- Email: [email protected]
Monte Carlo study of the temperature dependence of the hydrophobic hydration of benzene
5 November 1999
Chemical Physics Letters 313 Ž1999. 235–240 www.elsevier.nlrlocatercplett
Monte Carlo study of the temperature dependence of the hydrophobic hydration of benzene Sergio Urahata, Sylvio Canuto ´
)
Instituto de Fısica, UniÕersidade de Sao ´ ˜ Paulo, CP 66318, 05315-970 Sao ˜ Paulo, SP, Brazil Received 28 January 1999; in final form 17 May 1999
Abstract We present results for the temperature dependence of the hydrophobic hydration of benzene in water. Using long Monte Carlo simulations, we studied structural characteristics of the system formed by one molecule of benzene surrounded by 343 molecules of water. The temperature ranged from 280 to 340 K. We verify that molecules of water make stronger hydrogen bonds in the first hydration shell of benzene than in the bulk region, indicating the formation of a more organized structure around benzene. Also, the reduced number of hydrogen bonds per molecule of water close to benzene gives additional insight about its hydrophobic behavior. The effect of temperature on hydrogen bonds in water close to benzene is analyzed in detail. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Non-polar molecules have low solubility in water, over a wide range of temperatures w1x. This is the so-called hydrophobic effect w2,3x. The analysis of this effect is usually divided in two topics: hydrophobic hydration w6,11x and hydrophobic interaction w12,15x. The first uses thermodynamics and structural and dynamic properties of the solvent to deal with the complex hydration process of one non-polar molecule. The latter focuses on the solvent-induced interaction between two or more molecules of solute. The thermodynamic explanation for the imiscibility of non-polar molecules with water derives from
) Corresponding author. Fax: q55-11-818-6831; e-mail: [email protected]
several experimental observations w2,3x. In general, when a non-polar solute is transferred from the gas phase to aqueous solution, the variation of the Gibbs free energy is positive w4x. As the variation of enthalpy is negative for solvation, the entropy variation should be negative, suggesting that the solvent structure surrounding a non-polar molecule is more organized w5x. The presence of a non-polar solute favors the hydrogen bonding among the molecules of water in its hydration shell, increasing the degree of structuring of water. This increased order would be responsible for the imiscibility of non-polar molecules in water, since the entropic term is responsible for the largest contribution to the free energy w5x. Increasing temperature could favor even more that contribution. However, the temperature dependence of the hydrophobic hydration is more complex, and there has been some recent theoretical interest derived from computer simulation w7,8,11x.
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 1 8 - 0
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S. Urahata, S. Canutor Chemical Physics Letters 313 (1999) 235–240
The modern view of the hydrophobic effect involves the hydrogen bonds between the molecules of water surrounding the non-polar solute. This relates to several chemical and biological processes w2,16,17x. Cheng and Rossky w18x studied the dynamics of bond formation and bond breaking in the condensed phase, showing that the processes involved are not simple, with both bond creation and bond destruction rates described by non-linear kinetics. This suggests a complex engagement of hydrogen bonds around a non-polar solute. In an attempt to obtain better understanding of these processes, computer simulations emerge as an important tool to analyze microscopically the properties of these solutions. Simulations provide control of macroscopic parameters that affect liquid properties, as well as an excellent molecular visualization, which is rather difficult to obtain experimentally. Motivated by the partial success of these simulations in the description of such aqueous solutions w6–19x, we present here a computational study of the hydrophobic hydration of benzene as a function of temperature. Recent works have been performed with other non-polar compounds, such as ethane w7x, methane w11,12x and noble gases w13x. The dilute aqueous benzene system has been studied before using both molecular dynamics w20x and Monte Carlo simulations w21,22x. Laaksonen et al. w23x studied the hydration of benzene in water at a fixed Žroom. temperature, addressing the molecular and reorientational motion of benzene. Experimental studies of the hydration of benzene in water have been performed using NMR techniques w23,24x. However, a theoretical analysis of the temperature dependence of the benzene–water system is still lacking. Therefore in this Letter, we perform a Monte Carlo simulation of benzene in water to study the hydrophobic hydration. We pay particular attention to the hydrogen bonds both close and far from the non-polar solute.
2. Computational method Monte Carlo simulations are performed in the NVT ensemble w25x using the Metropolis sampling technique w26x. The system consists of one molecule of benzene and 343 molecules of water, keeping all individual molecular geometries rigid during the
whole simulation. These molecules are in the equilibrium geometrical structure: benzene has a D6 h ˚ rCH s 1.09 A˚ and u HCH structure with rCC s 1.44 A, s 1208, and water has a C2 Õ structure with rOH s ˚ and u HO H s 109.478. The potential that de1.00 A scribes the intermolecular interactions is composed of the sum of Lennard-Jones and Coulomb potentials. We used the SPC potential w27x for water and OPLS w28x for benzene. All the molecules are initially randomly distributed inside a cubic box. As usual, we use periodic boundary conditions, image method, and a large cutoff radius R c . The temperatures ranged from 280 to 340 K, to avoid proximity to the transition points of water. For each temperature the water density was obtained from the experimental results w29x. Each simulation consisted of 51.6 = 10 6 Monte Carlo steps after the equilibration stage, which consisted of 1.7 = 10 6 steps. These long simulations are made to assure stable and reliable results for the hydration structures w6x.
3. Results and discussion Table 1 shows the experimental water densities used in the simulation and the calculated average configurational energy per molecule for the different temperatures. The liquid reflects the elevation of temperature with a corresponding increase of the intermolecular energy of all molecules. Varying the temperature from T s 280 to 340 K increases the average energy by less than 1 kcalrmol. To obtain information of the liquid structure, we focus our attention on the pair distribution function g Ž r .. The oxygen–oxygen g Ž r . for water is shown Table 1 Temperature, experimental value of the water density w29x and calculated average internal energy per molecule T ŽK.
r Žgrcm3 .
U Ž kcalr mol .
280 290 300 310 320 330 340
0.9999 0.9985 0.9965 0.9930 0.9894 0.9848 0.9790
y8.71"0.08 y8.48"0.08 y8.28"0.09 y8.10"0.08 y7.89"0.09 y7.72"0.09 y7.51"0.09
S. Urahata, S. Canutor Chemical Physics Letters 313 (1999) 235–240
˚ to around in Fig. 1. It shows a first shell from 2.5 A ˚ In this region, the curves exhibit variations 4.0 A. with temperature that indicate loss of structure of the liquid water with the increase of temperature. This is noted from the relative positions and intensities of the maxima and minima of the curves. The elevation of temperature results in a lowering of all the maxima, showing also that for larger temperatures the second and third peaks nearly disappear. At T s 340 ˚ Hence, for this K g Ž r . is nearly flat beyond 3.5 A. temperature only a first solvation shell of water is well defined. Overall, this result is similar to those obtained with other hydrocarbons such as, for instance, ethane w7x and there is indeed no significant difference with the case of pure bulk water w30x. The carbonŽbenzene. –oxygenŽwater. g Ž r . is shown in Fig. 2. The first hydration shell is clearly discernible for all temperatures with the minima ˚ In the recent literature, an insensibility around 5.6 A. to temperature of the carbon–oxygen pair distribution function is also verified for methane–water w7x and ethane–water w8x. However, even if the curves do not present any significant alteration with temperature elevation, it is clear that the first hydration shell suffers small changes in the intensity and position of the first peak. In a complementary way, the position of the second peak does not change. Therefore, the structural change of the solvent happens inside the first hydration shell. The number of solvent molecules surrounding a solute can be calculated with the integration of the pair distribution function w26x. For the first hydration shell we inte˚ At T s 300 K, there is an grate g CO up to 5.6 A.
Fig. 2. Calculated carbon–oxygen pair distribution function between benzene and water.
average number of 17.2 water molecules in the first solvation shell of benzene. This number, however, changes with temperature and the change is monotonous. The temperature elevation decreases the average number of molecules of water located in the first hydration shell of benzene. From T s 280 to 340 K, the average number of water molecules in the first hydration shell decreases from 17.5 to 15.2. For comparison in the case of methane in water w8x this change in temperature reduces the number of water molecules in the first hydration shell by approximately one molecule, compared to 2.3 found here for the case of benzene–water. We now analyze the carbon–oxygen effective potential. The effective benzene–water intermolecular interaction can be obtained from the so-called potential of mean force w3,31,32x, Ueff , that can be obtained inverting g Ž r ., Ueff Ž r . s yk B T ln Ž g Ž r . . ,
Fig. 1. Calculated oxygen–oxygen pair distribution function of water.
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Ž 1.
where T is the liquid temperature and k B is the Boltzmann constant. We will now verify the way that temperature affects this effective interaction between the molecules of water and the solute. The results are shown in Fig. 3. Also, we show for comparison the intermolecular potential of benzene and water, given by the Lennard-Jones parameters. Fig. 3 shows that the effective interaction between benzene and water is less intense than in the Lennard-Jones benzene–water interaction. As a consequence of the aqueous environment, the benzene–
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Fig. 3. Carbon–oxygen potential of mean force Žkcalrmol. between benzene and water. LJ stands for the curve obtained with the Lennard-Jones potential and the SPCŽwater. and OPLSŽbenzene. parameters. See text.
water interaction decreases. In a previous work, we have shown that the benzene–benzene interaction increases w19x. The solubility of benzene in water, already small, decreases with the temperature. To analyze the hydrogen bonds between the water molecules, we evaluate their structure in the different hydration shells of benzene. To identify one hydrogen bond from the simulations, we adopt the structural definition w7x. In this way, hydrogen bonds are defined according to the rule that oxygen–oxygen ˚ . and hydrogen distance should be smaller than Ž4 A bond angle must be smaller than 308. Using the definitions above, we evaluate the hydrogen bonds in different regions of the hydration of benzene. The bonds will be classified according to three types Žfirst shell, interface and bulk., in agreement with its respective location w8x. When two molecules of water are both located inside the first hydration shell, the hydrogen bond will be classified as first shell hydrogen bond. If both molecules are located outside the first shell, we will have the hydrogen bond of the bulk. Finally, when one molecule is located in the first shell and the other is in the bulk, we have the hydrogen bond of the interface. Fig. 4a shows the average oxygen–oxygen distances of all computed hydrogen bonds. For all temperatures considered the hydrogen bonds of the water in the first solvation shell are shorter than for those in the bulk. At T s 300 K the average oxygen–oxygen distance in the first hydration shell ˚ as compared with 2.91 A˚ in the is found as 2.89 A
˚ is significant and is bulk. This decrease of 0.02 A clearly due to the proximity with the solute benzene molecule. As a hydrogen bond is stronger when the distance between two molecules of water is shorter, our results show stronger hydrogen bonds in the first hydration shell than in the bulk region for all temperatures. Similar behavior is of course found if one uses oxygen–hydrogen distances. This is one direct evidence of the strong hydrogen bond network surrounding benzene. Complementing this result, Fig. 4b shows that the hydrogen bonds close to benzene have a smaller hydrogen bond angle than in the bulk, showing again its stronger character. This reinforces the idea of an enhanced structure of the solvent surrounding the non-polar solute, in order to maintain the hydrogen bond network. Consequently, increasing order in the first hydration shell induces a negative contribution to entropy, that would lead to a lower solubility of benzene with increase of temperature. The average values of the hydrogen bond distance of the interface region are larger than in the first shell and bulk. This is expected, and it just reflects the fact that two molecules of water are located in different hydration shells. The statistical errors oscillate around 13% for T s 280 K and 15%
Fig. 4. Average oxygen–oxygen distance Ža. and the average hydrogen bond angle Žb. in the different hydration shells. The hydrogen bond angle is that formed by the imaginary line between the oxygen atoms and the OH donor bond ŽO PPP OH..
S. Urahata, S. Canutor Chemical Physics Letters 313 (1999) 235–240
for T s 340 K. It is interesting that our results for the benzene–water system shows shorter hydrogen bond distances, and therefore stronger water–water interaction, in the first hydration shell than in the bulk. In the case of methane–water w8x this was seen only after explicit consideration of the average binding energy. In a previous work w19x, we showed that on average the O–H bond of the nearest water is parallel to the plane of benzene. A similar result regarding the relative orientation of the O–H bond near a non-polar solute has been obtained by Guillot et al. w13x. Just as in the non-polar gas dissolved in water w33x, where each gas molecule is wrapped up in a clathrate structure composed of molecules of water, the hydration shell of benzene should be similar to this ‘cage’. The increase of temperature induces a partial disruption of those bonds with a reduction in the number of molecules located in the benzene neighborhood. Previous molecular dynamics simulations w8x and experimental results w24,23x suggest that the enhanced structure of water in the first hydration shell, leads to a smaller mobility of benzene in water. We thus calculate the average number of hydrogen bonds per water ŽNH 2 O .. We show these results in Fig. 5 for all temperatures considered in the simulations and for the water molecules located inside the first shell and in the bulk regions. At T s 300 K every water molecule makes on the average 3.42 hydrogen
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bonds. This number is lower than that for the water molecules in the bulk region. Far from solute benzene, every water molecule makes on average 3.58 hydrogen bonds, as compared to the value of 3.60 for pure bulk water. Thus the water molecules outside the first hydration shell are found to be insensitive to the benzene. The number of hydrogen bonds for the first hydration shell of benzene is found to be smaller than for ethane, indicating that the hydrophobic effect is larger in the benzene case. Indeed, the difference between the coordination number in the first hydration shell of benzene and the bulk is considerably larger than that found for the case for ethane w7x. Fig. 5 also shows how the temperature influences the number of hydrogen bonds per water in the two different hydration regions. Increasing the temperature leads to a monotonic decrease of this number. In particular, molecules of water located close to benzene have on the average a smaller number of hydrogen bonds than in the bulk region. However, at high temperatures this difference decreases. Laaksonen et al. w23x studied at T s 300 K the relative rotational and translational movements of benzene in water, CCl 4 and CS 2 using molecular dynamics and NMR spectroscopy techniques. They found evidence that the average distance of benzene to water is closer than either to CCl 4 or CS 2 , leading to a reduction of the rotational dynamics of benzene. In a recent experimental work, Nakahara et al. w24x studied the dynamics of hydrophobic hydration of benzene using NMR spectroscopy techniques for different temperatures. Their results show that for low temperatures the molecule of benzene possesses larger rotational freedom, suggesting that a clathrate cage is formed around benzene. Our calculated average center of mass distance of benzene to its nearest molecules of water shows a monotonic decrease with the increase in temperature. This is in agreement with the rotational dynamics results of Nakahara et al. w24x. As the temperature increases the average benzene–water distance decreases hindering the rotational freedom. 4. Conclusions
Fig. 5. Average number of hydrogen bonds per water inside the first shell of benzene as compared to those in the bulk.
In this Letter, the hydrophobic hydration of benzene is investigated, and its dependence on tempera-
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ture is analyzed. We demonstrate the existence of a stronger hydrogen bond network around the molecule of benzene, as compared to the bulk region, for all temperatures considered Ž280 - T - 340 K.. We find also that the temperature increase results in a reduction of the number of molecules of water in the first hydration shell of benzene. The molecules of water have their hydrogen bonds weakened on temperature elevation. However, the effects of temperature on the structure of the first hydration shell are larger than in the second shell or in the bulk. This agrees with the idea that the nearest water molecules promote some reorientation, in order to maintain their hydrogen bonds. The water molecules in the first hydration shell make fewer hydrogen bonds than in the bulk region.
Acknowledgements We acknowledge FAPESP and CNPq for financial support. The authors are grateful to Dr. K. Coutinho for continuous discussions. Most of the computations were performed at LCCA–USP.
References w1x H.S. Frank, M.W. Evans, J. Chem. Phys. 13 Ž1945. 507. w2x C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Krieger Publ., Florida, 1991. w3x A. Ben-Naim, Hydrophobic Interactions, Plenum, New York, 1980. w4x M.H. Abraham, J. Am. Chem Soc. 104 Ž1982. 2085. w5x W. Blokzijl, J.B.F.N. Engberts, Angew. Chem., Int. Ed. Engl. 32 Ž1993. 1545. w6x J. Hernandez-Cobos, I. Ortega-Blake, J. Chem. Phys. 103 ´ Ž1995. 9261. w7x R.L. Mancera, A.D. Buckingham, J. Phys. Chem. 99 Ž1995. 14632.
w8x C.H. Bridgeman, A.D. Buckingham, N.T. Skipper, Chem. Phys. Lett. 253 Ž1996. 209. w9x M.H. Abraham, J. Am. Chem. Soc. 104 Ž1982. 2085. w10x P.H.K. de Jong, J.E. Wilson, G.W. Neilson, A.D. Buckingham Mol. Phys. 91 Ž1997. 99. w11x R.L. Mancera, J. Chem. Soc., Faraday Trans. 92 Ž1996. 2547. w12x D. van Belle, S.J. Wodak, J. Am. Chem. Soc. 115 Ž1993. 647. w13x B. Guillot, Y. Guissani, J. Chem. Phys. 99 Ž1993. 8075. w14x C. Pangali, M. Rao, B.J. Berne, J. Chem. Phys. 71 Ž1979. 2982. w15x R.L. Mancera, A.D. Buckingham, Chem. Phys. Lett. 234 Ž1994. 296. w16x K.A. Dill, Biochemistry 79 Ž1990. 7133. w17x J.S. Finer-Moore, L. Liu, D.L. Birdsall, R. Brem, J. Apfeld, D.V. Santi, R.M. Stroud, J. Mol. Biol. 276 Ž1998. 113. w18x Y. Cheng, P.J. Rossky, Nature 392 Ž1998. 696. w19x S. Urahata, K. Coutinho, S. Canuto, Chem. Phys. Lett. 274 Ž1997. 269. w20x P. Linse, J. Am. Chem. Soc. 112 Ž1990. 1744. w21x P. Linse, G. Karlstrom, J. Am. Chem. Soc. 106 ¨ B. Jonson, ¨ Ž1984. 4096. w22x G. Ravishanker, P.K. Mehrotra, M. Mezei, D.L. Beveridge, J. Am. Chem. Soc. 106 Ž1984. 4102. w23x A. Laaksonen, P. Stilbs, R.E. Wasylishen, J. Chem. Phys. 108 Ž1998. 455. w24x M. Nakahara, C. Wakai, Y. Yoshimoto, N. Matubayasi, J. Phys. Chem. 100 Ž1996. 1345. w25x K. Coutinho, S. Canuto, DICE: A Monte Carlo Program for Molecular Liquid Simulation. University of Sao ˜ Paulo, Brazil. w26x M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford Publ., 1989. w27x H.J.C. Berendsen, J.P.M. Postma W.F. van Gunsteren, J. Hermans, in: B. Pullmam ŽEd.., Intermolecular Forces, Reidel, Dordrecht, 1981, p. 331. w28x W.L. Jorgensen, J.D. Madura, C.J. Swenson, J. Am. Chem. Soc. 106 Ž1984. 6638. w29x D.R. Lide ŽEd.., Handbook of Chemistry and Physics, 73rd edn., CRC, Boca Raton, FL, 1993. w30x W.L. Jorgensen, J. Gao, C. Ravimohan, J. Phys. Chem. 89 Ž1985. 3470. w31x L.R. Pratt, D. Chandler, J. Chem. Phys. 67 Ž1977. 3683. w32x G. Ravishanker, M. Mezei, D.L. Beveridge, Faraday Symp. Chem. Soc. 17 Ž1982. 79. w33x D.T. Bowron, A. Filipponi, C. Lobban, J.L. Finney, Chem. Phys. Lett. 293 Ž1998. 33.
Chemical Physics Letters 313 Ž1999. 235–240 www.elsevier.nlrlocatercplett
Monte Carlo study of the temperature dependence of the hydrophobic hydration of benzene Sergio Urahata, Sylvio Canuto ´
)
Instituto de Fısica, UniÕersidade de Sao ´ ˜ Paulo, CP 66318, 05315-970 Sao ˜ Paulo, SP, Brazil Received 28 January 1999; in final form 17 May 1999
Abstract We present results for the temperature dependence of the hydrophobic hydration of benzene in water. Using long Monte Carlo simulations, we studied structural characteristics of the system formed by one molecule of benzene surrounded by 343 molecules of water. The temperature ranged from 280 to 340 K. We verify that molecules of water make stronger hydrogen bonds in the first hydration shell of benzene than in the bulk region, indicating the formation of a more organized structure around benzene. Also, the reduced number of hydrogen bonds per molecule of water close to benzene gives additional insight about its hydrophobic behavior. The effect of temperature on hydrogen bonds in water close to benzene is analyzed in detail. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Non-polar molecules have low solubility in water, over a wide range of temperatures w1x. This is the so-called hydrophobic effect w2,3x. The analysis of this effect is usually divided in two topics: hydrophobic hydration w6,11x and hydrophobic interaction w12,15x. The first uses thermodynamics and structural and dynamic properties of the solvent to deal with the complex hydration process of one non-polar molecule. The latter focuses on the solvent-induced interaction between two or more molecules of solute. The thermodynamic explanation for the imiscibility of non-polar molecules with water derives from
) Corresponding author. Fax: q55-11-818-6831; e-mail: [email protected]
several experimental observations w2,3x. In general, when a non-polar solute is transferred from the gas phase to aqueous solution, the variation of the Gibbs free energy is positive w4x. As the variation of enthalpy is negative for solvation, the entropy variation should be negative, suggesting that the solvent structure surrounding a non-polar molecule is more organized w5x. The presence of a non-polar solute favors the hydrogen bonding among the molecules of water in its hydration shell, increasing the degree of structuring of water. This increased order would be responsible for the imiscibility of non-polar molecules in water, since the entropic term is responsible for the largest contribution to the free energy w5x. Increasing temperature could favor even more that contribution. However, the temperature dependence of the hydrophobic hydration is more complex, and there has been some recent theoretical interest derived from computer simulation w7,8,11x.
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 1 8 - 0
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The modern view of the hydrophobic effect involves the hydrogen bonds between the molecules of water surrounding the non-polar solute. This relates to several chemical and biological processes w2,16,17x. Cheng and Rossky w18x studied the dynamics of bond formation and bond breaking in the condensed phase, showing that the processes involved are not simple, with both bond creation and bond destruction rates described by non-linear kinetics. This suggests a complex engagement of hydrogen bonds around a non-polar solute. In an attempt to obtain better understanding of these processes, computer simulations emerge as an important tool to analyze microscopically the properties of these solutions. Simulations provide control of macroscopic parameters that affect liquid properties, as well as an excellent molecular visualization, which is rather difficult to obtain experimentally. Motivated by the partial success of these simulations in the description of such aqueous solutions w6–19x, we present here a computational study of the hydrophobic hydration of benzene as a function of temperature. Recent works have been performed with other non-polar compounds, such as ethane w7x, methane w11,12x and noble gases w13x. The dilute aqueous benzene system has been studied before using both molecular dynamics w20x and Monte Carlo simulations w21,22x. Laaksonen et al. w23x studied the hydration of benzene in water at a fixed Žroom. temperature, addressing the molecular and reorientational motion of benzene. Experimental studies of the hydration of benzene in water have been performed using NMR techniques w23,24x. However, a theoretical analysis of the temperature dependence of the benzene–water system is still lacking. Therefore in this Letter, we perform a Monte Carlo simulation of benzene in water to study the hydrophobic hydration. We pay particular attention to the hydrogen bonds both close and far from the non-polar solute.
2. Computational method Monte Carlo simulations are performed in the NVT ensemble w25x using the Metropolis sampling technique w26x. The system consists of one molecule of benzene and 343 molecules of water, keeping all individual molecular geometries rigid during the
whole simulation. These molecules are in the equilibrium geometrical structure: benzene has a D6 h ˚ rCH s 1.09 A˚ and u HCH structure with rCC s 1.44 A, s 1208, and water has a C2 Õ structure with rOH s ˚ and u HO H s 109.478. The potential that de1.00 A scribes the intermolecular interactions is composed of the sum of Lennard-Jones and Coulomb potentials. We used the SPC potential w27x for water and OPLS w28x for benzene. All the molecules are initially randomly distributed inside a cubic box. As usual, we use periodic boundary conditions, image method, and a large cutoff radius R c . The temperatures ranged from 280 to 340 K, to avoid proximity to the transition points of water. For each temperature the water density was obtained from the experimental results w29x. Each simulation consisted of 51.6 = 10 6 Monte Carlo steps after the equilibration stage, which consisted of 1.7 = 10 6 steps. These long simulations are made to assure stable and reliable results for the hydration structures w6x.
3. Results and discussion Table 1 shows the experimental water densities used in the simulation and the calculated average configurational energy per molecule for the different temperatures. The liquid reflects the elevation of temperature with a corresponding increase of the intermolecular energy of all molecules. Varying the temperature from T s 280 to 340 K increases the average energy by less than 1 kcalrmol. To obtain information of the liquid structure, we focus our attention on the pair distribution function g Ž r .. The oxygen–oxygen g Ž r . for water is shown Table 1 Temperature, experimental value of the water density w29x and calculated average internal energy per molecule T ŽK.
r Žgrcm3 .
U Ž kcalr mol .
280 290 300 310 320 330 340
0.9999 0.9985 0.9965 0.9930 0.9894 0.9848 0.9790
y8.71"0.08 y8.48"0.08 y8.28"0.09 y8.10"0.08 y7.89"0.09 y7.72"0.09 y7.51"0.09
S. Urahata, S. Canutor Chemical Physics Letters 313 (1999) 235–240
˚ to around in Fig. 1. It shows a first shell from 2.5 A ˚ In this region, the curves exhibit variations 4.0 A. with temperature that indicate loss of structure of the liquid water with the increase of temperature. This is noted from the relative positions and intensities of the maxima and minima of the curves. The elevation of temperature results in a lowering of all the maxima, showing also that for larger temperatures the second and third peaks nearly disappear. At T s 340 ˚ Hence, for this K g Ž r . is nearly flat beyond 3.5 A. temperature only a first solvation shell of water is well defined. Overall, this result is similar to those obtained with other hydrocarbons such as, for instance, ethane w7x and there is indeed no significant difference with the case of pure bulk water w30x. The carbonŽbenzene. –oxygenŽwater. g Ž r . is shown in Fig. 2. The first hydration shell is clearly discernible for all temperatures with the minima ˚ In the recent literature, an insensibility around 5.6 A. to temperature of the carbon–oxygen pair distribution function is also verified for methane–water w7x and ethane–water w8x. However, even if the curves do not present any significant alteration with temperature elevation, it is clear that the first hydration shell suffers small changes in the intensity and position of the first peak. In a complementary way, the position of the second peak does not change. Therefore, the structural change of the solvent happens inside the first hydration shell. The number of solvent molecules surrounding a solute can be calculated with the integration of the pair distribution function w26x. For the first hydration shell we inte˚ At T s 300 K, there is an grate g CO up to 5.6 A.
Fig. 2. Calculated carbon–oxygen pair distribution function between benzene and water.
average number of 17.2 water molecules in the first solvation shell of benzene. This number, however, changes with temperature and the change is monotonous. The temperature elevation decreases the average number of molecules of water located in the first hydration shell of benzene. From T s 280 to 340 K, the average number of water molecules in the first hydration shell decreases from 17.5 to 15.2. For comparison in the case of methane in water w8x this change in temperature reduces the number of water molecules in the first hydration shell by approximately one molecule, compared to 2.3 found here for the case of benzene–water. We now analyze the carbon–oxygen effective potential. The effective benzene–water intermolecular interaction can be obtained from the so-called potential of mean force w3,31,32x, Ueff , that can be obtained inverting g Ž r ., Ueff Ž r . s yk B T ln Ž g Ž r . . ,
Fig. 1. Calculated oxygen–oxygen pair distribution function of water.
237
Ž 1.
where T is the liquid temperature and k B is the Boltzmann constant. We will now verify the way that temperature affects this effective interaction between the molecules of water and the solute. The results are shown in Fig. 3. Also, we show for comparison the intermolecular potential of benzene and water, given by the Lennard-Jones parameters. Fig. 3 shows that the effective interaction between benzene and water is less intense than in the Lennard-Jones benzene–water interaction. As a consequence of the aqueous environment, the benzene–
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Fig. 3. Carbon–oxygen potential of mean force Žkcalrmol. between benzene and water. LJ stands for the curve obtained with the Lennard-Jones potential and the SPCŽwater. and OPLSŽbenzene. parameters. See text.
water interaction decreases. In a previous work, we have shown that the benzene–benzene interaction increases w19x. The solubility of benzene in water, already small, decreases with the temperature. To analyze the hydrogen bonds between the water molecules, we evaluate their structure in the different hydration shells of benzene. To identify one hydrogen bond from the simulations, we adopt the structural definition w7x. In this way, hydrogen bonds are defined according to the rule that oxygen–oxygen ˚ . and hydrogen distance should be smaller than Ž4 A bond angle must be smaller than 308. Using the definitions above, we evaluate the hydrogen bonds in different regions of the hydration of benzene. The bonds will be classified according to three types Žfirst shell, interface and bulk., in agreement with its respective location w8x. When two molecules of water are both located inside the first hydration shell, the hydrogen bond will be classified as first shell hydrogen bond. If both molecules are located outside the first shell, we will have the hydrogen bond of the bulk. Finally, when one molecule is located in the first shell and the other is in the bulk, we have the hydrogen bond of the interface. Fig. 4a shows the average oxygen–oxygen distances of all computed hydrogen bonds. For all temperatures considered the hydrogen bonds of the water in the first solvation shell are shorter than for those in the bulk. At T s 300 K the average oxygen–oxygen distance in the first hydration shell ˚ as compared with 2.91 A˚ in the is found as 2.89 A
˚ is significant and is bulk. This decrease of 0.02 A clearly due to the proximity with the solute benzene molecule. As a hydrogen bond is stronger when the distance between two molecules of water is shorter, our results show stronger hydrogen bonds in the first hydration shell than in the bulk region for all temperatures. Similar behavior is of course found if one uses oxygen–hydrogen distances. This is one direct evidence of the strong hydrogen bond network surrounding benzene. Complementing this result, Fig. 4b shows that the hydrogen bonds close to benzene have a smaller hydrogen bond angle than in the bulk, showing again its stronger character. This reinforces the idea of an enhanced structure of the solvent surrounding the non-polar solute, in order to maintain the hydrogen bond network. Consequently, increasing order in the first hydration shell induces a negative contribution to entropy, that would lead to a lower solubility of benzene with increase of temperature. The average values of the hydrogen bond distance of the interface region are larger than in the first shell and bulk. This is expected, and it just reflects the fact that two molecules of water are located in different hydration shells. The statistical errors oscillate around 13% for T s 280 K and 15%
Fig. 4. Average oxygen–oxygen distance Ža. and the average hydrogen bond angle Žb. in the different hydration shells. The hydrogen bond angle is that formed by the imaginary line between the oxygen atoms and the OH donor bond ŽO PPP OH..
S. Urahata, S. Canutor Chemical Physics Letters 313 (1999) 235–240
for T s 340 K. It is interesting that our results for the benzene–water system shows shorter hydrogen bond distances, and therefore stronger water–water interaction, in the first hydration shell than in the bulk. In the case of methane–water w8x this was seen only after explicit consideration of the average binding energy. In a previous work w19x, we showed that on average the O–H bond of the nearest water is parallel to the plane of benzene. A similar result regarding the relative orientation of the O–H bond near a non-polar solute has been obtained by Guillot et al. w13x. Just as in the non-polar gas dissolved in water w33x, where each gas molecule is wrapped up in a clathrate structure composed of molecules of water, the hydration shell of benzene should be similar to this ‘cage’. The increase of temperature induces a partial disruption of those bonds with a reduction in the number of molecules located in the benzene neighborhood. Previous molecular dynamics simulations w8x and experimental results w24,23x suggest that the enhanced structure of water in the first hydration shell, leads to a smaller mobility of benzene in water. We thus calculate the average number of hydrogen bonds per water ŽNH 2 O .. We show these results in Fig. 5 for all temperatures considered in the simulations and for the water molecules located inside the first shell and in the bulk regions. At T s 300 K every water molecule makes on the average 3.42 hydrogen
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bonds. This number is lower than that for the water molecules in the bulk region. Far from solute benzene, every water molecule makes on average 3.58 hydrogen bonds, as compared to the value of 3.60 for pure bulk water. Thus the water molecules outside the first hydration shell are found to be insensitive to the benzene. The number of hydrogen bonds for the first hydration shell of benzene is found to be smaller than for ethane, indicating that the hydrophobic effect is larger in the benzene case. Indeed, the difference between the coordination number in the first hydration shell of benzene and the bulk is considerably larger than that found for the case for ethane w7x. Fig. 5 also shows how the temperature influences the number of hydrogen bonds per water in the two different hydration regions. Increasing the temperature leads to a monotonic decrease of this number. In particular, molecules of water located close to benzene have on the average a smaller number of hydrogen bonds than in the bulk region. However, at high temperatures this difference decreases. Laaksonen et al. w23x studied at T s 300 K the relative rotational and translational movements of benzene in water, CCl 4 and CS 2 using molecular dynamics and NMR spectroscopy techniques. They found evidence that the average distance of benzene to water is closer than either to CCl 4 or CS 2 , leading to a reduction of the rotational dynamics of benzene. In a recent experimental work, Nakahara et al. w24x studied the dynamics of hydrophobic hydration of benzene using NMR spectroscopy techniques for different temperatures. Their results show that for low temperatures the molecule of benzene possesses larger rotational freedom, suggesting that a clathrate cage is formed around benzene. Our calculated average center of mass distance of benzene to its nearest molecules of water shows a monotonic decrease with the increase in temperature. This is in agreement with the rotational dynamics results of Nakahara et al. w24x. As the temperature increases the average benzene–water distance decreases hindering the rotational freedom. 4. Conclusions
Fig. 5. Average number of hydrogen bonds per water inside the first shell of benzene as compared to those in the bulk.
In this Letter, the hydrophobic hydration of benzene is investigated, and its dependence on tempera-
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ture is analyzed. We demonstrate the existence of a stronger hydrogen bond network around the molecule of benzene, as compared to the bulk region, for all temperatures considered Ž280 - T - 340 K.. We find also that the temperature increase results in a reduction of the number of molecules of water in the first hydration shell of benzene. The molecules of water have their hydrogen bonds weakened on temperature elevation. However, the effects of temperature on the structure of the first hydration shell are larger than in the second shell or in the bulk. This agrees with the idea that the nearest water molecules promote some reorientation, in order to maintain their hydrogen bonds. The water molecules in the first hydration shell make fewer hydrogen bonds than in the bulk region.
Acknowledgements We acknowledge FAPESP and CNPq for financial support. The authors are grateful to Dr. K. Coutinho for continuous discussions. Most of the computations were performed at LCCA–USP.
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