J. Phys. Chem. 1996, 100, 3989-3995
3989
Critical Study of Fluoride-Water Interactions Sotiris S. Xantheas* and Liem X. Dang* Theory, Modeling and Simulation, EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: October 23, 1995; In Final Form: December 5, 1995X
A new parametrization of the fluoride-water interaction within a polarizable water model is presented. Because of the absence of accurate experimental data for the enthalpy of formation of the F-(H2O) cluster, the results of ab-initio calculations were used to parametrize the ion-water interaction. The ab-initio results suggest that this interaction is 10% stronger than what was previously thought. The accuracy of the present parametrization was evaluated by comparing the model potential with the ab-initio results along the minimum energy profile for the fluoride-water interaction for various F-O separations. The energetic and structural properties of the clusters F-(H2O)n, n ) 1-10, as well as of aqueous fluoride solution are studied using molecular dynamics simulation techniques. The stronger ion-water interaction results in the appearance of interior states (configurations in which the ion is “solvated” by water molecules) for finite clusters with six or more water molecules. The results of the aqueous ionic solution simulations provide a reasonable description of many structural and thermodynamic properties of the solvated ion such as the solvation enthalpy, the radial distribution function, and the hydration number.
I. Introduction Computer simulations have been proved to be useful tools in examining many gas and condensed phase problems such as ionic solvation,1-3 ion-ion interactions,4,5 and ionic solvation at liquid/liquid6-9 and vapor/liquid10-13 interfaces. These studies are not only able to characterize the static features of these systems at the molecular level but also provide a method for describing many dynamical processes in these media, such as solvation and transport mechanisms. The reliability of these simulations depends critically on the potential models describing the interactions among the various components of the systems under investigation. Interaction potentials for ion-water systems are commonly parametrized using available experimental data for the structures and energetics of small clusters. Oftentimes, the experimental uncertainties are large or there exist several sets of them that span a wide range of values. In a recent study of the OH-(H2O)n clusters,14 we have shown the merit of using ab-initio quantum mechanical calculations in order to evaluate the accuracy of the experimental enthalpies of formation which, for the n ) 1 cluster, the reported values vary between 22.1 and 34.5 kcal/mol.15 Solvation of ions in water clusters has been the subject of extensive computational and experimental studies.16-20 Several approaches and methodologies have been applied to model ionwater interactions and elucidate the structures and dynamic properties of small ion-water clusters. Molecular dynamics (MD) simulations of ion-water clusters with nonadditive potential models have been carried out by Kollman and coworkers,16 Perera and Berkowitz,17 and Dang.18 Quantum mechanical calculations of ion-water clusters include, for example, the work of Clementi and co-workers,19 Kestner and co-workers,20 and Xantheas and Dunning.14,21,22 Experimental thermodynamic studies of ion solvation in clusters were first reported by Kebarle and co-workers.23 By employing highpressure mass-spectrometric techniques they determined the incremental enthalpies of formation ∆Hn-1,n for the successive addition of solvent molecules to an ion to form an ionic cluster. In a recently study, Markovich et al.24 used photoelectron X
Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-3989$12.00/0
spectroscopy to measure the vertical photodetachment energies BEv(n) of the ionic clusters I-(H2O)n, n ) 1-15, and related the solvation-induced stabilization of the electron binding energy to the ion-water interaction energy. Our research efforts focus on the study of structural and energetic properties of water and ion-water clusters using polarizable (nonadditive) potential models that are derived from ab-initio calculations. We begin the effort by developing a polarizable potential model for the interaction between F- and H2O in order to study the energetic and structural properties of the F-(H2O)n, n ) 1-10, clusters and the aqueous ionic solution using MD simulation techniques. This system has been previously studied by Dang18 and Perera and Berkowitz17 using nonadditive models that were parametrized to the experimental thermodynamic data reported by Kebarle and co-workers.23 However, more recent experimental measurements by Hiraoka et al.25 yielded enthalpies of formation that are 3%-15% larger than Kebarle’s estimates for the n ) 2-5 clusters. The range of Hiraoka’s measurements is within 0.3 kcal/mol (n ) 2) and 1.3 kcal/mol (n ) 3) from the results of recent ab-initio calculations21 which, at the same time, suggested a value for the enthalpy of formation of the n ) 1 cluster that is 20% higher than Kebarle’s estimate of -23.3 kcal/mol. Although Hiraoka et al. did not measure ∆H0,1, the agreement between their results and the ab-initio calculations21 for the n ) 2 and 3 clusters suggests that Kebarle’s estimate might indeed be too low. Such a notable (20%) difference in the dominant ion-water interaction will largely affect the solvation properties of F- in aqueous clusters and bulk water. We have therefore constructed a new fluoride-water interaction potential using the ab-initio data. In section II we briefly describe the development and parametrization of the polarizable potential model. In section III we outline the computational details of the MD and the abinitio calculations. In section IV we investigate the accuracy of the new potential by comparing extensive parts of the ionwater interaction potential energy surface to the corresponding ab-initio results and present the results of the MD simulations for the structures and energetics of the n ) 1-10 clusters as well as for the solvation of F- in bulk water. Final conclusions are drawn in section V. © 1996 American Chemical Society
3990 J. Phys. Chem., Vol. 100, No. 10, 1996
Xantheas and Dang
II. Potential Model In the following, we consider a rigid three-site interaction model potential for water.18 As in the usual pairwise potentials, there are fixed atomic charges and Lennard-Jones potential parameters associated with each atom site. In addition, there are point polarizabilities assigned to each atom to account for the nonadditive polarization energy. The total interaction energy can be expressed as
Utot ) Upair + Upol
(1)
where the pairwise additive part of the potential (Upair) is the sum of the Lennard-Jones and Coulombic interactions.
( [( ) ( ) ] )
Upair ) ∑∑ 4 i
j
σij
12
-
rij
σij rij
6
+
qiqj rij
(2)
Here, rij is the distance between atom sites i and j, q is the atom charge, and σ and are the Lennard-Jones parameters. The nonadditive polarization energy (Upol) is given by
Upol ) -1/2∑µiEi0
(3)
i
where E0i is the electric field at site i produced by the fixed charges in the system
Ei0 ) ∑ j*i
qjrij (4)
rij3
The induced dipole moment at atom site i, µi, is defined as
µi ) RiEi
(5)
Ei ) Ei0 + ∑Tijµj
(6)
where
j*i
In the above, Ei is the total electric field at atom i, Ri is the polarizability of atom i, and Tij is the dipole tensor
(
)
1 3rijrij Tij ) 3 -1 rij rij2
(7)
During the MD simulations, an iterative procedure is used to solve eqs 5 and 6. The convergence is achieved when the deviations of the dipole moment from two sequential interactions fall within 0.001 debye/atom. The development of the potential parameters is as follows. The parameters for the water-water interaction polarizable model were taken from our previous work.18 The LennardJones parameters for the ion-water interaction were parametrized in order to reproduce the ab-initio enthalpy of formation and R(F-O) separation for the F-(H2O) cluster21 by carrying out a series of MD simulations using the assumed functional forms described in eqs 2 and 3. This parametrization intrinsically includes the water relaxation effects that are not explicitly taken into account because of the use of a rigid water model. We used a value of 1.05 Å3 for the ion polarizability.26 The new potential parameters are listed in Table 1. These parameters
TABLE 1: Lennard-Jones Parameters (σ and E), Charges (q), and Atomic Polarizabilities (r) Used in the Potential Modela atom type
σ (Å)
(kcal/mol)
q
R (Å3)
O H F-
3.205
0.160
3.3587
0.100
-0.7300 +0.3650 -1.0000
0.528 0.170 1.05b
a
The water-water interaction potential parameters are taken from ref 18. b Reference 26.
were subsequently used in the simulation of the larger (n e 10) clusters and the aqueous ionic solutions. III. Computational Details A typical cluster MD simulation consists of a 75 ps equilibration period followed by 200 ps of data collection. The dynamics were performed with a time step of 2 fs in the microcanonical ensemble, and the rotational and translational motions were removed only at the beginning of the simulation. For the aqueous ionic solution simulation the sample consisted of a single ion and 215 water molecules in a cubic cell of length 18.6 Å with three-dimensional periodic boundary conditions. We used temperature and pressure coupling constants of 0.2 and 0.5 (ref 25), respectively, and a time step of 2 fs. The SHAKE27 procedure was adapted to constrain all the bond lengths to their equilibrium values, and the nonbonded interactions were cut off at 9 Å. The Born correction28 was applied to the calculation of the enthalpies of solvation, for which the error bars were estimated by taking the difference between the computed values during the first half and the last half of the total trajectory. The ab-initio interaction energies were estimated at the fourthorder Møller-Plesset perturbation theory (MP4) using the augmented correlation-consistent polarized valence basis sets29 of double (aug-cc-pVDZ)- and triple (aug-cc-pVTZ)-ζ quality. We retained only the pure spherical harmonic components of the polarization functions (five component d’s and seven component f’s). During the MP4 calculations only the valence electrons were correlated. Basis set superposition error (BSSE) corrections to the interaction energy were estimated using the function counterpoise method proposed by Boys and Bernardi.30 All calculations were performed with the MOLPRO-94 suite of programs.31 IV. Results and Discussion A. Energy Profile Along the Association Coordinate R(F-O). The quality of the new interaction potential was evaluated by comparing its energy profile (EP) for the ionwater interaction along the association coordinate R(F-O) with the analogous one obtained at the ab-initio level. The comparison was performed along several values of the F-O separation for each of which the rest of the internal coordinates of the F-(H2O) cluster were optimized. The EP with the new model was obtained as a result of MD simulations near 0 K. The optimal values of the internal coordinates along the EP for various F-O separations are listed in Table 2. All optimized geometries were found to have Cs symmetry. It should be noted that since we use a rigid water model there is only one additional degree of freedom under Cs symmetry for each F-O separation, namely, the orientation angle β of the water molecule with respect to the ion (cf. Figure 1). Its optimal values along the EP are shown in parentheses in Table 2. The values at R(FO) ) ∞ correspond to the optimal internal coordinates of water at the MP4 level with the two basis sets, respectively. The internal coordinates of water in the potential are fixed at R(O-
Critical Study of Fluoride-Water Interactions
J. Phys. Chem., Vol. 100, No. 10, 1996 3991
TABLE 2: Optimal Internal Coordinates of the F-(H2O) Cluster for Various F-O Separationsa R(F-O), Å
R(O-H1), Å
R(O-H2), Å
φ(H1-O-H2), deg
2.2 2.3 2.4 2.487 (m) 2.5 2.6 2.8 3.0 3.5 4.0 5.0 6.0 7.0 8.0 ∞
1.0556 1.0643 1.0577 1.0477 1.0468 1.0357 1.0172 1.0044 0.9867 0.9782 0.9709 0.9687 0.9683 0.9680 0.9670
MP4/aug-cc-pVDZ 0.9669 103.00 0.9668 103.54 0.9666 102.20 0.9663 101.52 0.9667 101.43 0.9666 100.96 0.9666 100.55 0.9667 100.49 0.9669 100.73 0.9672 101.03 0.9682 101.49 0.9686 102.25 0.9683 102.76 0.9680 103.07 0.9670 103.88
2.2 2.3 2.4 2.451 (m) 2.5 2.6 2.8 3.0 3.5 4.0 5.0 6.0 7.0 8.0 ∞
1.0648 1.0754 1.0637 1.0550 1.0470 1.0331 1.0130 1.0000 0.9825 0.9739 0.9665 0.9640 0.9637 0.9631 0.9627
MP4/aug-cc-pVTZ 0.9630 102.10 0.9627 102.10 0.9622 102.30 0.9621 101.84 0.9621 101.51 0.9622 100.70 0.9621 100.50 0.9621 100.50 0.9626 100.90 0.9630 101.19 0.9639 101.20 0.9640 102.50 0.9637 102.80 0.9631 103.50 0.9627 104.06
β, deg 0.54 (1.57) 0.78 (2.67) 1.47 (3.91) 2.09 2.17 (5.13) 2.84 (6.37) 4.29 (9.04) 5.82 (12.26) 10.12 (20.37) 15.95 (31.46) 35.05 (54.16) 51.10 (54.4) 51.39 (54.4) 51.50 (55.7) 51.94 (54.8) 0.66 (1.57) 0.88 (2.67) 1.27 (3.91) 1.64 2.01 (5.13) 2.83 (6.37) 4.29 (9.04) 5.80 (12.26) 10.10 (20.37) 15.86 (31.46) 35.06 (54.16) 51.09 (54.4) 51.16 (54.4) 51.30 (55.7) 52.03 (54.8)
a For the labeling of the atoms see Figure 1. The optimal values of β with the new potential are shown in parentheses. The potential minimum for the new model is at R(F-O) ) 2.446 Å, β ) 4.42°. (m) denotes the minimum for the ab-initio calculations.
Figure 2. Variation of the orientation angle β (cf. Figure 1) of the ion with respect to water along the association coordinate R(F-O). Solid line, filled symbols: MP4/aug-cc-pVTZ results. Broken line, open symbols: MD results.
TABLE 3: Ion-Water Interaction Energies for Various F-O Separationsa ∆E (kcal/mol) R(F-O), Å
MP4/aug-cc-pVDZ
MP4/aug-cc-pVTZ
potential
2.2 2.3 2.4 2.5 2.6 2.8 3.0 3.5 4.0 5.0 6.0 7.0 8.0
-18.4 (-15.5) -23.5 (-21.1) 25.8 (-23.7) -26.3 (-24.4) -25.7 (-24.2) -23.2 (-22.1) -20.2 (-19.4) -14.0 (-13.5) -9.9 (-9.6) -5.7 (-5.6) -3.8 (-3.8) -2.8 (-2.7) -2.1 (-2.1)
-20.6 (-18.7) -25.2 (-23.6) -26.8 (-25.5) -26.9 (-25.8) -26.1 (-25.1) -23.4 (-22.6) -20.3 (-19.7) -13.9 (-13.6) -9.8 (-9.6) -5.6 (-5.6) -3.8 (-3.8) -2.7 (-2.7) -2.1 (-2.1)
-20.3 -24.4 -26.3 -26.2 -25.2 -21.9 -18.2 -12.7 -9.2 -5.7 -4.0 -2.9 -2.2
a For each R(F-O), the rest of the internal coordinates were optimized. Numbers in parentheses correspond to the BSSE-corrected results.
Figure 1. Labeling of the atoms and definition of the orientation angle β for the F-(H2O) cluster.
H1) ) R(O-H2) ) 1.0 Å and φ(H1-O-H2) ) 109.5°. Figure 2 traces the variation of the orientation angle β of the ion with respect to water along the EP at the MP4/aug-cc-pVTZ level of theory (solid line, filled symbols) and the new potential model (broken line, open symbols). The ab-initio and the new potential model results exhibit the same qualitative variation of β along the EP: at short F-O separations they both suggest an almost linear hydrogen bond (β ≈ 0°), whereas at larger F-O separations they yield a “bifurcated” arrangement in which the ion lies along the dipole moment vector of water, having two equidistant hydrogen bonds. The latter can be rationalized in terms of an electrostatic charge-dipole interaction which seems to dominate for R(F-O) g 6 Å. It is obvious that the limiting value of β for R(F-O) f ∞ is one-half the water bending angle. It should be noted that our MD model does not explicitly contain any charge transfer terms that will account for the charge redistribution that has been shown to be significant near the minimum. Combariza and Kestner reported that 0.122 electrons are transferred from the lone pairs of the ion to water using a
natural bond orbital (NBO) analysis.20 However, part of this effect is implicitly included in the polarization term (eq 3). The ab-initio and the model interaction energies (∆E in kcal/ mol) along the EP are listed in Table 3 for the various R(F-O) separations. For the ab-initio results, numbers in parentheses correspond to the BSSE-corrected values. The minimum energy profiles at the MP4/aug-cc-pVTZ level of theory and with the new model (near 0 K) are shown in Figure 3. The solid lines correspond to the ab-initio (filled symbols: uncorrected, open symbols: BSSE-corrected) whereas the broken line traces the MD results. The agreement of the BSSE-corrected ab-initio with the MD results around the minimum (inset of Figure 2) is quite satisfactory especially when taking into account the fact that the only information used to parametrize the ion-water potential was the structure and enthalpy of formation (at 300 K) of the minimum geometry. This agreement is evident from the fact that the first derivatives of the potential along the association coordinate with respect to R(F-O), shown in Figure 4, follow each other very closely. In contrast, the potential EP exhibits a “shoulder” that rises more steeply in the region between 3 and 4 Å (cf. Figure 3). The disagreement in the curvature between the model and ab-initio EPs can probably be attributed both to the choice of the functional form (eqs 2 and 3), and the use of a rigid water molecule will give rise to different predictions for the intermolecular harmonic vibrational frequencies and their anharmonic corrections.
3992 J. Phys. Chem., Vol. 100, No. 10, 1996
Figure 3. Energy profiles (EPs) for the ion-water interaction along the association coordinate R(F-O). For each F-O separation the rest of the internal coordinates are optimized. Solid line: filled symbols, MP4/aug-cc-pVTZ results; open symbols, BSSE-corrected MP4/augcc-pVTZ results. Broken line: model potential results (near 0 K). Inset shows the EPs around the minimum.
Figure 4. First derivatives of the potentials along the association coordinate R(F-O).
The analytic form of the interaction energy for the potential model (eqs 2 and 3) makes it feasible to decompose the total interaction energy to its various components along the EP. Figure 5 displays the Lennard-Jones (LJ), Coulombic (COU), and polarization (POL) components of the total interaction energy along the EP. The short-range LJ contribution at the minimum of the potential energy surface is quite small, while the electrostatic energy (Coulombic plus polarization) is significant. The polarization contribution is negligible after 5 Å, the total interaction being purely electrostatic at longer distances. This assessment is consistent with our previous observation that for R(F-O) g 5 Å the optimal orientation of the ion around water can be rationalized by simple electrostatic arguments (cf. Figure 2). In contrast to the nonpolarizable interaction potentials, our present model accounts for the change in the dipole moment of each fragment due to its environment in a self-consistent manner. The total and induced dipole moments of water along the EP are shown in Figure 6. As expected, at short distances both the total and induced dipole moments of the water molecule are significantly increased due to the strong field induced by the F- ion. They monotonically decrease with R(F-O), the induced dipole moment becoming negligible and the total dipole moment approaching the gas phase value as the F-O separation
Xantheas and Dang
Figure 5. The model potential energy components of the F-(H2O) cluster along the minimum energy path.
Figure 6. The total (µtot) and induced (µind) dipole moments of water along the EP. The arrow indicates the location of the minimum.
becomes large. The difference between the total and induced dipole moment at R(F-O) f ∞ is a constant, namely, the permanent dipole moment (2.02 debye) arising from the charges on the atoms. The fact that at the minimum energy geometry (indicated by the arrow in Figure 6) the induced dipole moment is ∼1.0 debye justifies the importance of using a polarizable model for ionic systems. B. Structures and Energetics of the Clusters n ) 1-10. We have used the new parametrization of the fluoride-water interaction to carry out MD simulations for the F-(H2O)n, n ) 1-10, clusters. For the n ) 1-3 clusters we optimized the geometries (near 0 K) in order to compare them with present and previous21 ab-initio results. The minimum energy configurations are shown in Figure 7. The new model predicts a minimum geometry for the F-(H2O) cluster [R(F-O) ) 2.446 Å, β ) 4.42°] that is in very close agreement with the corresponding one at the MP4/aug-cc-pVTZ level of theory [R(F-O) ) 2.451 Å, R(O-H1) ) 1.055 Å, R(O-H2) ) 0.962 Å, φ(H1-O-H2) ) 101.84°, and β ) 1.64°]. For the n ) 2 cluster it produces two unequal F-O separations of 2.457 and 2.508 Å, which are within 0.07 Å of the ab-initio results21 of 2.533 and 2.549 Å, respectively. The resulting (O-F-O) angle is 75.2°, which is substantially smaller than the ab-initio value
Critical Study of Fluoride-Water Interactions
J. Phys. Chem., Vol. 100, No. 10, 1996 3993 TABLE 4: Incremental Association Enthalpies (in kcal/mol) of F-(H2O)n, n ) 1-10, at 300 K and Comparison with the Two Sets of Experimental Data and Previous ab-Initio Results expt n
this study
-26.5 ( 0.5 -21.6 ( 0.4 -19.2 ( 0.5 -18.3 ( 0.3 -15.3 ( 0.4 -13.8 ( 0.3 -13.9 ( 0.4 -10.9 ( 0.1 -12.3 ( 0.4 -10.5 ( 0.4 -10.9 ( 0.3 -10.4 ( 0.4 -10.4 ( 0.3 -8.7 ( 0.4 -11.2 ( 0.4 -13.6 ( 0.4 -11.1 ( 0.5 -13.1 ( 0.4 ∼(-11)
1 2 3 4 5 6 7 8 9 10 a
Figure 7. Minimum energy configurations (near 0 K) of the ionic clusters with 1, 2, and 3 water molecules, respectively.
of 91.4°. It should, however, be noted that the potential energy surface with respect to this angle is extremely flat and anharmonic,21 a subtlety that diminishes its importance in structural determination. The optimal geometry of the n ) 3 cluster resembles the pyramidal minimum obtained by previous21 ab-initio calculations. It exhibits a near C3 symmetry with R(FO) ) 2.51 Å and R(O-O) ) 3.07 Å. The corresponding MP2/ aug-cc-pVDZ results21 are R(F-O) ) 2.61 Å and R(O-O) ) 3.25 Å. It is evident that the underestimation of the O-O
Figure 8. Snapshots for the ionic clusters F-(H2O)n, n ) 4-9 at 300 K.
Hiraoka et al.a Kebarle et al.b -23.3 -16.6 -13.7 -13.5 -13.2
MDc
-16.3 -11.8 -12.6 -10.2 -12.7 -9.6 -9.8 -9.9
ab initiod -26.7 -19.5 -16.9
Reference 25. b Reference 23. c Reference 17. d Reference 21.
separation is a consequence of the water-water interaction potential, an issue that will be addressed in a future study. We performed MD simulations of the larger (n ) 4-9) clusters at 300 K in order to estimate their total and incremental association enthalpies. During these simulations, we examined the position of the ion relative to the center of mass of the water cluster and observed a competition between surface and interior states. We noticed that interior states dominate for clusters having six or more water molecules. Snapshots of random configurations of the n ) 4-9 clusters, shown in Figure 8, clearly support this observation. The results for the incremental association enthalpies of formation of the n ) 1-10 clusters are listed in Table 4 together with the two sets of experimental data23,25 and the results of previous MD17 and ab-initio21 calculations. We computed the incremental association enthalpies using the method outlined in ref 16. The agreement between the MD and ab-initio results with the set of experimental data by Hiraoka et al. suggests that Kebarle’s predictions for the incremental enthalpies of formation might indeed be too low for the n ) 1-3 clusters. A previous MD study by Perera and Berkowitz17 using the same model potential plus three-body exchange repulsion (ion-water-water) terms produced results
3994 J. Phys. Chem., Vol. 100, No. 10, 1996
Xantheas and Dang
TABLE 5: Structural and Thermodynamic Properties of Fin Water at 300 K
a
property
this study
expta
R(F-O) (Å) R(F-H) (Å) coordination no. ∆Hsol (kcal/mol)
2.7 1.7 6 -115 ( 4
2.6-2.8 6 -116
Reference 32.
Figure 9. Calculated radial distribution functions gF-O (solid line) and function gF-H (broken line) obtained from molecular dynamics simulations of an aqueous solution of F- at room temperature.
that more or less span the same range with the ones of the present study. We note that for n g 8 there is a larger deviation between our results for the incremental association enthalpies and experiment. This might be attributed to the fact that the MD simulations for n g 8 were performed at 200 K to avoid cluster evaporation. C. Aqueous Ionic Solution Simulations. We have computed selective structural and thermodynamic properties for a single F- ion in aqueous solution in order to assess the ability of the potential to reproduce solution data. A summary of the calculated solution phase properties is compiled in Table 5, along with results from experimental work on comparable systems. The calculated radial distribution functions gF-O (solid line) and gF-H (broken line) are shown in Figure 9. The peak positions for gF-O (2.7 Å) and gF-H (1.7 Å) are similar to the results of previous simulations and agree with experimental data. The coordination number was found to be 6. The mean value for the enthalpy of solvation (∆Hsol) of -115 ( 4 kcal/mol is in excellent agreement with the experimental estimate of -116 kcal/mol. It seems clear that the present model reliably represents the thermodynamic and structural properties of ionic solutions. V. Conclusions Due to the lack of accurate experimental information regarding the enthalpy of formation of the F-(H2O) cluster we have used the results of ab-initio calculations to reparametrize the ion-water interaction within a polarizable model potential. The results of our previous21 and current ab-initio calculations suggest that the ion-water interaction is 10% stronger than the value used earlier to parametrize interaction potentials for this system. Our new parametrization of the fluoride-water interaction potential was critically evaluated by comparing the EP with the corresponding one obtained by ab-initio calculations. We found that the agreement between the two methods is quite satisfactory for a wide range of the F-O separation. We used
these potential parameters in a series of MD simulations to examine the incremental association enthalpies and structural features of the ionic clusters with up to 10 water molecules. The near 0 K minimum energy structures for the n ) 1-3 clusters are quite similar to the corresponding structures obtained by ab-initio calculations.21 From the MD simulations at finite temperature (300 K), we observed a competition between surface and interior states with the interior states dominating for the clusters with six or more water molecules. The relative stability between the interior (I) and surface (S) states is clearly an interplay between the strengths of the ion-water and waterwater interactions as it was previously reported by Combariza, Kestner and Jortner.20 For example, due to the fact that the fluoride-water interaction is more than twice as strong than the chloride-water one, the interior states appear earlier20 (for a smaller number of water molecules) in the former than in the latter case. A configuration in which the ion lies on or close to the surface of a water cluster exhibits, in general, less ionwater and more water-water bonding. In contrast, the I states have more ion-water interactions than the S states. In the current study, by increasing the strength of the ion-water interaction by 10% we have effectively made the total stabilization energy due to ion-water interactions more competitive with respect to the corresponding one due to water-water interactions. This clearly results in reducing the number of water molecules needed to form an interior state in a finite cluster. Indeed, the results of this study indicate that I states appear “earlier” (for smaller n) than in a previous study18 that used the weaker ion-water parametrization. This previous parametrization included an additional three-body exchange repulsion (ionwater-water) interaction term which was, however, omitted in the current study. Perera and Berkowitz17 used this term in their study of the n ) 2-15 clusters and estimated that it contributes 2% and 4% to the total energies of the n ) 2 and 3 clusters, respectively. Xantheas and Dunning21 have estimated that the (ion-water-water) component of the three-body interaction energy accounts for 9% and 15.5% of the total energy of the n ) 2 and 3 clusters, respectively. The direct comparison of the ab-initio with the results of Perera and Berkowitz is difficult since the polarization term (POL) has parts of the higher order many-body energy terms to infinite order. Nevertheless, this study suggests that the effect that the exchange repulsion term has can probably be compensated by the parametrization of the ion-water interaction term. Acknowledgment. This work was performed under the auspices of the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy under Contract DE-AC06-76RLO 1830 with Battelle Memorial Institute, which operates the Pacific Northwest Laboratory, a multiprogram national laboratory. Computer resources were provided by the Division of Chemical Sciences and by the Scientific Computing Staff, Office of Energy Research, at the National Energy Research Supercomputer Center (Livermore, CA). We wish to thank Drs. G. K. Schenter and B. C. Garrett for many helpful discussions and comments prior to publication. References and Notes (1) Chandrasekhar, J.; Spellmeyer, D. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1984, 106, 903. (2) Aqvist, J. J. Phys. Chem. 1990, 94, 8021. (3) Kozack, R. E.; Jordan, P. C. J. Chem. Phys. 1993, 99, 2987, and references therein. (4) Berkowitz, M.; Karim, O. A.; McCammon, J. A.; Rossky, P. J. Chem. Phys. Lett. 1987, 105, 577. (5) Smith, D. E.; Dang, L. X. J. Chem. Phys. 1994, 100, 3757. (6) Benjamin, I. Science 1993, 261, 1558. Schweighofer, K. J.; Benjamin, I. J. Phys. Chem. 1995, 99, 9974.
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