while chaotropic ions have a positive ¢SII.
`The experiments show that water is ordered by small or
`multivalent ions and disordered by large monovalent ions.
`Therefore, water ordering has generally been interpreted in terms
`of ion charge densities.17,27 Charge densities are high on ions
`that have a small radius and/or a large charge.
`A related property is the Hofmeister effect.28 In 1888,
`Hofmeister reported that salts affect the solubilities of proteins
`in water to varying degrees. This has been interpreted as a
`modulation of the hydrophobic effect by salts because it is also
`found that increasing salt concentration reduces the solubilities
`of simple hydrophobic solutes such as benzene in aqueous
`solutions.29,30 The Hofmeister series is a list of ions rank-ordered
`in terms of how strongly they modulate hydrophobicity. Such
`salt effects on nonpolar solubilities correlate with charge
`densities of the salts. Small ions tend to cause “salting out”,
`that is, to reduce hydrophobic solubilities in water, whereas large
`ions tend to cause “salting-in”, increasing nonpolar solubilities.
`The Hofmeister series, however, does not correlate perfectly
`with ionic charge density: while lithium is smaller than sodium,
`lithium has a weaker Hofmeister effect.
`The Hofmeister effect is directly proportional to salt con-
`centration and modeled by the Setschenow equation:31
`
`ln[ci/ci(0)] ) -kscs
`
`(2)
`
`where ci and ci(0) are the molar solubilities of the hydrophobe
`in a salt solution and water, respectively, cs is the molar
`concentration of the salt, and ks is the salt’s Setschenow salting-
`out coefficient.
`There are various microscopic perspectives on these proper-
`ties. Smith32 and Kalra et al.33 have calculated Setschenow
`
`(26) Kaminsky, M. Discuss. Faraday Soc. 1957, 24, 171-179.
`(27) Collins, K. D. Biophys. J. 1997, 72, 65-76.
`(28) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247-260.
`(29) McDevit, W. F.; Long, F. A. J. Am. Chem. Soc. 1952, 74, 1773-1777.
`(30) von Hippel, P. H.; Schleich, T. Acc. Chem. Res. 1969, 2, 257-265.
`(31) Baldwin, R. L. Biophys. J. 1996, 71, 2056-2063.
`(32) Smith, P. E. J. Phys. Chem. B 1999, 103, 525-534.
`
`coefficients from molecular dynamics simulations. In their
`simulations, the hydrophobe-ion pair distribution functions
`show that strongly salting-out (small) ions are generally excluded
`from the nonpolar solute’s first water shell.
`In 1957, Samoilov15,16 proposed that dynamic properties, such
`as the viscosity, could be understood in terms of the activation
`energy required to strip a water molecule away from the first
`solvation shell of an ion as compared to that for another water,
`¢Ei ) Ei - E0. E0 is the activation energy for the process of
`transferring a water molecule from a first shell around another
`water molecule to its next coordination shell, and Ei is the
`corresponding activation energy for a water molecule in an ion
`coordination shell.15 A water molecule “binds” to a small ion
`more tightly than it binds to a neighboring water molecule,
`resulting in a positive activation energy, while water molecules
`next to big ions are more mobile than bulk water molecules
`(¢Ei < 0).
`Collins27 proposed that ion effects on water structure could
`be explained by a competition between ion-water interactions,
`which are dominated by charge density effects, and water-
`water interactions, which are dominated by hydrogen bonding.
`He explained that anions are stronger than cations at water
`ordering because of the asymmetry of charge in a water
`molecule:
`the negative end of water’s dipole is nearer to the
`center of the water molecule than the positive end. Therefore,
`anions see a larger electrostatic potential at the surface of a water
`molecule than cations see. Our preliminary calculations indi-
`cate34 that the solvation model of Collins yields qualitative
`agreement with the experimental data. We were motivated by
`Collins’ insightful qualitative model to make a more quantitative
`statistical mechanical model.
`
`2. The Model and Simulation
`
`We wanted a model that (1) is physical, that is, based on an
`energy function related to the structure of water, and (2) is
`computationally efficient enough to sample the spatial and
`energetic distributions of water molecules. High-resolution all-
`atom simulations are computationally intensive, particularly for
`studies, such as Hofmeister effects, that involve three species:
`water, ion, and nonpolar solute. Here we use the MB model, in
`which each water molecule is represented as a two-dimensional
`disk that interacts with other waters through a Lennard-Jones
`(LJ) interaction and through an orientation-dependent hydrogen-
`bonding (HB) interaction. The name “MB” arises because there
`are three hydrogen-bonding arms, arranged as in the Mercedes
`Benz logo (Figure 1). There are various anomalous properties
`of pure water35-39 including the density anomaly, a minimum
`in isothermal compressibility, and a large heat capacity; they
`are reproduced qualitatively by the MB model.40 The model
`
`(33) Kalra, A.; Tugcu, N.; Cramer, S.; Garde, S. J. Phys. Chem. B 2001, 105,
`6380-6386.
`(34) Kalyuzhnyi, Yu. V.; Vlachy, V.; Dill, K. Acta Chim. SloV. 2001, 48, 309-
`316.
`(35) Eisenberg, D.; Kauzmann, W. The Structure and Properties of Water;
`Oxford University Press: Oxford, 1969.
`(36) Franks, F., Ed. Water, A ComprehensiVe Treatise; Plenum Press: New York,
`1972-1982; Vols. 1-7.
`(37) Stillinger, F. H. Science 1980, 209, 451-457.
`(38) Zhu, S. B.; Singh, S.; Robinson, G. W. AdV. Chem. Phys. 1994, 85, 627-
`731.
`(39) Robinson, G.; Zhu, S. B.; Singh, S.; Evans, M. Water in Biology, Chemistry,
`and Physics: Experimental OVerViews and Computational Methodologies;
`World Scientific: Singapore, 1996.
`(40) Silverstein, K. A.; Haymet, A. D. J.; Dill, K. A. J. Am. Chem. Soc. 1998,
`120, 3166-3175.
`
`J. AM. CHEM. SOC. 9 VOL. 124, NO. 41, 2002 12303
`
`MYLAN INST. EXHIBIT 1121 PAGE 2
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`

`

`A R T I C L E S
`
`Hribar et al.
`
`center of each water molecule, at a distance 0.35 rHB from the
`surface of the water disk. A single positive charge is put onto
`one of the H-bonding arms, at a distance 0.165 rHB from the
`center and 0.185 rHB from the molecule surface. The other two
`H-bonding arms are uncharged. This position was chosen to
`match the radius of a Na+ ion, because sodium ions are found
`experimentally to cause no change in the entropy of nearby
`water molecules (¢SII ) 0).17
`Several other dipole orientations with two or three charges
`were also tested. However, the model described here was unique
`in giving qualitatively correct results for water-water liberation
`free energies and assumed structuring and was used for further
`analysis.
`An ion interacts with the charges on a water molecule through
`a screened potential:
`
`Ucharge
`
`
`
`) zizjj(cid:15)HB
`
`jRexp(-(cid:20)rij)
`rij
`
`(7)
`
`Figure 1. The MB-dipole model. (a) Two MB-dipole waters forming a
`hydrogen bond. (b) A cation and an MB-dipole water oriented in its most
`favorable orientation (180(cid:176) with respect to the vector connecting the
`molecular centers). Also an anion and a water oriented in its most favorable
`orientation (0(cid:176)).
`
`also captures qualitatively the properties of the water as a solvent
`for nonpolar solutes41,42 - the hydrophobic effect.40,43
`In the MB model, the energy of interaction between two
`waters is
`
`Uww(Xi, Xj) ) ULJ(rij) + UHB(Xi, Xj)
`
`(3)
`
`where rij is the distance between the ion center and a charge on
`a water dipole, and the valences zi (zj) are +1 or -1. All of the
`distances are in the units of rHB. Various considerations are
`involved in choosing this functional form. First, while a
`logarithmic dependence on r is appropriate for a true 2-D
`system, our model interactions are chosen to be consistent with
`three-dimensional Coulomb’s law. Our model r-1 dependence
`is appropriate for a two-dimensional slice through a three-
`dimensional system. Second, following others,44-47 we use a
`screened Coulomb potential, rather than a simple Coulombic
`interaction. We use this for computational efficiency. Several
`groups have shown that when the properties of interest involve
`only near-neighbor effects, such as those of interest here, the
`screened Coulomb potential represents an excellent approxima-
`tion to the Coulomb potential.48-51 The parameter (cid:20) ) 0.1 is
`small enough that the interaction potential at short distances
`would not differ substantially from that of a pure Coulombic
`potential. Decreasing the screening parameter (cid:20) did not influence
`the results.
`The last parameter, R ) 2.27, is chosen so that when a
`negative ion with a radius 0.35 rHB (the distance of a negative
`charge from the surface of a water molecule) or a positive ion
`with a radius 0.185 rHB is in its most favorable position relative
`to a water molecule, the electrostatic energy equals the hydrogen
`bond energy ((cid:15)HB ) -1).
`The ion-water pair potential is
`Uiw(Xi, Xj) ) ULJ(rij) + (cid:229)
`
`Ucharge(Xi, Xj)
`
`(44) Hassan, S. A.; Guarnieri, F.; Mehler, E. L. J. Phys. Chem. B 2000, 104,
`6478-6489.
`(45) Ferreira, P. G.; Dymitrowska, M.; Belloni, L. J. Chem. Phys. 2000, 113,
`9849-9862.
`(46) Bhattacharya, A.; Mahanti, S. D. J. Phys.: Condens. Matter 2001, 13,
`1413-1428.
`(47) Hassan, S. A.; Mehler, E. L. Int. J. Quantum Chem. 2001, 183, 193-202.
`(48) Larsen, B.; Rodge, S. A. J. Chem. Phys. 1980, 72, 2578-2586.
`(49) Rodge, S. A.; Hafskjold, B. Acta Chem. Scand. 1981, A35, 263-273.
`(50) Leote de Carvalho, R. J. F.; Evans, R. Mol. Phys. 1997, 92, 211-228.
`(51) Hribar, B.; Vlachy, V. Langmuir 2001, 17, 2043-2046.
`
`The notation is the same as in previous papers: Xi denotes a
`vector representing both the coordinates and the orientation of
`the ith water molecule, and rij is the distance between the
`molecular centers of molecules i and j. The LJ term is
`
`ULJ(rij) ) 4(cid:15)LJ[((cid:243)LJ
`)12
`
`rij
`
`)6]
`-((cid:243)LJ
`
`rij
`
`(4)
`
`where (cid:15)LJ and (cid:243)LJ are the well-depth and contact parameters,
`respectively. In addition, neighboring water molecules form an
`explicit hydrogen bond when an arm of one water molecule
`aligns with an arm of another water molecule, with an energy
`function that is a Gaussian function of separation and angle:
`
`UHB(Xi, Xj) ) (cid:15)HBG(rij
`
`3
`
`- rHB) (cid:229)
`
`k,l)1
`
`G(ik
`
`(cid:226)uij
`
`
`
`- 1)G(jl(cid:226)uij
`
`+ 1)
`
`where G(x) is an unnormalized Gaussian function:
`G(x) ) exp[-x2/2(cid:243)2]
`
`(5)
`
`(6)
`
`The unit vector ik represents the kth arm on the ith particle
`(k ) 1, 2, 3), and uij is the unit vector joining the center of
`molecule i to the center of molecule j (Figure 1a). H-bonding
`arms are not distinguished as donors or acceptors; only the
`degree of alignment of two arms determines the strength of a
`hydrogen bond.
`The model parameters are as defined previously.40 The
`parameters (cid:15)HB ) -1 and rHB ) 1 define the optimal hydrogen
`bond energy and bond length, respectively. The same width
`parameter (cid:243) ) 0.085 is used for both the distance and the angle
`deviation of a hydrogen bond. The interaction energy in the
`Lennard-Jones potential function, (cid:15)LJ, is 1/10 of (cid:15)HB, and the LJ
`contact distance is 0.7 of that of rHB.40 Radii for ions are given
`in units of rHB.
`Here, we modified the MB model by including an electrostatic
`dipole (see Figure 1b). A single negative charge is put at the
`
`(41) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological
`Membranes; Wiley: New York, 1980.
`(42) Ben-Naim, A. Hydrophobic Interactions; Plenum Press: New York, 1983.
`(43) Southall, N. T.; Dill, K. A. J. Phys. Chem. B 2000, 104, 1326-1331.
`
`12304 J. AM. CHEM. SOC. 9 VOL. 124, NO. 41, 2002
`
`+,-
`The diameter, (cid:243)LJ, is different for different ions ((cid:243)LJ ) ((cid:243)ion +
`(cid:243)water)/2), while the well depth for the Lennard-Jones potential,
`(cid:15)LJ, is taken to be the same for all ions, for simplicity. More
`realistic models would use different LJ parameters for each ion
`
`(8)
`
`MYLAN INST. EXHIBIT 1121 PAGE 3
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`

`How Ions Affect the Structure of Water
`
`Table1. The Crystal Ionic Radii, and Experimentally Obtained
`Thermodynamics of the Ion Solvationa
`
`ion
`Li+
`Na+
`K+
`Rb+
`Cs+
`F-
`Cl-
`Br-
`I-
`
`rM
`0.060
`0.095
`0.133
`0.148
`0.169
`0.136
`0.181
`0.195
`0.216
`
`hydration
`number
`
`4.1
`5.9
`7.2
`7.8
`9.6
`6.4
`7.4
`7.2
`8.1
`
`¢Ghyd
`-116
`-62
`-41
`-35
`-26
`-73
`-46
`-44
`-34
`
`¢Hhyd
`-129
`-70
`-46
`-39
`-29
`-80
`-49
`-47
`-36
`
`¢Shyd
`-32
`-22
`-13
`-11
`-8
`-24
`-13
`-11
`-7
`
`a Shown are the crystal ionic radii, rM,55 with the experimentally obtained
`thermodynamics of the ion solvation: change of Gibbs free energy, ¢Ghyd,
`enthalpy, ¢Hhyd, and entropy, ¢Shyd, of hydration58 per first-shell water
`molecule. Hydration numbers are taken from ref 60. Ion radii are given in
`nanometers, ¢Ghyd is in units of kJ/mol/hydration number, ¢Hhyd is in kJ/
`mol/hydration number, and ¢Shyd is in J/K/hydration number.
`
`Figure2. Pair correlation functions of water around ions. (a) Cations and
`(b) anions. Smaller ions have tighter water shells, at reduced temperature
`T* ) 0.20.
`
`type.52 While adding such a parameter is likely to improve our
`agreement with experiments, our aim here is to develop the
`simplest model for studying ion charge density effects. This
`model is also simplified in that the dipole on each water
`molecule interacts only with ions, not with dipoles on other
`waters. One of the reasons for using the explicit hydrogen bonds
`versus a dipole-dipole interaction is its quantum mechanical
`character which is better treated with the “effective” pair
`potential.53 Further, the two-dimensional water models using
`only an electrostatic interaction were unsuitable for describing
`the anomalous volumetric properties of water.54
`Ion sizes in our model were taken from crystal ionic radii.55
`The crystal radii are collected in Table 1, and the model ion
`sizes are collected in Table 2. The relative sizes were calculated
`from crystal radii. The conversion factor was determined
`assuming that the negative proportion of the water molecule
`used by Collins27 (rneg ) 1.78 Å) corresponds to the MB-dipole
`water molecule radius, (cid:243)/2 ) 0.35 rHB. Reduced units are used
`throughout this paper - all energies and temperatures are
`normalized to the strength of an optimal hydrogen bond energy
`(e.g., T* ) kBT/j(cid:15)HBj, U* ) U/j(cid:15)HBj. Similarly, all distances
`are scaled by the length of an idealized hydrogen bond (e.g.,
`V* ) V/rHB
`2 ). We call this the MB-dipole model.
`We studied this model through Monte Carlo simulations in
`the isobaric (NPT) ensemble.56 A single (positive or negative)
`ion was fixed in the center of a simulation box. Monte Carlo
`
`(52) Hummer, G.; Pratt, L. R.; Garcia, A. E. J. Phys. Chem. 1996, 100, 1206-
`1215.
`(53) Ben-Naim, A. Water and Aqueous Solutions; Plenum Press: New York,
`1974.
`(54) Okazaki, K. J. Chem. Phys. 1981, 75, 5874-5884.
`(55) Marcus, Y. Ion SolVation; Wiley-Interscience: New York, 1985.
`(56) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford
`University Press: Oxford, 1987.
`
`A R T I C L E S
`
`Figure3. Angular distribution functions for waters in the first shell around
`an ion, for (a) cations and (b) anions at T* ) 0.20. Large cations help
`promote hydrogen bonding of neighboring waters, leading to a single peak.
`For small cations, the electrostatic mechanism competes with the hydrogen
`bond mechanism for ordering waters. The reverse applies to anions. For
`small anions, the electrostatic mechanism dominates; for large anions,
`electrostatic and hydrogen-bonding mechanisms compete.
`
`steps are displacements and rotations of the water molecules;
`details are given in ref 40. The simulations were usually
`performed on 120 water molecules. The first 107 steps were
`used to equilibrate the system, and then statistics were collected
`over the following 5 (cid:2) 108 steps. Pair distribution functions,
`gij(r), and thermodynamic properties (energy, enthalpy, volume)
`were calculated as ensemble averages.56 In addition, the free
`energy, enthalpy, and entropy of transferring an ion or a
`hydrophobe into a solution were calculated using the Widom
`test-particle method57 and using related fluctuation formulas.40
`The results were compared to the molar Gibbs free energy,
`enthalpy, and entropy of hydration and the standard partial molar
`volume of ions.55,58 The experimental values are adjusted to
`correspond the process of ion transfer into the solution studied
`here as defined by the Ben-Naim standard state.58
`Because Hofmeister effects are linear in ion concentration8,9
`and because anion and cation effects are generally additive and
`independent,8,9 we study Hofmeister effects using a water box
`that contains a single nonpolar solute and a single ion. We
`performed model hydrophobe transfers (with a disk of the same
`size as water molecule, (cid:243) ) 0.7) from an isolated phase into
`equilibrated systems of an ion and 60 water molecules.
`Hofmeister effects in the MB-dipole model were also calculated
`by examining the potential of mean force (pmf) between an
`individual ion and a nonpolar solute at infinite dilution, using
`the Widom method of Shimizu and Chan.59 The potential of
`mean force converged to a value near zero at the largest
`separations measured and did not require other adjustments to
`attain values near zero.
`
`3. Results: Water Ordering around Ions
`
`First, we studied the structure of MB-dipole water around
`ions. Figure 2a and b shows the ion-water pair distribution
`functions for cations and anions of different sizes. The sizes
`represent very small (Li+, F-), intermediate (Na+, Cl-), and
`large (Cs+, I-) ions. These figures show that the smaller ions
`are bound more closely to water molecules than are larger ions.
`Figure 3 shows the angular distributions of first-shell waters
`around ions. The angle is of a water’s dipole vector relative to
`the vector connecting the water and ion centers. The favored
`angle is ı ) 0 for a water molecule adjacent to an anion, because
`water points the positive end of its dipole directly at the anion
`(see Figure 3b). The favored angle is ı ) 180(cid:176)
`for a water
`
`(57) Widom, B. J. Chem. Phys. 1963, 39, 2808-2812.
`(58) Marcus, Y. Biophys. Chem. 1994, 51, 111-127.
`(59) Shimizu, S.; Chan, H. S. J. Am. Chem. Soc. 2001, 123, 2083-2084.
`
`J. AM. CHEM. SOC. 9 VOL. 124, NO. 41, 2002 12305
`
`MYLAN INST. EXHIBIT 1121 PAGE 4
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`MYLAN INST. EXHIBIT 1121 PAGE 4
`
`

`

`A R T I C L E S
`
`Hribar et al.
`
`Table2. Ion Diameters Used in the MB-Dipole Model, and Ion Insertion Thermodynamics into MB-Dipole Watera
`
`ion
`Li+
`Na+
`K+
`Rb+
`Cs+
`F-
`Cl-
`Br-
`I-
`
`(cid:243)
`
`0.24
`0.37
`0.52
`0.58
`0.66
`0.53
`0.71
`0.77
`0.85
`
`hydration
`number
`
`3.29
`3.50
`4.01
`4.38
`4.53
`4.12
`4.35
`4.55
`4.83
`
`¢Ghyd
`-16.01 ( 0.04
`-12.09 ( 0.06
`-8.22 ( 0.03
`-6.82 ( 0.03
`-5.78 ( 0.03
`-14.1 ( 0.1
`-7.78 ( 0.08
`-6.4 ( 0.1
`-4.62 ( 0.03
`
`¢Hhyd
`-30.2 ( 0.2
`-24.7 ( 0.3
`-19.4 ( 0.4
`-17.5 ( 0.4
`-16.5 ( 0.5
`-25 ( 3
`-16 ( 2
`-13 ( 1
`-10.8 ( 0.4
`
`¢Shyd
`-24.2 ( 0.3
`-21.6 ( 0.5
`-19.1 ( 0.6
`-18.2 ( 0.8
`-18.2 ( 0.7
`-18 ( 4
`-13 ( 4
`-11 ( 2
`-10.5 ( 0.7
`
`Eel
`-28.59 ( 0.07
`-23.25 ( 0.07
`-17.8 ( 0.1
`
`-14.25 ( 0.05
`-31.9 ( 0.1
`-18.99 ( 0.06
`-16.28 ( 0.05
`-13.5 ( 0.1
`
`a Shown are ion diameters used in the MB-dipole model, (cid:243), and the change in Gibbs free energy, ¢Ghyd, enthalpy, ¢Hhyd, entropy, ¢Shyd, and electrostatic
`energy, ¢Eel, per first-shell water molecule, for ion insertion in MB-dipole water, as obtained from the Widom insertion method at T* ) 0.20. Ion radii are
`given in reduced units for the MB-dipole model. ¢Ghyd, ¢Hhyd, and ¢Shyd have the same units as in Table 11, assuming (cid:15)HB in the MB-dipole model has
`an energy of 24.37 kJ/mol.53
`
`molecule adjacent to a cation, because water points the positive
`end of its dipole directly away from the ion (Figure 3a). Figure
`3 shows that first-shell waters around an ion are highly oriented,
`dominated by these preferred orientations.
`Figure 3 shows that water orientations result from a balance
`between this electrostatic ordering mechanism and the water-
`water hydrogen-bonding ordering mechanism. For the smallest
`anions (F- and Cl-), the electrostatic mechanism dominates:
`water molecules orient to achieve the most favorable electrostatic
`orientation with respect to the ion. This is supported by all-
`atom classical force-field studies of anions in small clusters of
`water.60-64 Yet for larger anions (I-), the first-shell water
`orientational distribution has two peaks. In that case, water’s
`orientation is a compromise between the electrostatic tendency
`to orient the dipole with respect to the ion and the hydrogen-
`bonding tendency to orient two adjacent water molecules in the
`ion’s first shell.
`The same balance applies to cations, except that the size
`tendency is reversed. Figure 3a shows that the large cations
`(Cs+) cause a single-peaked and narrow angular distribution of
`water because the electrostatic tendency is compatible with the
`hydrogen-bonding tendency in this case. In contrast, the smaller
`cations lead to double-peaked distributions, implying that the
`water-water hydrogen bonds are “bending” the dipole angles.
`Such configurations are also seen in all-atom calculations of
`intermediate size cation-water cluster structures.65-68 The
`exception is the Li+ water cluster structure69 which will be
`discussed in more detail below.
`Figure 4 shows the average number of hydrogen bonds made
`by a water molecule within the first water shell around an ion.
`This quantity shows the balance between electrostatics and
`hydrogen bonding. It shows that for the large cations, electro-
`statics assists in the formation of water-water hydrogen bonds,
`while for all other ions, electrostatics competes against hydrogen
`bond formation. The ions having the highest charge densities
`
`(60) Lee, S. H.; Rasaiah, J. C. J. Phys. Chem. 1996, 100, 1420-1425.
`(61) Xantheas, S. S.; Dang, L. X. J. Phys. Chem. 1996, 100, 3989-3995.
`(62) Bryce, R. A.; Vincent, M. A.; Malcolm, N. O. J.; Hillier, I. H. J. Chem.
`Phys. 1998, 109, 3077-3085.
`(63) Sremaniak, L. S.; Perera, L.; Berkowitz, M. L. J. Phys. Chem. 1996, 100,
`1350-1356.
`(64) Ayala, R.; Martinez, J. M.; Pappalardo, R. R.; Marcos, E. S. J. Phys. Chem.
`A 2000, 104, 2799-2807.
`(65) Kollman, P. A.; Kuntz, I. D. J. Am. Chem. Soc. 1972, 94, 9236-9237.
`(66) Kollman, P. A.; Lybrand, T.; Cieplak, P. J. Chem. Phys. 1988, 88, 8017.
`(67) Caldwell, J. W.; Kollman, P. A. J. Phys. Chem. 1992, 96, 8249-8251.
`(68) Ramaniah, L. M.; Bernasconi, M.; Parinello, M. J. Chem. Phys. 1999, 111,
`1587-1591.
`(69) Lyubartsev, A. P.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 2001, 114,
`3120-3126.
`
`12306 J. AM. CHEM. SOC. 9 VOL. 124, NO. 41, 2002
`
`Figure4. The average number of the water-water hydrogen bonds, Æ HBæ ,
`per water molecule in the first shell around various ions at T* ) 0.20.
`
`Figure5. Snapshots of waters in the first (shaded) and second shell (white)
`around an ion (black), showing likely configurations of water as inferred
`from statistics of pair distributions, angular orientations, and hydrogen
`bonding at T* ) 0.20.
`
`(F-, for example) are the most disruptive of water-water
`hydrogen bonding. All-atom ion-water simulations show
`overall breaking of hydrogen bonds (relative to bulk water) in
`small clusters around ions with high charge density.70,71
`However, in contrast to our MB-dipole model results, hydrogen
`bond formation is more probable between water molecules
`clustered around anions than around cations.71
`Figure 5 summarizes these results. Small cations orient first-
`shell waters through an electrostatic mechanism, disrupting
`hydrogen bonding among first-shell waters. Increasing the cation
`size diminishes the electrostatic force of the ion on the water,
`leading to increased water-water hydrogen bonding, as would
`be seen around nonpolar solutes. A similar trend occurs for
`anions: water structure around small anions is controlled by
`
`(70) Combariza, J. E.; Kestner, N. R. J. Phys. Chem. 1995, 99, 2717-2723.
`(71) Topol, I. A.; Tawa, G. J.; Burt, S. K.; Rashin, A. A. J. Chem. Phys. 1999,
`111, 10998-11014.
`
`MYLAN INST. EXHIBIT 1121 PAGE 5
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`MYLAN INST. EXHIBIT 1121 PAGE 5
`
`

`

`How Ions Affect the Structure of Water
`
`A R T I C L E S
`
`an electrostatic mechanism, while water structure around larger
`anions is controlled by hydrogen bonding. A notable difference
`between anions and cations is the ion size required to achieve
`a given level of water ordering. Larger anions have the same
`effect on water ordering as smaller cations. For example, F-
`and Li+ affect water ordering to about the same degree even
`though F- is a larger ion. This arises in the MB-dipole model,
`as it does in the Collins hypothesis,27 from the anisotropic charge
`distribution of the water dipole. In its optimal configuration,
`the + end of a water dipole is about the same distance from
`the center of a F- ion as the - end of a water dipole is from
`the center of a Li+ ion. This sort of asymmetry is also reflected
`in the experimental properties, as indicated below.
`
`4. Viscosity Experiments on Chaotropes and
`Kosmotropes
`
`To test the MB-dipole model against these water structuring
`experiments, we follow the idea of Chong and Hirata,72 who
`proposed that the viscosity enhancement or reduction due to
`ion effect, as reflected in Samoilov’s E0 and Ei, is proportional
`to the