- Email: [email protected]
Fluoride—fluoride association in water from molecular dynamics simulations
Volume 200, number 1,2
CHEMICAL PHYSICS LETTERS
27 November 1992
Fluoride-fluoride association in water from molecular dynamics simulations Liem X. Dang Molecular theory, Modeling and Simulation, Molecular Science Research Center, Pacific Northwest Laboratory, P.O. Box 999, Richland, WA 99352, USA
Received 4 August 1992; in final form 9 September 1992
The potential ofmean force (PMF) for an F--F- ion pair at room temperature was calculated using a rigid simple point charge (SPC/E) water model and molecular dynamics techniques. The PMF displayed a minimum at an ion-ion separation of 4.3 A with a barrier height of approximately 1.5 kcal/mol. The barrier height is a result, in part, of the presence of two water molecules that simultaneously hydrogen bond to both fluoride ions. To investigate the effect of the ionic charge on the hydration properties of an ion pair, we also computed the PMF for the F+-F+ ion pair. Our calculations indicated that the barrier height of this PMF is less significant than the corresponding barrier height observed in the computed PMF of the F--F- ion pair. This result is reasonable because of the absence of the highly favorable hydrogen bonding between water molecules and the ion pair. When comparing the present calculation with those reported in previous works on similar systems using integral equation techniques, our simulated F--F- PMF displays more structure and the minimum well depth is shallower; however, the barrier to dissociation is comparable.
1. Introduction An accurate determination of the interionic potential of mean force (PMF) or solvent-averaged force of an ion pair in water by computer simulation or theoretical techniques remains a central problem in the chemical physics of salvation [ 11. For example, the PMFs for an F--F- ion pair in water or a water-like solvent have been calculated using integral equation techniques [ 2,3]. These calculations indicated strong attractions between the ions near contact. Friedman et al. [l] computed the distinct diffusion coefficients for the F--F- ion pair in water and compared the results with the experimental measurements. They suggested that the PMF with a strong attraction near contact gave incorrect distinct diffusion coefficients. On the other hand, experimental evidence from NMR relaxation studies by Hertz et al. [4,5] on the association of the F--Fion pair in water was inconclusive. Thus, at present,
it appears that a reliable PMF, including the related thermodynamic properties for an F--F- ion pair in water has not yet been established. We feel it is important to compute the PMF using a different approach, such as a computer simulation technique. In this Letter, we present the PMFs obtained from molecular dynamics simulations for an F--F- ion pair in water, In addition to the PMFs, computer simulations also provide detailed solvent configurations around the ion pair. This information will help in understanding the characteristics of the PMF. We computed the PMF for an F+-F+ ion pair in water and compared this information with the PMF of the F--F- ion pair in water. By doing this, we were able to examine how the sign of the ionic charge affects the hydration properties of the ion pair. Details of the calculations and the potential functions are given in section 2. The results are presented and discussed in section 3, our conclusions are summarized in section 4.
Correspondence to: L. X. Dan& Molecular theory, Modeling and Simulation, Molecular Science Research Center, Pacific Northwest Laboratory, P.O. Box 999, Richland, WA 99352, USA.
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
21
CHEMICAL PHYSICS LETTERS
Volume 200, number 1,2
2. Computational methodology We computed the PMF for an ion pair in water using the SPC/E model of water [ 61. This model is a rigid, three-point charge model that predicts the thermodynamic and structural properties of water as well. We derived the ion-water potential parameters so that selective properties of ionic solutions, such as the structural properties and solvation enthalpy, were in accord with experimental data. The functional form of the water-water and ion-water system is given as
(1) where qi and qj refer to charges of different molecules, and A and C are the LJ parameters. The parameters for the SPC/E model and the F- ion are tabulated in table 1. For this particular study, we focused on using the effective pair potentials. Future work will include many-body potentials [ 71. The following expression was used to compute the PMF [8]: A,-A,=-kTln(exp[-/3(U,-Uo)])o.
(21
In this equation, the free energy difference between a reference system, 0, and a perturbed system, 1, is given as a function of the average energy difference between two systems. Here, ( )0 indicates that the average is calculated corresponding to the potential energy describing state 0; k is the Boltzmann constant; T is the absolute temperature; and @equals l/ kT. By performing a series of such calculations along the reaction coordinate, the resulting accumulated free energy changes yield the PMF. The simulations using the Ewald summation tech-
27 November 1992
nique [ 91 consisted of 2 14 water molecules and a pair of ions in a cubic box with a length of 18.62 A. For each calculation, a total of 15 simulations were carried out; a typical simulation consisted of a 7.5 ps equilibration period followed by 60 ps of data collection for each ion-ion separation with a timestep of 1.5 fs. The SHAKE procedure [IO] was adopted to constrain all the bond lengths to their equilibrium values. The average temperature of the system was kept constant at 298 K with the use of a constant temperature algorithm [ 111.
3. Results and discussion Before we discuss the ion-ion PMF, we present selective structural and thermodynamic properties for a single F- ion in water and compare these results with other computer simulations and the experimental data on these systems. The ion-water radial distribution functions, g(r), are shown in fig. 1. The peak positions of gr_o, and gF_Hare identical to the results from computer simulations using many-body potentials [ 71. The peak heights are taller, however, suggesting that the water molecules in the first hydration shell are tightly held by the fluoride ion. In table 2, the results obtained from this work, from
Table 1 Van der Waals parameters and charges for various atoms Atom type
a (A)
E (kcal/mol)
g
0
3.169 0.000 3.118 3.118
0.155 0.000 0.180 0.180
-0.8476 “) 04238 ‘) - 1.0000 t 1.oooo
H FF+ *) Ref. [7].
Fig. 1. Calculated g~_o (solid line) and the g,_, (dashed line) obtained from molecular dynamics simulation of aqueous solutionofF-.
Volume 200, number I ,2
CHEMICAL PHYSICS LETTERS
Table 2 Structural and thermodynamic properties of the F- ion in water at 300 K. Obtained from molecular dynamics simulations
RX, (A) Rm (A) coordination number A&
This work
Ref. [7]
2.70 1.70 6.2 -118
2.70 1.70 5.8 -114
Table 3 Results for the potential of mean force for an aqueous fluoride ion pair from the molecular dynamics simulations at 300 K
Expt.
6.0 I’ -116b’
a) Ref. [ 121. ‘) Ref. [ 131.
F-F pmf/Ewold
L_
2
3
1
5
B
I
27 November 1992
8
r.A
Fig. 2. The PMF for the F--F- ion pair in water of a molecular dynamics simulation at room temperature using an EwaId summation technique.
r (A)
W(r) (kcal/mol)
3.625 3.750 3.875 4.000 4.125 4.250 4.375 4.500 4.625 4.750 4.875 5.000 5.125 5.250 5.375 5.500 5.625 5.750 5.875 6.000 6.125 6.250 6.375 6.500 6.625 6.750 6.875 7.000
3.375 1.782 0.524 0.028 -0.234 -0.299 -0.069 0.141 0.303 0.682 0.972 1.262 I .280 1,248 1.055 0.875 0.620 0.486 0.454 0.378 0.378 0.422 0.511 0.618 0.738 0.736 0.678 0.677
the minimum distance of 4.3 8, is consistent with the requirement for a water molecule with both hydrogens linearly bonded to both F- ions. Fig. 3 displays the computed PMFs for the F--F- ion pair in water as a function of the accumulative time. In general, the shape of these PMFs are very similar, including the positions of the minimum well depths. From these results, we concluded that the simulations with 60 ps of averaging for each ion-ion separation converge reasonably well, and we used these results throughout the analysis. When comparing the present calculations with those reported in previous works on similar systems by Kusalik and Patey [ 3 ] and Friedman et al. [ 11, our simulated F--F- PMF displays more strncture, the minimum well depth is shallower, and the corresponding minimum distance is much larger. However, the barrier to dissociation is comparable. These Also,
other molecular dynamics simulations studies, and from experimental work on these systems are summarized. The PMF for an F--F- interaction in water is shown in fig. 2. The numerical value of the PMF at 7 A corresponds to the primitive model result with a dielectric constant of approximately 70 [ 141. Table 3 contains the PMF as a function of ion-ion separations. This result indicates the presence of a minimum at an ion-ion separation of 4.3 A, with a barrier to dissociation of 1.5 kcal/mol. This minimum is a result, in part, of the highly favorable configurations in which water molecules are simultaneously hydrogen bonded to both fluoride ions. These favorable interactions, including other interactions, result in a sufficiently effective solvent-averaged attraction to offset the repulsion between the ion pair.
23
Volume 200, number 1,2
CHEMICAL PHYSICS LETTERS
27 November 1992
culations using many-body potentials [ 161.
Acknowledgement
0
t
Fig. 5. The PMFs for the ion pair in water of a molecular dynamics simulation using an Ewald summation technique. Circles are the results for the F--F- and the crosses are for the F+-F+.
PMF for the F--F- ion pair interaction. We found that the PMF displays a minimum at an ion-ion separation of 4.3 A with a barrier height of approximately 1.5 kcal/mol. This first PMF minimum is a result of a competition between the effective solventmediated potential and the repulsion between the ion pair. On the molecular level, this strong barrier height is due to the favorable hydrogen bonding between water molecules and the ion pair. These features are similar to those found by Dang et al. [ 15] in their molecular dynamics simulations of the potential of mean force for the Cl--Cl- ion pair in water. To examine the effect of the ionic charge, we computed the PMF for the F+-F+ ion pair in water. From these calculations, we concluded that the sign inversion of the ionic charge produces a significant effect on the characteristics of the PMF of an ion pair in water. We used the approach taken in this study to calculate the PMFs for Na+-F- and Na+-Na+ ion pairs in water. Even though no experimental data on these PMFs exists, one can test the calculated PMFs against various solution measurements, such as the distinct diffusion coefficients [ 11. In closing, it will be of interest to compare the present results with the cal-
I wish to thank Professor Monte Pettitt at the University of Houston for many helpful discussions and continuing support. This work was performed under the auspices of the Division of Chemical Sciences, Offrce of Basic Energy Sciences, US Department of Energy (DOE) under Contract DE-AC06-76RLO 1830 with Battelle Memorial Institute, which operates the Pacific Northwest Laboratory.
References [ 1] H.L. Friedman, F.O. Raineri and M.D. Wood, Chem. Scripta 29A (1989) 49. [2] B.M. Pettitt and P.J. Rossky, .I. Chem. Phys. 84 (1986) 5836. [3] PG. Kusalik and G.N. Patty, J. Chem. Phys. 89 (1988) 5843. [4] H.G. Hertz and C. Radle, Ber. Bunsenges. Physik. Chem. 78 (1974) 509. [ 5 1K.J. Muller and H.G. Hertz, Ber. Bunscnges. Physik. Chem. 140 (1984) 31. [ 61 H.J.C. Berendsen, J.R. Grigera andT.P. Straatsma, J. Phys. Chem. 87 (1987) 6269. [7] L.X. Dang, J. Chem. Phys. 96 (1992) 6970. [S] J.G. Kirkwood, J. Chem. Phys. 3 (1930) 300; R.W. Zwanzig, J. Chem. Phys. 22 (1954) 1420. [9] S.W. de Leeuw, J.W. Perram and E.R. Smith, Proc. Roy. Sot. A 373 (1980) 27. [ 10[ J.-P. Ryckaert, G. Ciccotti and H.J.C. Berendsen, J. Comput. Phys. 23 (1977) 327. [ll] H.J.C. Berendsen, J.P.M. Postma, A. Di Nola, W.F. Van Gunsteren and J.R. Haak, J. Chem. Phys. 81 ( 1984) 3684. [ 121A.H. Narten, J. Phys. Chem. 74 (1970) 765. [ 131H.L. Friedman and C.V. Krischnan, in: Water: a comprehensive treatise, Vol. 6, ed. P. Franks (Plenum Press, NewYork, 1973) p. 1. [ 141M. Rami-Reddy and M. Berkowitz,Chem. Phys. Letters 155 (1989) 173; K. Watanabe and M.L. Klein, Chem. Phys. 131 (1989) 57. [ 151L.X. Dang and B.M. Pettitt, I. Chem. Phys. 86 ( 1987) 6560; J. Am. Chem. Sot. 109 (1987) 2507. [ 16] L.X. Dang, Research in progress.
25
CHEMICAL PHYSICS LETTERS
27 November 1992
Fluoride-fluoride association in water from molecular dynamics simulations Liem X. Dang Molecular theory, Modeling and Simulation, Molecular Science Research Center, Pacific Northwest Laboratory, P.O. Box 999, Richland, WA 99352, USA
Received 4 August 1992; in final form 9 September 1992
The potential ofmean force (PMF) for an F--F- ion pair at room temperature was calculated using a rigid simple point charge (SPC/E) water model and molecular dynamics techniques. The PMF displayed a minimum at an ion-ion separation of 4.3 A with a barrier height of approximately 1.5 kcal/mol. The barrier height is a result, in part, of the presence of two water molecules that simultaneously hydrogen bond to both fluoride ions. To investigate the effect of the ionic charge on the hydration properties of an ion pair, we also computed the PMF for the F+-F+ ion pair. Our calculations indicated that the barrier height of this PMF is less significant than the corresponding barrier height observed in the computed PMF of the F--F- ion pair. This result is reasonable because of the absence of the highly favorable hydrogen bonding between water molecules and the ion pair. When comparing the present calculation with those reported in previous works on similar systems using integral equation techniques, our simulated F--F- PMF displays more structure and the minimum well depth is shallower; however, the barrier to dissociation is comparable.
1. Introduction An accurate determination of the interionic potential of mean force (PMF) or solvent-averaged force of an ion pair in water by computer simulation or theoretical techniques remains a central problem in the chemical physics of salvation [ 11. For example, the PMFs for an F--F- ion pair in water or a water-like solvent have been calculated using integral equation techniques [ 2,3]. These calculations indicated strong attractions between the ions near contact. Friedman et al. [l] computed the distinct diffusion coefficients for the F--F- ion pair in water and compared the results with the experimental measurements. They suggested that the PMF with a strong attraction near contact gave incorrect distinct diffusion coefficients. On the other hand, experimental evidence from NMR relaxation studies by Hertz et al. [4,5] on the association of the F--Fion pair in water was inconclusive. Thus, at present,
it appears that a reliable PMF, including the related thermodynamic properties for an F--F- ion pair in water has not yet been established. We feel it is important to compute the PMF using a different approach, such as a computer simulation technique. In this Letter, we present the PMFs obtained from molecular dynamics simulations for an F--F- ion pair in water, In addition to the PMFs, computer simulations also provide detailed solvent configurations around the ion pair. This information will help in understanding the characteristics of the PMF. We computed the PMF for an F+-F+ ion pair in water and compared this information with the PMF of the F--F- ion pair in water. By doing this, we were able to examine how the sign of the ionic charge affects the hydration properties of the ion pair. Details of the calculations and the potential functions are given in section 2. The results are presented and discussed in section 3, our conclusions are summarized in section 4.
Correspondence to: L. X. Dan& Molecular theory, Modeling and Simulation, Molecular Science Research Center, Pacific Northwest Laboratory, P.O. Box 999, Richland, WA 99352, USA.
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
21
CHEMICAL PHYSICS LETTERS
Volume 200, number 1,2
2. Computational methodology We computed the PMF for an ion pair in water using the SPC/E model of water [ 61. This model is a rigid, three-point charge model that predicts the thermodynamic and structural properties of water as well. We derived the ion-water potential parameters so that selective properties of ionic solutions, such as the structural properties and solvation enthalpy, were in accord with experimental data. The functional form of the water-water and ion-water system is given as
(1) where qi and qj refer to charges of different molecules, and A and C are the LJ parameters. The parameters for the SPC/E model and the F- ion are tabulated in table 1. For this particular study, we focused on using the effective pair potentials. Future work will include many-body potentials [ 71. The following expression was used to compute the PMF [8]: A,-A,=-kTln(exp[-/3(U,-Uo)])o.
(21
In this equation, the free energy difference between a reference system, 0, and a perturbed system, 1, is given as a function of the average energy difference between two systems. Here, ( )0 indicates that the average is calculated corresponding to the potential energy describing state 0; k is the Boltzmann constant; T is the absolute temperature; and @equals l/ kT. By performing a series of such calculations along the reaction coordinate, the resulting accumulated free energy changes yield the PMF. The simulations using the Ewald summation tech-
27 November 1992
nique [ 91 consisted of 2 14 water molecules and a pair of ions in a cubic box with a length of 18.62 A. For each calculation, a total of 15 simulations were carried out; a typical simulation consisted of a 7.5 ps equilibration period followed by 60 ps of data collection for each ion-ion separation with a timestep of 1.5 fs. The SHAKE procedure [IO] was adopted to constrain all the bond lengths to their equilibrium values. The average temperature of the system was kept constant at 298 K with the use of a constant temperature algorithm [ 111.
3. Results and discussion Before we discuss the ion-ion PMF, we present selective structural and thermodynamic properties for a single F- ion in water and compare these results with other computer simulations and the experimental data on these systems. The ion-water radial distribution functions, g(r), are shown in fig. 1. The peak positions of gr_o, and gF_Hare identical to the results from computer simulations using many-body potentials [ 71. The peak heights are taller, however, suggesting that the water molecules in the first hydration shell are tightly held by the fluoride ion. In table 2, the results obtained from this work, from
Table 1 Van der Waals parameters and charges for various atoms Atom type
a (A)
E (kcal/mol)
g
0
3.169 0.000 3.118 3.118
0.155 0.000 0.180 0.180
-0.8476 “) 04238 ‘) - 1.0000 t 1.oooo
H FF+ *) Ref. [7].
Fig. 1. Calculated g~_o (solid line) and the g,_, (dashed line) obtained from molecular dynamics simulation of aqueous solutionofF-.
Volume 200, number I ,2
CHEMICAL PHYSICS LETTERS
Table 2 Structural and thermodynamic properties of the F- ion in water at 300 K. Obtained from molecular dynamics simulations
RX, (A) Rm (A) coordination number A&
This work
Ref. [7]
2.70 1.70 6.2 -118
2.70 1.70 5.8 -114
Table 3 Results for the potential of mean force for an aqueous fluoride ion pair from the molecular dynamics simulations at 300 K
Expt.
6.0 I’ -116b’
a) Ref. [ 121. ‘) Ref. [ 131.
F-F pmf/Ewold
L_
2
3
1
5
B
I
27 November 1992
8
r.A
Fig. 2. The PMF for the F--F- ion pair in water of a molecular dynamics simulation at room temperature using an EwaId summation technique.
r (A)
W(r) (kcal/mol)
3.625 3.750 3.875 4.000 4.125 4.250 4.375 4.500 4.625 4.750 4.875 5.000 5.125 5.250 5.375 5.500 5.625 5.750 5.875 6.000 6.125 6.250 6.375 6.500 6.625 6.750 6.875 7.000
3.375 1.782 0.524 0.028 -0.234 -0.299 -0.069 0.141 0.303 0.682 0.972 1.262 I .280 1,248 1.055 0.875 0.620 0.486 0.454 0.378 0.378 0.422 0.511 0.618 0.738 0.736 0.678 0.677
the minimum distance of 4.3 8, is consistent with the requirement for a water molecule with both hydrogens linearly bonded to both F- ions. Fig. 3 displays the computed PMFs for the F--F- ion pair in water as a function of the accumulative time. In general, the shape of these PMFs are very similar, including the positions of the minimum well depths. From these results, we concluded that the simulations with 60 ps of averaging for each ion-ion separation converge reasonably well, and we used these results throughout the analysis. When comparing the present calculations with those reported in previous works on similar systems by Kusalik and Patey [ 3 ] and Friedman et al. [ 11, our simulated F--F- PMF displays more strncture, the minimum well depth is shallower, and the corresponding minimum distance is much larger. However, the barrier to dissociation is comparable. These Also,
other molecular dynamics simulations studies, and from experimental work on these systems are summarized. The PMF for an F--F- interaction in water is shown in fig. 2. The numerical value of the PMF at 7 A corresponds to the primitive model result with a dielectric constant of approximately 70 [ 141. Table 3 contains the PMF as a function of ion-ion separations. This result indicates the presence of a minimum at an ion-ion separation of 4.3 A, with a barrier to dissociation of 1.5 kcal/mol. This minimum is a result, in part, of the highly favorable configurations in which water molecules are simultaneously hydrogen bonded to both fluoride ions. These favorable interactions, including other interactions, result in a sufficiently effective solvent-averaged attraction to offset the repulsion between the ion pair.
23
Volume 200, number 1,2
CHEMICAL PHYSICS LETTERS
27 November 1992
culations using many-body potentials [ 161.
Acknowledgement
0
t
Fig. 5. The PMFs for the ion pair in water of a molecular dynamics simulation using an Ewald summation technique. Circles are the results for the F--F- and the crosses are for the F+-F+.
PMF for the F--F- ion pair interaction. We found that the PMF displays a minimum at an ion-ion separation of 4.3 A with a barrier height of approximately 1.5 kcal/mol. This first PMF minimum is a result of a competition between the effective solventmediated potential and the repulsion between the ion pair. On the molecular level, this strong barrier height is due to the favorable hydrogen bonding between water molecules and the ion pair. These features are similar to those found by Dang et al. [ 15] in their molecular dynamics simulations of the potential of mean force for the Cl--Cl- ion pair in water. To examine the effect of the ionic charge, we computed the PMF for the F+-F+ ion pair in water. From these calculations, we concluded that the sign inversion of the ionic charge produces a significant effect on the characteristics of the PMF of an ion pair in water. We used the approach taken in this study to calculate the PMFs for Na+-F- and Na+-Na+ ion pairs in water. Even though no experimental data on these PMFs exists, one can test the calculated PMFs against various solution measurements, such as the distinct diffusion coefficients [ 11. In closing, it will be of interest to compare the present results with the cal-
I wish to thank Professor Monte Pettitt at the University of Houston for many helpful discussions and continuing support. This work was performed under the auspices of the Division of Chemical Sciences, Offrce of Basic Energy Sciences, US Department of Energy (DOE) under Contract DE-AC06-76RLO 1830 with Battelle Memorial Institute, which operates the Pacific Northwest Laboratory.
References [ 1] H.L. Friedman, F.O. Raineri and M.D. Wood, Chem. Scripta 29A (1989) 49. [2] B.M. Pettitt and P.J. Rossky, .I. Chem. Phys. 84 (1986) 5836. [3] PG. Kusalik and G.N. Patty, J. Chem. Phys. 89 (1988) 5843. [4] H.G. Hertz and C. Radle, Ber. Bunsenges. Physik. Chem. 78 (1974) 509. [ 5 1K.J. Muller and H.G. Hertz, Ber. Bunscnges. Physik. Chem. 140 (1984) 31. [ 61 H.J.C. Berendsen, J.R. Grigera andT.P. Straatsma, J. Phys. Chem. 87 (1987) 6269. [7] L.X. Dang, J. Chem. Phys. 96 (1992) 6970. [S] J.G. Kirkwood, J. Chem. Phys. 3 (1930) 300; R.W. Zwanzig, J. Chem. Phys. 22 (1954) 1420. [9] S.W. de Leeuw, J.W. Perram and E.R. Smith, Proc. Roy. Sot. A 373 (1980) 27. [ 10[ J.-P. Ryckaert, G. Ciccotti and H.J.C. Berendsen, J. Comput. Phys. 23 (1977) 327. [ll] H.J.C. Berendsen, J.P.M. Postma, A. Di Nola, W.F. Van Gunsteren and J.R. Haak, J. Chem. Phys. 81 ( 1984) 3684. [ 121A.H. Narten, J. Phys. Chem. 74 (1970) 765. [ 131H.L. Friedman and C.V. Krischnan, in: Water: a comprehensive treatise, Vol. 6, ed. P. Franks (Plenum Press, NewYork, 1973) p. 1. [ 141M. Rami-Reddy and M. Berkowitz,Chem. Phys. Letters 155 (1989) 173; K. Watanabe and M.L. Klein, Chem. Phys. 131 (1989) 57. [ 151L.X. Dang and B.M. Pettitt, I. Chem. Phys. 86 ( 1987) 6560; J. Am. Chem. Sot. 109 (1987) 2507. [ 16] L.X. Dang, Research in progress.
25