J. Phys. Chem. B 2007, 111, 14271-14278
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Solvation of Calcium Ions in Methanol-Water Mixtures: Molecular Dynamics Simulation Emilia Owczarek, Marcin Rybicki, and Ewa Hawlicka* Institute of Applied Radiation Chemistry, Chemistry Department, Technical UniVersity, 94-924 Lodz, Zeromskiego 116, Poland ReceiVed: August 3, 2007; In Final Form: September 11, 2007
Molecular dynamics simulations of CaCl2 solutions in water and methanol-water mixtures, with methanol concentrations of 5, 10, 50, and 90 mol %, at room temperature, have been performed. The methanol and water molecules have been modeled as flexible three-site bodies. Solvation of the calcium ions has been discussed on the basis of the radial and angular distribution functions, the orientation of the solvent molecules, and their geometrical arrangement in the coordination shells. Analysis of the H-bonds of the solvent molecules coordinated by Ca2+ has been done. Residence time of the solvent molecules in the coordination shell has been calculated. The preferential hydration of the calcium ions has been found over the whole range of the mixture composition. The water concentration in the first and second coordination shells of Ca2+ significantly exceeds the water content in the solution, despite the very similar interaction energy of the calcium ion with water and methanol. In aqueous solution and methanol-water mixtures, the first coordination shell of Ca2+ is irregular and long-living. The solvent molecules prefer the antidipole arrangement, but, in aqueous solutions and water-rich mixtures, the water molecules in the primary shell have only one H-bonded neighbor.
1. Introduction Calcium ion plays a key role in many biological processes, and its biochemical activity probably depends on ion hydration. This accounts for the great interest in the hydration of Ca2+. The structure of its primary hydration shell has been investigated by diffraction techniques,1-13 molecular dynamics (MD) simulation,4,7,12-16 and ab initio calculations.12,17 Despite this attention, a clear and consistent picture of Ca2+ hydration has not been established. In diluted aqueous solutions, the first coordination shell of Ca2+ contains at least eight water neighbors,4,7 but a higher value (about 12) has also been deduced from freezing point depression.18 Unlike other divalent ions, the hydration shell of Ca2+ does not show a regular symmetry, either tetrahedral or octahedral,4,8,10 and the number of molecules coordinated by this ion depends on the salt concentration7,8 and temperature.18 The hydration number of Ca2+ decreases when the salt concentration increases and, for c > 4 M, is less than 6.7 The influence of temperature is similar, and the hydration number decreases with the increasing temperature. As mentioned above, the freezing point depression yields 12 at -22 °C, whereas other colligative properties, such as boiling point elevation and vapor pressure measurements, yield about 7 at 100 °C, but only about 5 at 200 °C.18 The concentration dependence of the Ca2+ hydration number is, however, a very delicate problem. Experimental methods (X-ray and neutron diffraction) may fail in precise determination of the coordination number because of an unfortunate coincidence of the uncertainty of the method and the uncertainty due to a physical character of Ca2+.18 The subtle nature of the Ca2+ hydration shell may play an important role in the process of the ion dehydration that affects the ion biochemical activity. Experimental studies of the ion translations have shown that methanol and other alcohols induce * Corresponding author. Tel.: (+48)-42 6313195. Fax: (+48)-42 6365008. E-mail:
[email protected].
a dehydration of the monovalent ions.19 Thus the purpose of this work was to investigate whether methanol also induces a dehydration of Ca2+ ion. A partial dehydration of Ca2+ in a methanol-water mixture may be expected because the Ca2+ ion coordinates only six methanol molecules, as seen from X-ray diffraction11,19 and MD and Monte Carlo simulation.11,20-22 Moreover, in methanol, the primary coordination shell has stable octahedral symmetry,11,20 and the influence of the salt concentration on the number of the coordinated methanol molecules is weaker,11 as compared with that on the hydration number. Different coordination numbers and different symmetries of the Ca2+ coordination shells in aqueous and methanol solutions suggest that the size of the coordination shell may depend on the methanol content. Indeed, in aqueous solutions containing small amounts of methanol, a hydrodynamic radius of Ca2+ is smaller relative to that in aqueous solutions. The smallest hydrodynamic radius of Ca2+ was observed in mixed solvent containing 10 mol% of methanol.23 A similar influence of methanol on the hydrodynamic radius of Na+ 24 was explained as being due to a destabilization of the first coordination shell of Na+ ions25 induced in the methanol-water mixtures. Although X-ray and neutron scattering measurements are used to gain direct insight into the ion shell structure, their results cannot be decisive for calcium ions in a methanol-water mixture because of the physical nature of this particular ion. X-ray experiments11 have proved that average distances between the calcium ion and the oxygen atoms of water and methanol molecules are almost the same. Moreover, a direct correlation between the cations and carbon atoms is lacking; therefore the Ca2+-C peak is broad and badly defined, and it overlaps with maxima due to other interactions, for example, of oxygen atoms with chloride ions and carbon atoms.11 In such cases, the MD simulation may be used as a tool to provide additional information concerning the structure of the ion shell in a mixed solvent.
10.1021/jp076233v CCC: $37.00 © 2007 American Chemical Society Published on Web 12/07/2007
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Solutions of CaCl2 in mixtures containing 5 and 10 mol % of methanol have been simulated previously.16 In this simulation, potentials of the Lennard-Jones type were applied to describe the interactions of the ions. These MD simulations have shown an aggregation of methanol molecules around the Ca2+ ion. Such results are inconsistent with the self-diffusion experiments. The aggregation of methanol around calcium ions would strongly retard the methanol translations, and, in consequence, the methanol self-diffusion coefficient would be significantly reduced. Experiments did not show any significant influence of CaCl2 on the methanol self-diffusion coefficient in the methanol-water mixture.23,26 A disagreement of MD simulations with experiments has confirmed what we noticed previously:25 that potentials of the Lennard-Jones type do not represent the ion-solvent interaction correctly. Thus the new pair potentials for the interactions between calcium ion and methanol sites were derived from ab initio calculations and verified by the simulation of the CaCl2 solution in methanol.22 Satisfying agreement of the MD simulation results with those of X-ray and self-diffusion experiments led us to believe that this new potential can better describe interactions between the calcium ion and the methanol molecule. This new potential is consistent with the potentials used in the previous simulations of CaCl2 aqueous solution4 and NaCl solutions in methanol27 and methanol-water mixtures.28 We hope that these potentials may provide a more reliable picture of Ca2+ solvation. 2. Details of Potential and Simulations Details of the potentials for methanol and water used in these simulations have been described previously.29,30 Therefore, we briefly summarize only the aspects that are relevant to this work. Molecules of both solvents are treated as three-site bodies. In the water molecule, the partial charges are located on the oxygen (-0.66 e) and hydrogen (+0.33 e), whereas, in the methanol molecule, the partial charges are centered on oxygen (-0.6 e), hydroxyl hydrogen (+0.35 e), and the methyl group, which is considered the pseudo-atom (+0.25 e). The flexible models of the water and methanol molecules permit internal molecular motions; therefore, total pair potentials consist of intra- and intermolecular parts. The intramolecular parts are expressed as the power series of internal coordinates,31 whereas the intermolecular parts are the sum of the Coulomb and non-Coulomb terms. All interactions involving ions are expressed as follows:
Vij(r) )
Qij Aij + + Bij‚exp(-Cij‚rij) rij rnij
(1)
ij
Here rij denotes the distance between ions or between the ion and sites of the solvent molecule. The Qij term represents the Coulomb interactions, and parameters Aij, Bij, and Cij, employed to describe non-Coulomb interactions, do not have any physical meaning. The parameters of the pair potentials for ions are summarized in Table 1. The energies for the complexes of Ca2+ and the solvent molecules (water and methanol) obtained from ab initio calculations and those computed for the pair potentials used in the MD simulation are shown in Figure 1 as functions of the cation-oxygen distance for the most favored antidipole orientation. As seen, the energies for Ca2+-water and Ca2+-methanol complexes are very close. In the global minimum, the energy difference does not exceed 10%.
TABLE 1: Parameters Qij, Aij, Bij, and Cij in Eq 1 for All Interactions of Ions i
A
Ca Ca Ca Ca Ca Cl Cl Cl Cl Cl Ca Cl Ca
Om Hm Me Ow Hw Om Hm Me Ow Hw Ca Cl Cl
QiR AiR [kJ Å mol-1] [kJ Ån mol-1] -1667.3 972.58 694.70 -1832.56 916.28 833.61 -486.27 -347.34 916.28 -458.14 5557.6 1389.4 2778.8
-1372.6 933.29 -474.93 -1572.6 626.39 127.00 -193.37 6.7657 9.34 -68.27 -15198 -28672 -353.01
Bia [kJ mol-1]
CiR [Å-1]
n refs
2.5970 × 105 8.3273 × 102 5.1660 × 104 2.5860 × 104 1.2022 × 105 1.4529 × 105 2.5086 × 104 5.9250 × 105 1.1749 × 105 9.029 × 104 2.6010 × 106 9.1704 × 105 3.6608 × 105
3.4900 0.9600 2.7930 3.4900 6.7900 3.1999 3.3082 3.2984 2.6727 4.542 4.4870 3.3863 3.0100
2 2 2 2 2 2 2 2 2 2 6 6 2
22 22 22 4 4 27 27 27 28 28 22 27 4
MD simulations were carried out for a microcanonical NVE ensemble. In all simulations the cubic boxes contained 400 solvent molecules and four CaCl2 molecules. Details of the simulated solutions are listed in Table 2. The box lengths were calculated from the experimental solution densities at 298 K. For all electrostatic interactions, the Ewald summation was used, whereas, for the non-Coulombic ones, the shifted-force potential method32 with a cutoff distance equal to the half of the both length was applied. The starting configurations were obtained by a random displacement of the particles in the cube. The time step was 0.25 fs. After about 10 ps of equilibration, the simulation of each system was extended over 150 ps. Temperatures shown in Table 2 were averaged over the whole simulation runs of the equilibrated systems. 3. Results and Discussion 3.1. Radial Distribution Function of the Cation. The nearest environment of Ca2+ in the methanol-water mixture can be described by five radial distribution functions, two of them for the sites of water (Ow and Hw) and three for the sites of methanol (Om, Hm, and CH3). The characteristic parameters of these functions, that is, the positions of the first (Rmax1) and second (Rmax2) maxima, the heights of the maxima, g(Rmax), and the positions of the first (rmin1) and second (rmin2) minima are summarized in Table 3. In aqueous solution, the radial distribution function for the cation and water’s oxygen, gCaOw(r), exhibits a sharp first maximum at 0.237 ( 0.003 nm. Its position agrees excellently with the average distance between Ca2+ and water’s oxygen atoms (about 0.24 nm), deduced from X-ray and neutron scattering experiments.1-11 Almost the same distance (about 0.25 nm) has been found for Ca2+ and methanol’s oxygen.11,16 This agrees with ab initio calculations, which give very similar energies of Ca2+ interactions with water and methanol molecules (see Figure 1). In such a case, one may expect that the addition of methanol will not affect the position of the first peak of the gCaOw(r) function. Indeed, in mixed solvent, the first maximum of the gCaOw(r) function remains at about 0.24 nm. However, the first peak of the gCaOw(r) function heightens with increasing methanol concentration. In a water deficit mixture, when the water content is 10 mol %, the first maximum of the gCaOw(r) function is about 5 times higher than its height in aqueous solution. A similar feature, although less substantial, has been observed previously for Na+ in a methanol-water mixture.25,28 Such significant enhancement of the gCaOw(r) maximum may result from either a preferential hydration of the calcium ions and/or a significant stabilization of the first coordination shell.
Solvation of Ca2+ in Methanol-Water Mixtures
J. Phys. Chem. B, Vol. 111, No. 51, 2007 14273
Figure 1. Comparison of the potential energies of Ca2+ interactions with water (solid line) and methanol (dashed line) molecules for the effective potentials, used in the simulations (left) and obtained from ab initio calculations (right) for the antidipole orientation of the solvent molecules (see the inset).
TABLE 2: Parameters of the Simulated CaCl2 Solutions average methanol CaCl2 experimental box mole fraction concentration density at 298 K length temperature K xm g‚cm-3 nm mol‚dm-3 0.00 0.05 0.10 0.50 0.90
0.557 0.527 0.506 0.356 0.266
1.04520 1.02633 1.01926 0.91577 0.83426
2.2992 2.3411 2.3738 2.6662 2.9345
297 ( 6 296 ( 6 295 ( 6 297 ( 6 298 ( 6
In aqueous solution, the gCaOw(r) function exhibits the second and third maximum. These peaks are very clearly separated, as can be seen from Figure 3. The position of the second peak, between 0.4 and 0.5 nm, coincides with the average distances of the second water neighbors deduced from X-ray scattering.11 The influence of methanol on the second peak is like that on the first peak; that is, the position of the peak is independent of the methanol content, but its shape changes. In aqueous solution, the second maximum of the gCaOw(r) function is split into two peaks of similar heights, at 0.43 and 0.49 nm, respectively. When methanol is added, this splitting becomes less visible, and it vanishes in equimolar mixture. Such changes may be due to different structures of water and the equimolar methanolwater mixture. In mixed solvent, interactions of the calcium ions with water molecules are favored, despite the similarities of the Ca2+water and Ca2+-methanol potentials. It can be deduced from the gCaOm(r) function. In methanol deficit solvents, when the methanol concentration does not exceed 10 mol %, the first and second maxima of the gCaOm(r) function, expected to be at about 0.25 and 0.49 nm, are absent. This means that, in the methanol deficit mixtures, the methanol molecules do not enter the first and even the second coordination shell of Ca2+. The first and second maxima of the gCaOm(r) function appear at the expected positions when the methanol content reaches 50 mol %, that is, when the concentrations of both solvent components are the same. The positions of the gCaOm(r) peaks are found at about 0.25 and 0.49 nm, which means that the average distance between the calcium ion and the methanol’s oxygen is independent of the water content. The presence of water, however, affects the height of the first maximum. In equimolar mixtures, the first peak of the gCaOm(r) function is about 4 times lower than that in methanol solution (see Table 3). This suggests that
Ca2+ coordinates less methanol molecules. Water content less than 50 mol % does not influence the height of the second gCaOm(r) peak. Radial distribution functions of the calcium ion and hydroxyl hydrogen are drawn in Figure 2, and their characteristic parameters are summarized in Table 3. In aqueous solution, the gCaHw(r) function shows a well-formed first peak at about 0.31 nm. Its position, as compared with that of the gCaOw(r) function, is shifted to a longer distance of about 0.07 nm. This suggests an antidipole orientation of the water molecules in the first coordination shells of the calcium ion. The position of the gCaHw(r) first peak is independent, as expected, of the methanol concentration, which indicates that the methanol addition does not influence the orientation of water molecules in the primary coordination shell. In methanol and methanol-rich mixtures, the gCaHm(r) function exhibits a sharp first maximum at about 0.33 nm. Its position, independent of the methanol concentration, is shifted about 0.08 nm as compared with the position of the gCaOm(r) peak, what indicates that methanol molecules in the first shell of Ca2+ also prefer the antidipole orientation. In methanol and methanol-rich solutions, the radial distribution function for the cation and methyl group gCaMe(r) shows a sharp peak at 0.33 nm. Its position agrees with the average distance between Ca2+ and the carbon atoms extracted from the X-ray diffraction.11 Diffraction studies8,9,11,12 of concentrated aqueous solutions of CaCl2 supported the existence of the contact and solventseparated ion pairs. The distances between opposite ions were about 0.28 and 0.5 nm11,12 for the contact and solvent-shared ion pairs, respectively. In all simulated systems, we did not find any maximum of the gCaCl(r) function. This means that the ion pairing does not occur for moderate salt concentrations. 3.2. Coordination Numbers of the Cation. The numbers of the solvent molecules in the first and second coordination shells, (ni)1 and (ni)2, respectively, were computed by the integration of the gij(r) function within the boundaries of the coordination shells, r1 and r2, respectively:
∫rr
ni ) 4πFi
2
1
gij(r)r2dr
(2)
where Fi is the number density of the corresponding site. The boundaries of the shells resulted from the peaks of the g(r)
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TABLE 3: Characteristic Parameters of the Radial Distribution Functions: Positions (in nm) of Maxima Rmax and Minima rmin, Heights of Maxima g(Rmax), and Numbers of Solvent Molecules in the Coordination Shells n(rmin) xM
Rmax1
g(Rmax1)
rmin1
n(rmin1)
0.00
0.237
15.65
0.340
Water’s Oxygen 10
0.05
0.240
17.31
0.300
9.6
0.10
0.240
18.67
0.300
9.7
0.50 0.90
0.237 0.232
35.88 105.93
0.305 0.310
6.8 2.3
0.00 0.05 0.10 0.50 0.90
0.307 0.307 0.312 0.312 0.310
5.93 6.19 7.57 30.69 42.35
0.380 0.380 0.382 0.382 0.370
Water’s Hydrogen 20 20 19.4 13.6 4.5
Rmax2
g(Rmax2)
rmin2
n(rmin2)
0.430 0.49 0.430 0.48 0.440 (0.49) 0.45
2.82 (2.31) 3.19 (2.40) 2.80 (2.45) 2.38
0.552
27
0.558
28
0.564
23
0.558
7
0.500 0.505 0.512 0.518
1.41 2.37 2.28 3.50
0.620 0.620 0.620 0.623
59 58 51 15
0.652 0.478 0.480 0.488
1.90 3.05 3.47 3.05
0.760 0.555 0.565 5.65
∼5 8 ∼10 9
0.732 0.545 0.550 0.562
1.58 2.38 2.41 2.19
0.825 0.623 0.635 0.635
∼5 ∼6,5 ∼12 ∼11
0.510 0.540 0.560
2.46 2.15 1.85
0.653 0.635 0.640
14 ∼20 ∼21
Methanol’s Oxygen 0.05 0.10 0.50 0.90 1.00a
0.252 0.250 0.247
5.75 15.6 22.03
0.332 0.347 0.362
1.7 5.7 7.6
Methanol’s Hydroxyl Hydrogen 0.05 0.10 0.50 0.90 1.00a
0.337 0.335 0.332
2.96 8.46 11.90
0.419 0.440 0.400
1.7 5.7 7.6 Methyl Group
0.05 0.10 0.50 0.90 1.00a a
0.335 0.342 0.335
2.50 6.18 8.41
0.417 0.410 0.425
∼2 5.7 7.7
From ref 22.
functions. They were assumed to be r1 ) 0 and r2 ) rmin1 for the first coordination shell, and r1 ) rmin1 and r2 ) rmin2 for the second coordination shell. The results of integration are listed in Table 2. In aqueous solution, the first coordination shell of Ca2+ contains 10 water molecules. A similar number of coordinated water molecules, nw ) 9.5, was deduced from the freezing point depression,18 whereas the X-ray experiments9,11 yielded smaller numbers. Such a difference was expected, because the number of the coordinated water molecules depends on the salt concentration. Ca2+ coordinates eight water molecules in 1 M solution,11 therefore 10 coordinated water molecules in 0.56 M aqueous solution seems to be reasonable result. Although the energies of Ca2+ interactions with water and methanol molecules are very close (see Figure 1), the calcium ion coordinates only eight or seven methanol molecules.22 Thus we may expect that the methanol addition will slightly reduce the coordination number, but we do not expect any preferential solvation of Ca2+, which means that the composition of the first coordination shell should depend only on the composition of the mixed solvent. The picture derived from the MD simulations is different. As mentioned above, in methanol deficit solvent, when the methanol concentration does not exceed 10 mol %, the methanol molecules do not enter the first and second coordination shells of Ca2+. A few methanol molecules appear in the first coordination shell of Ca2+ when the methanol content in the mixed solvent reaches 50 mol %, but the water concentration in the vicinity of Ca2+ exceeds the water content in the bulk solvent. The methanol mole fraction in the first coordination
shells of the calcium ions, observed in the MD simulation, can be calculated as follows:
xm(observed) )
(nm)k (nm)k + (nw)rk
(3)
where (nm)k and (nw)k are the numbers of the methanol and water molecules, respectively, in either the first or second coordination shell, summarized in Table 3. The observed methanol mole fraction in the first and second shell of Ca2+ is compared with the methanol content in the bulk solution in Figure 4. The density of the methanol-water mixture decreases nonlinearly with increasing methanol mole fraction xm; therefore, the methanol content in the coordination shell is not the same as that in the bulk solvent, even when a preferential solvation does not occur. The expected mole fraction of methanol in the ion surrounding can be calculated as follows:33
Fm(xm)
nom‚ xm(expected) )
Fm(xm) nom‚ o Fm
Fom +
Fw(xm) now‚ o Fw
(4)
Here now and nom are the numbers of the coordinated solvent molecules in pure water and methanol, Fow and Fom denote the number densities of water and methanol in the aqueous and methanol solutions of CaCl2, while Fw(xm) and Fm(xm) are the
Solvation of Ca2+ in Methanol-Water Mixtures
Figure 2. Radial distribution functions of Ca2+ and sites of water (top) and methanol (bottom): oxygen (solid lines) and hydrogen (dashed lines) atoms in mixed solvents. The methanol mole fraction is written in the inset of each panel.
number densities of water and methanol in the CaCl2methanol-water systems. This expected methanol mole fraction is also presented in Figure 4.
J. Phys. Chem. B, Vol. 111, No. 51, 2007 14275
Figure 3. Radial distribution functions, beyond the first maximum, of Ca2+ and water’s (solid lines) and methanol’s (dashed lines) oxygen atoms in various solvents: (a) pure water and pure methanol, (b) 10 mol % of methanol, (c) 50 mol % of methanol, (d) 90 mol % of methanol.
The nonlinear changes of the mixed solvent density should give a slight excess of methanol in the primary coordination
14276 J. Phys. Chem. B, Vol. 111, No. 51, 2007
Figure 4. Dependence of the methanol mole fraction in the first (9) and second (3) coordination shell of Ca2+on the methanol mole fraction in the bulk solution. The dashed line represents the expected methanol content, calculated from eq 4.
shell of Ca2+. The results of MD simulation, however, show an opposite behavior, and the water content in the first coordination shell of Ca2+ is much higher as compared with that in the mixed solvent. In water-rich solvents, the first coordination shell of Ca2+ contains only water molecules. When the water concentration in the bulk solutions decreases to 50 mol %, the first Ca2+ shell contains about 80 mol % of water. This content is reduced to 30 mol % in water deficit solvent, when the bulk solution contains only 10 mol % of water. This leads to the conclusion that, in methanol-water mixtures, the Ca2+ ion is preferentially hydrated. The preferential hydration occurs despite the very similar interactions of Ca2+ with water and methanol molecules. This agrees with the results of selfdiffusion experiments. We have not observed any influence of CaCl2 on the methanol self-diffusion coefficient,23,26 even in the methanol deficit solutions, but we have noticed a slow down of the water translation, and, in water deficit solutions, the water self-diffusion coefficient is about 1 order of magnitude smaller than that of a methanol-water mixture of the same composition.26 This preference for water molecules also concerns the second coordination shell. In water-rich mixtures, the second coordination shell of Ca2+, similar to the primary shell, consists only of the water molecules. As can be seen from Figure 4, over the whole solvent composition, the water concentration in the second coordination shell of Ca2+ is higher than can be expected. This means that the preferential hydration of Ca2+ is extended beyond the nearest surrounding of the cation. This phenomenon may induce the phase separation observed for higher concentrations of CaCl2.26 Integration of the second maximum of the gCaOw(r) function shows that the second coordination shell contains 27-28 water molecules. A smaller number, about 13 water molecules in the second shell of the cation, has been deduced from the X-ray diffraction. The reasons for this discrepancy might be different. First of all, X-ray diffraction was done for the more concentrated solutions, where the ion-pairing occurs. Formation of the solvent-separated and solvent-shared ion pairs must partially destroy the second and even the first coordination shells. Moreover, the distance between Ca2+ and the oxygen atom of the second neighbors (0.4-0.5 nm) coincides with the distances between ions in the solvent-separated ion pairs and between oxygen atoms in the first coordination shells of calcium and
Owczarek et al. chloride ions;11 therefore, the diffraction methods fail in the precise determination of the coordination numbers.11 Comparison of the first and second coordination numbers indicates that, in aqueous and water-rich solutions, almost any water molecule in the first shell has three neighbors in the second shell. The number of the neighbors in the second shell decreases rapidly with increasing methanol concentration. The water and methanol molecules in the first shell of Ca2+ have only two neighbors in the second shell, when the methanol content in the solution reaches 50 mol %, and they have only one neighbor in the second shell, when the solution contains 90 mol % of methanol. We have analyzed whether the molecules in the primary coordination shell are hydrogen bonded with those in the second shell. To calculate the average number of H-bonds per molecule 〈nHB〉, a geometric definition of H-bond34 was applied. This criterion assumed two molecules to be H-bonded when the distances between two oxygen atoms does not exceed 0.350 nm, the distance between the oxygen atom of the HBbond acceptor and hydrogen atom of the H-bond donor is smaller than 0.250 nm, and the angle between the vector connecting the oxygen atoms and the OH bond of the H-bond donor does not exceed 30°. This definition corresponds to an energetic criterion, which treats two molecules as being Hbonded when their interaction energy is lower than -8 kJ/mol.34 The average numbers of the H-bonds 〈nHB〉 were calculated in 0.001 ps intervals over the whole simulation runs. In aqueous solutions of CaCl2, the average number of H-bonds per water molecule, 〈nHB〉w ) 3.1, is the same as that in NaCl solution.34 This value is slightly smaller as compared with the average number of H-bonds in pure water, 〈nHB〉w ) 3.5. This means that the addition of CaCl2 slightly destroys the H-bonded network of water, and the influences of calcium and sodium chloride on the water structure are very similar. A discrepancy between NaCl and CaCl2 aqueous solutions appears when we compare the average numbers of H-bonds per molecule in the first coordination shells of the Ca2+ and Na+ ions. Most of the water molecules in the first shell of Ca2+ have only one H-bonded neighbor, [〈nHB〉w]Ca2+ ) 1.2, whereas all water molecules in the first shell of Na+ have two H-bonded neighbors, [〈nHB〉w]Na+ ) 2. This discrepancy is probably due to the different structures of the first coordination shells of both ions. The sizes of the hydration shells of both ions are very close. The gCaOw(r) function shows the first minimum at 0.34 nm, whereas the first minimum of the gNaOw(r) function has been found at 0.32 nm.28 Their radii in crystal are almost the same: the radius of Ca2+ is 0.100 nm, whereas that of Na+ is 0.102 nm.35 The Na+ shell consists of six water molecules, which display the antidipole orientation. The Ca2+ hydration shell is the same size, but contains 10 water molecules; therefore, its structure must be more compact, and some of the water molecules in the Ca2+ shell cannot be properly oriented to form two H-bonds as the H-bond donors. The influence of 5 mol % methanol on the H-bond formation of the coordinated water molecules confirms the above supposition. In this solution, the water molecules coordinated by Ca2+ form less H-bonds with their neighbors, [〈nHB〉w]Ca2+ ) 1.1. It is known that 5 mol % of methanol enhances the tetrahedral water structure and strengthens the H-bonds between water molecules.36 This probably causes a worse fit of the irregular structure of the Ca2+ coordination shell to the more ordered tetrahedral structure of the mixture. A weakening of the water network with higher methanol content was observed.36 Thus the coordination shell of Ca2+ may expand, and, when the methanol content reaches
Solvation of Ca2+ in Methanol-Water Mixtures
Figure 5. Angular distribution functions of the nearest water (left) and methanol (right) molecules around Ca2+ in various solvents: pure water (∆), 5 mol % of methanol (O), 50 mol % of methanol (3), 90 mol % of methanol (0), pure methanol (left triangle).
50 mol %, the average number of the H-bonds per water molecule in the Ca2+ first shell increases, [〈nHB〉w]Ca2+ = 1.9. The methanol molecules appear in the primary shell of Ca2+ in the methanol-rich mixtures. These molecules have one H-bonded neighbor ([〈nHB〉m]Ca2+ = 1). This agrees with the supposition that solvent molecules display the antidipole orientation. 3.3. Orientation of the Solvent Molecules in the First Coordination Shell of Ca2+. The orientation of the solvent molecules around the cation is characterized by an angle θ between the vector connecting the ion with the oxygen atom and the dipole moment of the solvent molecule (see inset in Figure 5). The angle distributions are shown in Figure 5. In aqueous solution, most of the water molecules around the Ca2+ ion exhibit the antidipole orientation, as it can be deduced from the dominant peak centered at cos θ ) -1. There is also a shoulder for cos θ = -0.7, which means that the dipole moments of a few water neighbors are tilted by about 45° from the antidipole orientation. Similar distribution has been reported previously.4 The shoulder is observed in water-rich solutions for 5 and 10 mol % of methanol. This shoulder vanishes and the dominant peak sharpens when the methanol content reaches 50 mol %. This is a consequence of the decreasing coordination number, which is about 10 in aqueous solution and about 7 in the equimolar mixture. The observed change of the θ angle distribution confirms the suggestion of Heinzinger et al.3 that only seven of the water molecules in the vicinity of the Ca2+ ion exhibit the antidipole orientation. Changes of the angular distribution are consistent with the increasing value of [〈nHB〉w]Ca2+ discussed above. The orientation of methanol molecules around the calcium ion is slightly different. Distribution of the angle θ exhibits a maximum at cos θ ) -0.9, which means that the methanol neighbors of the Ca2+ ion do not show the strict antidipole orientation, but their dipole moments are tilted by about 25°. The addition of water does not affect the position of that peak, which indicates that water neighbors do not influence the orientation of the methanol molecules in the solvation shell of Ca2+. To further describe the organization of the solvent molecules in the cation solvation shell, the distributions of the angle O-Ca2+-O were calculated, without any distinction between oxygen atoms belonging to water and methanol molecules. In
J. Phys. Chem. B, Vol. 111, No. 51, 2007 14277 aqueous solution, the angle distribution shows two peaks at about φ = 67° and φ = 135°, respectively. These results agree with the most probable angles reported by Heinzinger et al.4 Greater Ow-Ca2+-Ow angles, about 92° and 176°, have been found by Jiao et al.37 Both peaks of the angle distribution are sharp, which suggests a high degree of order. Only the angle of about 67°, however, is close to the value, which might be expected for tetrahedral or hexahedral symmetry. The angle of about 135° cannot be correlated with any of these polyhedrons. This leads to the conclusion that the first coordination shell of Ca2+ shows a high degree of order without any particular symmetry. In methanol-water mixtures, despite the decreasing number of the molecules in the primary Ca2+ shell, both peaks of the angle distribution are shifted to slightly greater values. In methanol solution, when the Ca2+ ion coordinates either eight or seven molecules and the hexahedral symmetry of the first shell might be expected, the most probable Ow-Ca2+-Ow angles are 75° and 145°, respectively. Only the first of these angles agrees with the hexahedral arrangement, but the second peak does not fit such a symmetry. 3.4. Residence Time of the Solvent Molecules in the Ca2+ Shell. The stability of the ion coordination shell is an important parameter, because it can affect the rate constant of biochemical processes. To characterize the stability of the coordination shell, we calculated the residence time of the solvent molecules. This time has been calculated from the time correlation function R(t):
R(t) )
1
nion nsolv
[κij(0)‚κij(t) ∑∑ j)1
nion‚nsolv i)1
(5)
where κij(t) is the step function, which is 1 if the solvent molecule j has been found in the coordination shell of the ion i at the time t, and 0 otherwise. The terms nion and nsolv denote the numbers of the ion and solvent molecules in the first coordination shell, respectively. The calculations of the R(t) functions were performed for at least 500 randomly chosen initial configurations. The time interval was ∆t ) 0.2 ps, which means that the solvent molecules could leave the coordination shell for a period shorter than ∆t; otherwise they were neglected in further calculations. Time correlation functions for the Ca2+ ions were computed independently for the water and methanol molecules. We found that the solvent composition does not influence the R(t) functions. In all studied systems, the R(t) functions for Ca2+ ions decrease rapidly during the period shorter than 1 ps; afterward, they reach a constant value, close to 0.95. This means that about 5% of the solvent molecules, either water or methanol, leave the coordination shell during 1 ps, whereas about 95% do not leave the coordination shell during the whole simulation time of 150 ps. Thus the coordination shell of Ca2+ is very stable, with the lifetime significantly exceeding 150 ps and being independent of the solvent composition. The long lifetime of the Ca2+ primary hydration shell (about 700 ps) was reported by Koneshan et al.14 The long residence time of the solvent molecules in the vicinity of Ca2+ ions was expected, because the hydrodynamic radius of the ion, calculated from the ion self-diffusion coefficient, noticeably exceeds the ion radius in crystal.23 This means that the Ca2+ ion moves with its coordination shell together,38 because the ion field controls the translations of all nearest neighbors.
14278 J. Phys. Chem. B, Vol. 111, No. 51, 2007 4. Conclusions The results presented above lead to the following conclusions: The number of solvent molecules coordinated by the calcium ions depends on the solvent composition, and it decreases from 10 water molecules forming the first coordination shell in aqueous solution to less than eight methanol molecules observed in the methanol solution of CaCl2. We observed a significant excess of water content around Ca2+, despite the very similar energies of its interactions with the water and methanol molecules. Over the whole range of the solvent composition, the content of water in the first and second coordination shells of Ca2+ exceeds the water concentration in the solution. This means that the calcium ions are preferentially hydrated. This conclusion agrees with the experimental results, which have shown that the addition of calcium chloride does not affect the self-diffusion coefficient of methanol, but noticeably affects the self-diffusion coefficient of water.26 Most of the solvent molecules in the first coordination shell of Ca2+ display the antidipole orientation, but they do not form any regular polyhedron. Although the antidipole orientation allows the molecules to act as H-bond donors, in aqueous solution and in water-rich mixtures, for 5 mol % of methanol, the average number of H-bonds per water molecule is significantly less than expected. Most of the water molecules in the first hydration shell have only one H-bonded neighbor, because the irregular first coordination shell of Ca2+ cannot fit the tetrahedral structure of water. The first coordination shell of Ca2+ is very stable, and this stability is independent of the solvent composition. Most of the solvent molecules, both water and methanol, reside in the first coordination shell over the whole time of the simulation. The long residence time, longer than 150 ps, agrees with the results of the self-diffusion coefficients and explains why the hydrodynamic radius of Ca2+ is much greater than the radius in crystal.23 Acknowledgment. The financial support of the Polish State Committee for Scientific Research under Grant No. N204 014 31/0293 and the Interdisciplinary Centre for Mathematical and Computational Modeling (ICM) of Warsaw University, Project Number G27-17, is gratefully acknowledged. E.O. is grateful for the financial support of Mechanizm Widdok (Z/210/112.6/ 04/05/U/2/06). References and Notes (1) Licheri, G.; Piccalunga, G.; Pinna, G. J. Phys. Chem. 1975, 63, 4412.
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