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Solvation of Ca2+ in aqueous methanol—MD simulation studies
Journal of Molecular Liquids 125 (2006) 151 – 157 www.elsevier.com/locate/molliq
Solvation of Ca2+ in aqueous methanol—MD simulation studies Katarzyna Bujnicka, Ewa Hawlicka * Institute of Applied Radiation Chemistry, Department of Chemistry, Technical University, Zeromskiego 116, 90-924 Lodz, Poland Available online 6 January 2006
Abstract MD simulations have been performed for solutions of CaCl2 in water and aqueous methanol. Both solvents have been described by flexible models, whereas the ions were modelled as charged Lennard – Jones spheres. An analysis of solvation shells has been based on radial and angular distribution functions. In aqueous solution the calcium ion coordinates either 8 or 9 water molecules. Addition of methanol reduces the number of the coordinated water molecules and the Ca2+ ion becomes selectively solvated by methanol. The coordination shell of the Cl ion, consisting of more than 10 water molecules, is poorly defined, but 6 of them form almost linear H – bonds with the anion. Addition of methanol does affect neither the coordination number nor the orientation of the water molecules in the shell of Cl and the anion is preferentially hydrated. In aqueous solution the association of unlike ions occurs. Addition of methanol reduces the association of unlike ions, but induces an aggregation of cations and formation of multi-ion aggregates, which are preferentially solvated by methanol molecules. When the methanol concentration increases these multi-ion aggregates become a nucleus of phase separation. D 2005 Elsevier B.V. All rights reserved. Keywords: MD simulations; Aqueous methanol; Solvation
1. Introduction The calcium ion plays a key role in several biological processes and its biochemical activity depends probably on the ion hydration. This explains the great interest in solvation of Ca2+. The structure of its first co-ordination shell, particularly in aqueous solutions, has been investigated by diffraction techniques [1 – 8], MD simulation [4,9– 11] and ab initio calculations [7]. In aqueous solutions, the first co-ordination shell of Ca2+ consists of 8 [7] or even more water molecules [11]. Recent ab inito calculations have shown that the binding energy per water molecule in the Ca2+(H2O)n cluster increases with increasing number of coordinated molecules and becomes comparable with energy of H-bonds between the water molecules for n > 8. [7]. This can explain both a decrease of Ca2+ hydration number with increasing salt concentration [11] and a decrease of the size of the Ca2+ hydration shell in aqueous methanol [12]. Recent X-ray experiments and ab initio calculations have shown [7] that in methanol the coordination number of the Ca2+ ion is smaller than in water and the cation becomes six-
* Corresponding author. Tel.: +48 42 6313195; fax: +48 42 6365008. E-mail address: [email protected] (E. Hawlicka). 0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2005.11.008
coordinated. The first coordination shell has very stable octahedral arrangement. Thus an influence of the salt concentration on the solvation number is very slight; less observable than in aqueous solution. Moreover the binding energy per solvent molecule in Ca2+(CH3OH)n clusters exceeds the energy in Ca2+(H2O)n clusters. Different coordination numbers of Ca2+ in aqueous and methanol solutions and slightly different binding energies of the solvent molecules suggest that in methanol – water mixtures a Ca2+ ion can be solvated selectively. Unfortunately such selective solvation cannot be investigated using the X-ray diffraction, because there is no significant difference between distances of oxygen atoms, either of water or of methanol, and Ca2+ [7]. Moreover, the peak due to interactions between Ca2+ and carbon atoms overlaps with other peaks resulting from interactions between two oxygen atoms of coordinated solvent molecules and between carbon and oxygen atoms. Thus this peak cannot provide reliably information about composition of the coordination shell. The hydration of Ca2+ in diluted solutions, below 1 M, cannot be investigated using the diffraction techniques, but information about the co-ordination shell of Ca2+ can be deduced from self-diffusion coefficients. Our recent studies of the self-diffusion coefficients [12] have shown a that small amount of methanol reduces the size of the first coordination
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K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
shell of Ca2+, but when the methanol content increases the radius of solvated cation also increases. The observed increase of the Ca2+ size suggests an aggregation of methanol around cations. MD simulation was performed to gain insight into coordination shells of Ca2+ and an effect of the methanol content on their composition and structure. 2. Details of potentials and simulations Water and methanol molecules were described by flexible potentials BJH [13] and PHH [14], respectively. Both water and methanol molecules contain three force centres. In the water molecule the partial charges are located on the oxygen ( 0.66 e) and hydrogen (+ 0.33 e) atoms. The methanol molecule consists of charged oxygen ( 0.6 e), hydroxyl hydrogen (+ 0.35 e) and the methyl group (+ 0.25 e) treated as a pseudo-atom. Non-Coulomb terms describing the O – O, O – H and H –H interactions of methanol and water molecules have been taken from the modified CF model of water [15]. Non-Coulomb interactions between methyl group and hydroxyl hydrogen have been neglected, and those between the methyl group and other sites have been represented by Lennard –Jones (L –J) potentials [16]. Non-Coulomb interactions of ions have been represented by Lennard –Jones potentials. L – J parameters ( ii and r ii for ions and water were taken from Ref. [9] and for methanol from Ref. [16]. Other LJ parameters have been calculated according to the standard combining rules: eij ¼
pffiffiffiffiffiffiffiffiffi eii Iejj
and rij ¼
rii þ rjj : 2
ð1Þ
All ion – solvent and ion – ion interactions have been expressed by the sum of Coulomb and non-Coulomb terms: Vij ðrÞ ¼
3. Results and discussion
Qij Aij Bij þ 12 6 : rij rij rij
ð2Þ
Parameters of the calcium ion potentials are summarized in Table 1 and the potentials for chloride ion have been reported previously [17]. Pair potentials for Ca2+ and solvent molecules are drawn as functions of the cation– oxygen distance for the coplanar arrangement and an anti-dipole orientation of the solvent molecule. As can be seen from Fig. 1 complexes of Ca2+ with water and methanol molecules exhibit the lowest binding Table 1 Parameters Q ij (kJ nm mol 1), A ij (kJ nm12 mol 1) and B ij (kJ nm6 mol 1 for interactions of Ca2+ with water, methanol and ions Ion
Site
Q ij a
A ij 106
B ij 103
Ca2+
OW HW OM HM CH3 Ca2+ Cl
183.26 91.63 166.75 97.27 69.48 555.83 277.91
3.444 0 3.444 0 26.180 3.680 20.090
2.290 0 2.290 0 8.847 1.028 5.796
2+
Ca Ca2+ a
energy at 0.24 nm. This position is in very good agreement with the average Ca2+ – oxygen distance in clusters of water and methanol [7]. The binding energy of water molecule, 144.2 kJ/mol is very close to the binding energy per water molecule in clusters containing more than 6 water molecules [7]. This is slightly higher than the binding energy of methanol molecule, 149.3 kJ/mol. Such feature is in good agreement with ab initio calculations, though they have shown even bigger difference between Ca2+ ion interactions with methanol and water [7]. All simulations were performed for standard NVE ensemble. The simulations were carried out for aqueous solution and mixtures containing 5 and 10 mol% of methanol in water. The concentration of CaCl2 was equal 0.55 M. Our self-diffusion studies have shown that this is the highest concentration for which the ion pairing, in aqueous solution, can be neglected. Thus the periodic cubes contained 400 solvent molecules, 4 cations and 8 anions. Their lengths were calculated from experimental densities at 298 K. Initial configurations were obtained by random placement of particles in the cubic box. Ewald summation was used for Coulomb interactions and the shifted force potential method for all non-Coulomb ones [18]. The simulation time step was 0.25 fs. After about 15 ps of equilibration, simulation of each system was extended up to 100 ps. Velocities and co-ordinates of all sites were collected in 1 fs intervals. In all simulations stability of the total energy was better than 0.01% and the average temperature deviates from the assumed 298 K by less than T 5 K. Three independent simulations, starting from different random placement of particles in the box, have been carried out for every solution and all results have been the same within statistical uncertainty.
Calculated using the BJH and PHH models of water and methanol, respectively.
The nearest surrounding of the Ca2+ ion in methanol – water mixture can be described by four radial distribution functions; two for water sites (OW and HW) and two for methanol sites (OM and HM). These radial distribution functions are shown in Fig. 2. Characteristic parameters of the radial distribution functions are listed in Table 2. There are positions of the first maximum R max and the maximum height, g ij (R max,). The coordination numbers n j (r min) were computed by integration of the corresponding g ij (r) peak to the first minimum r min: Z rmin nj ¼ 4IkIqj gij ðrÞr2 dr ð3Þ 0
q j denotes the number density of the j-th solvent component. These coordination numbers, n M and n W, were used to calculate the methanol mole fraction in the first coordination shell of ions, x Mshell: xshell M ¼
nM : nM þ nW
ð4Þ
The coordination numbers n j (r min) and the methanol mole fraction in the first coordination shell x Mshell are listed in Table 2.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
153
50
V(r), kJ/mol
0
-50
-100
-150 0.0
0.2
0.4
0.6 r, nm
0.8
1.0
1.2
Fig. 1. Potential energies of the Ca2+ complex with BJH water (solid) and PHH methanol (dotted) molecules as a function of the ion – oxygen distance for a coplanar, anti-dipole arrangement.
In aqueous solution both Ca2+ – OW and Ca2+ – HW radial distribution functions exhibit sharp peaks. The first maximum of g CaO(r) is found at 0.267 T 0.005 nm. Thus this average Ca2+ – OW distance is about 10% larger as compared with the results of X-ray and neutron diffractions, 0.246 nm [7] and 0.241 nm [8], respectively. That difference is not very significant and can be due to lower concentration of the simulated system, 0.55 M, than those investigated experimentally, 1.0 M [7] and 4.0 M [8], respectively. Although the Ca2+ hydration structure does not change dramatically with concentration, the neutron scattering experiments have shown a decrease of the Ca2+ – H distance with the increasing salt concentration. The discrepancy between
results of MD simulation and scattering experiments may be also due to an inadequate potential applied for ion interactions. We have noticed [17] that Lennard – Jones potentials slightly underestimate interactions of ions with BJH water and PHH methanol and in consequence they overestimate average distances between ions and sites of both solvents. We have however found that the kind of potential does not affect a composition of the ion coordination shell. In aqueous solution the sharp maximum of g CaH(r) function is observed at 0.34 nm and this distance is also about 10% larger as compared with the neutron scattering results [8]. However, the difference of the positions of the g CaO(r) and
gCa2+OM(r)
150
100
50
0 0.0
0.2
0.4
0.2
0.4
0.6
0.8
0.6
0.8
gCa2+OW(r)
10
5
0 0.0
r, nm Fig. 2. Ca2+ – methanol oxygen (upper) and Ca2+ – water oxygen (bottom) radial distribution functions in aqueous solution (dotted) and aqueous methanol, 5 mol% (dashed) and 10 mol% (solid).
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K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
Table 2 Characteristic parameters of the ion – oxygen radial distribution functions xM
Ion
Site
R M1
g(R M)
nj
0.0
Ca+ 2
OW H OW
0.267 0.340 0.365 (0.319) 0.267 (0.262) 0.267 0.340 0.270 0.325 0.360 0.265 0.375 0.282 0.267 0.340 0.270 0.330 0.360 (0.352) 0.267 (0.265) 0.365 (0.352) 0.270 (0.260)
10.3 4.09 2.87 (3.06) 1.88 (2.24) 4.55 1.58 130.0 41.9 3.01 2.03 1.89 1.17 4.34 1.37 71.7 27.2 3.06 (2.59) 3.22 (1.84) 0.99 (10.48) 1.37 (15.68)
8.5 17.3 16.7 (12.3) 6.5 (7.2) 3.4 6.7 4.7 5.2 11.3 6.4 0.3 0.1 3.1 6.3 5.6 6.2 6.3 (7.7) 6.3 (4.9) 0.2 (2.8) 0.2 (4.90)
Cl
HW 0.05
Ca+ 2
Cl
0.1
Ca+ 2
Cl
OW H OM HM OW HW OM HM OW H OM H OW HW OM HM
characterized by the angle / between two vectors; one of them is the vector connecting the ion and the oxygen atom of the solvent molecule, and the second is the dipole moment. Distributions of the angles have been calculated for water and methanol molecules independently and the results are presented in Fig. 3. In aqueous solution the angular distribution function exhibits a maximum at / ; 165-. This confirms that water molecules prefer almost anti-dipole orientation. In aqueous solution the g CaO(r) function shows also a broad peak at 0.505 T 0.005 nm. This represents the second coordination shell of calcium ions and its position agrees reasonably with the X-ray scattering result, 0.455 nm [7]. Although the fitting of the experimental structure functions gives this distance shorter of about 10%, one should notice that the resolution of the broad peak in the range 0.4 and 0.55 nm is not easy. This peak contains contributions of interactions of ions in solvent separated pairs and oxygen atoms in the coordination shells of ions. The most important feature seems to be the contribution of the solvent separated ion pairs, which are formed when a chloride ion replaces the water molecule in the second coordination shell of the calcium ion [5]. Thus in more concentrated CaCl2 solutions the second coordination hydration shell of Ca2+ may be partially distorted and the Ca2+ –O distance may be slightly shorter. The first coordination shell of Ca2+ consists of either 8 or 9 water molecules (n(r min) = 8.6). Usually the calcium ion is assumed to be eight-coordinated, but such slightly higher coordination number is in good agreement with results of other simulations [4,8,11]. Integration of the second peak of g CaO(r) gives 20 – 21 water molecules, whereas the fitting procedure of the experimental structure functions [7] leads to noticeably smaller numbers. It is worth stressing that the number of second neighbours depends on concentration and decreases from about 13 to 5 molecules when the concentration increases from 1 to 5 M [7]. In more concentrated solutions two chloride
x shell M
0.58 0.43
0.02 0.015
0.64 0.50
0.03 (0.26) 0.03 (0.50)
R max denotes the distance, where radial distribution function has a maximum of is the methanol the height g ij (R max), n j is the coordination number and x shell M mole fraction in the first co-ordination shell. Results for NaCl solution [17] are given in parentheses.
n (φ)
g CaH(r) peaks, about 0.073 nm (see Table 2), is in excellent agreement with the experimental results [8]. That difference suggests the water molecules in the coordination shell of Ca2+ prefer the anti-dipole orientation. The orientation of the solvent molecules in the coordination shell of the ion is usually
45
90
135
180
0
45
90
135
180
n (φ)
0
Fig. 3. Distribution functions of the angular orientation around Ca+ 2 of the nearest methanol (upper) and water (bottom) molecules in aqueous solution (solid) and in aqueous methanol solutions: 5 mol% of methanol (dashed) and 10 mol% of methanol (dotted). / is the angle between the dipole moment of the solvent molecule and the vector connecting Ca2+ and oxygen.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
ions (1.8 T 0.2 [9]) enter the second coordination shell of Ca2+ and a solvent shared ion pair is formed. An arrangement of such coordination shell must be changed, thus the number of water molecules in the second coordination shell decreases. Recent results of X-ray diffraction [7] have shown similar arrangement of methanol molecules around Ca2+ ions, although the average distance of Ca2+ –OM is slightly shorter than that of Ca2+ – OW. This similarity causes a difficulty to investigate a preferential solvation of ions in methanol –water mixtures [19] and the only measure of an eventual effect can be the location of methyl groups. But they are not coordinated by cations. Characteristic parameters of radial distribution functions listed in Table 2 confirm that the average distance between Ca2+ and oxygen of either methanol or water is almost the same. Similar feature is observed for Na+ ions [17]. However, the solvation of Na+ and Ca2+ in aqueous methanol shows a qualitative difference. As seen from Fig. 2 small amounts of methanol, 5 and 10 mol%, do not affect the position of the Ca2+ OW peak, but reduces the peak height of more than 50%. Integration of g(r) function shows a dramatic reduction of the number of water molecules coordinated by Ca2+. This number decreases from more than eight to less than four water molecules. The total number of solvent molecules coordinated by the calcium ion remains, however, unchanged, because methanol molecules enter the nearest environment of the cation. This peak of the Ca2+ OM radial distribution function at 0.27 nm, is very high and is followed by a broad second peak at 0.4 – 0.55 nm. The coordination numbers listed in Table 2 show that Ca2+ ions are preferentially solvated by methanol. The content of methanol in the coordination shells is very high, much higher than in bulk solution. The high concentration of methanol in the first coordination shell of Ca2+ causes some of the molecules not to show anti-dipole orientation, as it can be deduced from Fig. 3. A detailed analysis of the particle
155
configurations suggests that methanol molecules aggregate around Ca2+. Most of them can be found either in the first or the second coordination shell. Such behaviour was not expected, because interactions of Ca2+ with water and methanol are similar (see Fig. 1). A comparison of the characteristic parameters of the radial distribution functions for chloride ions in CaCl2 solutions with those for NaCl solutions [17] shows that a change of the counter-ion does not affect the Cl oxygen distance. In aqueous solution of CaCl2 the first maximum (see Fig. 4) is, however, lower but broader and the following maximum is very poorly defined. This indicates a rather fast exchange of the water molecules between the first coordination shell and bulk water. Integration of the first g ClO(r) peak gives more than 16 water molecules. This unreasonable high value results from the poorly defined position of the first minimum and suggests that interactions of the anion with water molecules are rather weak. The g ClH(r) function better describes the coordination shell of Cl. Its first maximum at 0.267 nm is sharper and is followed by a better defined minimum. As expected the Cl HW distance is shorter and indicates the OH bond orientation of water molecules in the Cl shell. The angular distribution function, shown in Fig. 5, with the maximum at / ; 50-, followed by a broad maximum at / ; 90- indicates that only some of the water molecules exhibit the OH bond orientation. The angular distribution function has been calculated independently for two different spheres around the anion. Their radii have corresponded to the minima the of g ClO(r) and g ClH(r) functions, respectively. As seen from Fig. 5 the angular distribution function, calculated for molecules in the smaller sphere, with the radius defined by the position of the g ClH(r) minimum, shows sharper maximum at / ; 50-, which represents OH oriented molecules. This means that the g ClH(r) function better represents the coordinated water molecule and
gCl-W(r)
4
2
0 0.0
0.2
0.4
0.2
0.4
0.6
0.8
0.6
0.8
gCl-OM(r)
2
1
0 0.0
r, nm Fig. 4. Cl water oxygen (upper) and Cl methanol oxygen (bottom) radial distribution functions in aqueous solution (dotted) and aqueous methanol 5 mol% (dashed) and 10 mol% (solid). Crosses in upper panel represent Cl HW radial distribution function.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
n (φ)
156
0
45
90 φ
135
180
Fig. 5. Distribution functions of the angular orientation of the water molecules in the coordination shell of Cl in aqueous solution (solid) and aqueous methanol 5 mol% (dashed) and 10 mol% (dotted). Angular orientation of water molecules within a small sphere (see text) in aqueous solution (?). / is the angle between the dipole moment of the solvent molecule and the vector connecting Cl and oxygen.
gCa2+Ca2+(r)
integration of this function gives a more reliable value of the coordination number. The result, n(r min) = 6.5, is in very good agreement with coordination number 6, extracted from X-ray diffraction in 1 M solution [7]. Addition of methanol does not affect the position of the g ClH(r) maximum but slightly reduces the Cl OW distance. With increasing methanol content the Cl OW first peak becomes slightly higher but sharper. Consequently the coordination number calculated by integration of g ClO(r) peak decreases. The first maximum of the Cl –HW function also increases with increasing methanol concentration, but the
number of hydrogen atoms in the vicinity of anion remains unchanged. When the methanol content reaches 10 mol% the coordination numbers calculated from both peaks, of the g ClO(r) and g ClH(r) functions, are the same. This suggests that addition of methanol stabilizes the H-bonded water molecules in the shell of chloride ions. In methanol –water solution of CaCl2 the chloride ion is preferentially hydrated and methanol molecules do not even enter the vicinity of the anion. Such feature is unexpected, because in NaCl solutions in methanol –water mixtures the strong preferential solvation of Cl by methanol molecules has
30 20 10 0
0.2
0.4
0.6
0.8
gCa2+Cl-(r)
15 10 5 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
gCl-Cl-(r)
2 1 0
0.2
0.4
0.6
0.8
r, nm Fig. 6. Radial distribution functions of ions: Ca2+ – Ca2+(upper), Ca2+ – Cl (middle) and Cl – Cl (bottom) in aqueous solution (solid line), 5% methanol (dashed line) and 10% methanol (dotted line).
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
been observed [17]. A detailed analysis shows that a broad, very poorly defined maximum of Cl OM maximum (see Fig. 2), does not represent the methanol molecules coordinated by Cl. These molecules are coordinated by the Ca2+ ions, engaged in the solvent separated pairs. Radial distribution functions of ions are shown in Fig. 6. In aqueous solution, unlike ions associate and the g CaCl(r) function exhibits the sharp maximum, located at 0.305 nm. This can be attributed to contact ion pairs [5,7]. The g CaCl(r) function can be used to compute the association constant K A [20]: Z rmin KA ¼ 4kINA I103 gþ ðrÞIr2 dr ð5Þ aþ þa
where (a + + a ) denotes the sum of the ionic radii in the crystal and r min is the position of the first minimum. In aqueous solution the association of unlike ions is negligible, because K A < 10. In aqueous methanol a decrease of the g CaCl(r) peak is accompanied by a rise of a new broad maximum at 0.55 –0.6 nm and a of peak the g CaCa(r) function (see Fig. 6), which suggests an aggregation of the cations. In aqueous solution the Ca2+ – Ca2+ function does not show any peak (see Fig. 6) and a detailed analysis of the positions of all particles confirms that the distribution of Ca2+ ions is random. Addition of methanol induces aggregation of Ca2+ ions. The well-defined g CaCa(r) peak, at about 0.7 nm is observed when the methanol content is very low, 5 mol%. When the methanol concentration increases two broad peaks are observed, at about 0.5 and 0.75 nm. A detailed analysis of the positions of all ions shows that the peak positions correspond to the distances between calcium ions in the big ion cluster [(Ca2+)4(Cl)5 – 6]. This cluster is preferentially solvated by methanol molecules and contains about 60% of all methanol molecules. This phenomenon may be considered as a nucleus of phase separation. It is worth to notice that formation of the cluster has been observed in all performed simulations, independently on the initial placement of particles in the cubic box.
ions results from a competition between ion – solvent interactions and a tendency of the solvent to preserve its H-bonded network. In aqueous methanol the cation seems to be selectively solvated by methanol, despite very similar interactions of the Ca2+ ion with water and methanol. One may suppose that both the coordination shell of Ca2+ consisting of 8 or more water molecules, and methanol molecules with a bulky methyl group, do not fit three dimensional water network. In consequence both, ions and methanol molecules are Fexcluded_ from the water structure. They aggregate and become a nucleus of a phase separation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
4. Conclusions Results presented above confirm our previous hypothesis [17] that in highly associated solvents, a selective solvation of
157
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Solvation of Ca2+ in aqueous methanol—MD simulation studies Katarzyna Bujnicka, Ewa Hawlicka * Institute of Applied Radiation Chemistry, Department of Chemistry, Technical University, Zeromskiego 116, 90-924 Lodz, Poland Available online 6 January 2006
Abstract MD simulations have been performed for solutions of CaCl2 in water and aqueous methanol. Both solvents have been described by flexible models, whereas the ions were modelled as charged Lennard – Jones spheres. An analysis of solvation shells has been based on radial and angular distribution functions. In aqueous solution the calcium ion coordinates either 8 or 9 water molecules. Addition of methanol reduces the number of the coordinated water molecules and the Ca2+ ion becomes selectively solvated by methanol. The coordination shell of the Cl ion, consisting of more than 10 water molecules, is poorly defined, but 6 of them form almost linear H – bonds with the anion. Addition of methanol does affect neither the coordination number nor the orientation of the water molecules in the shell of Cl and the anion is preferentially hydrated. In aqueous solution the association of unlike ions occurs. Addition of methanol reduces the association of unlike ions, but induces an aggregation of cations and formation of multi-ion aggregates, which are preferentially solvated by methanol molecules. When the methanol concentration increases these multi-ion aggregates become a nucleus of phase separation. D 2005 Elsevier B.V. All rights reserved. Keywords: MD simulations; Aqueous methanol; Solvation
1. Introduction The calcium ion plays a key role in several biological processes and its biochemical activity depends probably on the ion hydration. This explains the great interest in solvation of Ca2+. The structure of its first co-ordination shell, particularly in aqueous solutions, has been investigated by diffraction techniques [1 – 8], MD simulation [4,9– 11] and ab initio calculations [7]. In aqueous solutions, the first co-ordination shell of Ca2+ consists of 8 [7] or even more water molecules [11]. Recent ab inito calculations have shown that the binding energy per water molecule in the Ca2+(H2O)n cluster increases with increasing number of coordinated molecules and becomes comparable with energy of H-bonds between the water molecules for n > 8. [7]. This can explain both a decrease of Ca2+ hydration number with increasing salt concentration [11] and a decrease of the size of the Ca2+ hydration shell in aqueous methanol [12]. Recent X-ray experiments and ab initio calculations have shown [7] that in methanol the coordination number of the Ca2+ ion is smaller than in water and the cation becomes six-
* Corresponding author. Tel.: +48 42 6313195; fax: +48 42 6365008. E-mail address: [email protected] (E. Hawlicka). 0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2005.11.008
coordinated. The first coordination shell has very stable octahedral arrangement. Thus an influence of the salt concentration on the solvation number is very slight; less observable than in aqueous solution. Moreover the binding energy per solvent molecule in Ca2+(CH3OH)n clusters exceeds the energy in Ca2+(H2O)n clusters. Different coordination numbers of Ca2+ in aqueous and methanol solutions and slightly different binding energies of the solvent molecules suggest that in methanol – water mixtures a Ca2+ ion can be solvated selectively. Unfortunately such selective solvation cannot be investigated using the X-ray diffraction, because there is no significant difference between distances of oxygen atoms, either of water or of methanol, and Ca2+ [7]. Moreover, the peak due to interactions between Ca2+ and carbon atoms overlaps with other peaks resulting from interactions between two oxygen atoms of coordinated solvent molecules and between carbon and oxygen atoms. Thus this peak cannot provide reliably information about composition of the coordination shell. The hydration of Ca2+ in diluted solutions, below 1 M, cannot be investigated using the diffraction techniques, but information about the co-ordination shell of Ca2+ can be deduced from self-diffusion coefficients. Our recent studies of the self-diffusion coefficients [12] have shown a that small amount of methanol reduces the size of the first coordination
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K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
shell of Ca2+, but when the methanol content increases the radius of solvated cation also increases. The observed increase of the Ca2+ size suggests an aggregation of methanol around cations. MD simulation was performed to gain insight into coordination shells of Ca2+ and an effect of the methanol content on their composition and structure. 2. Details of potentials and simulations Water and methanol molecules were described by flexible potentials BJH [13] and PHH [14], respectively. Both water and methanol molecules contain three force centres. In the water molecule the partial charges are located on the oxygen ( 0.66 e) and hydrogen (+ 0.33 e) atoms. The methanol molecule consists of charged oxygen ( 0.6 e), hydroxyl hydrogen (+ 0.35 e) and the methyl group (+ 0.25 e) treated as a pseudo-atom. Non-Coulomb terms describing the O – O, O – H and H –H interactions of methanol and water molecules have been taken from the modified CF model of water [15]. Non-Coulomb interactions between methyl group and hydroxyl hydrogen have been neglected, and those between the methyl group and other sites have been represented by Lennard –Jones (L –J) potentials [16]. Non-Coulomb interactions of ions have been represented by Lennard –Jones potentials. L – J parameters ( ii and r ii for ions and water were taken from Ref. [9] and for methanol from Ref. [16]. Other LJ parameters have been calculated according to the standard combining rules: eij ¼
pffiffiffiffiffiffiffiffiffi eii Iejj
and rij ¼
rii þ rjj : 2
ð1Þ
All ion – solvent and ion – ion interactions have been expressed by the sum of Coulomb and non-Coulomb terms: Vij ðrÞ ¼
3. Results and discussion
Qij Aij Bij þ 12 6 : rij rij rij
ð2Þ
Parameters of the calcium ion potentials are summarized in Table 1 and the potentials for chloride ion have been reported previously [17]. Pair potentials for Ca2+ and solvent molecules are drawn as functions of the cation– oxygen distance for the coplanar arrangement and an anti-dipole orientation of the solvent molecule. As can be seen from Fig. 1 complexes of Ca2+ with water and methanol molecules exhibit the lowest binding Table 1 Parameters Q ij (kJ nm mol 1), A ij (kJ nm12 mol 1) and B ij (kJ nm6 mol 1 for interactions of Ca2+ with water, methanol and ions Ion
Site
Q ij a
A ij 106
B ij 103
Ca2+
OW HW OM HM CH3 Ca2+ Cl
183.26 91.63 166.75 97.27 69.48 555.83 277.91
3.444 0 3.444 0 26.180 3.680 20.090
2.290 0 2.290 0 8.847 1.028 5.796
2+
Ca Ca2+ a
energy at 0.24 nm. This position is in very good agreement with the average Ca2+ – oxygen distance in clusters of water and methanol [7]. The binding energy of water molecule, 144.2 kJ/mol is very close to the binding energy per water molecule in clusters containing more than 6 water molecules [7]. This is slightly higher than the binding energy of methanol molecule, 149.3 kJ/mol. Such feature is in good agreement with ab initio calculations, though they have shown even bigger difference between Ca2+ ion interactions with methanol and water [7]. All simulations were performed for standard NVE ensemble. The simulations were carried out for aqueous solution and mixtures containing 5 and 10 mol% of methanol in water. The concentration of CaCl2 was equal 0.55 M. Our self-diffusion studies have shown that this is the highest concentration for which the ion pairing, in aqueous solution, can be neglected. Thus the periodic cubes contained 400 solvent molecules, 4 cations and 8 anions. Their lengths were calculated from experimental densities at 298 K. Initial configurations were obtained by random placement of particles in the cubic box. Ewald summation was used for Coulomb interactions and the shifted force potential method for all non-Coulomb ones [18]. The simulation time step was 0.25 fs. After about 15 ps of equilibration, simulation of each system was extended up to 100 ps. Velocities and co-ordinates of all sites were collected in 1 fs intervals. In all simulations stability of the total energy was better than 0.01% and the average temperature deviates from the assumed 298 K by less than T 5 K. Three independent simulations, starting from different random placement of particles in the box, have been carried out for every solution and all results have been the same within statistical uncertainty.
Calculated using the BJH and PHH models of water and methanol, respectively.
The nearest surrounding of the Ca2+ ion in methanol – water mixture can be described by four radial distribution functions; two for water sites (OW and HW) and two for methanol sites (OM and HM). These radial distribution functions are shown in Fig. 2. Characteristic parameters of the radial distribution functions are listed in Table 2. There are positions of the first maximum R max and the maximum height, g ij (R max,). The coordination numbers n j (r min) were computed by integration of the corresponding g ij (r) peak to the first minimum r min: Z rmin nj ¼ 4IkIqj gij ðrÞr2 dr ð3Þ 0
q j denotes the number density of the j-th solvent component. These coordination numbers, n M and n W, were used to calculate the methanol mole fraction in the first coordination shell of ions, x Mshell: xshell M ¼
nM : nM þ nW
ð4Þ
The coordination numbers n j (r min) and the methanol mole fraction in the first coordination shell x Mshell are listed in Table 2.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
153
50
V(r), kJ/mol
0
-50
-100
-150 0.0
0.2
0.4
0.6 r, nm
0.8
1.0
1.2
Fig. 1. Potential energies of the Ca2+ complex with BJH water (solid) and PHH methanol (dotted) molecules as a function of the ion – oxygen distance for a coplanar, anti-dipole arrangement.
In aqueous solution both Ca2+ – OW and Ca2+ – HW radial distribution functions exhibit sharp peaks. The first maximum of g CaO(r) is found at 0.267 T 0.005 nm. Thus this average Ca2+ – OW distance is about 10% larger as compared with the results of X-ray and neutron diffractions, 0.246 nm [7] and 0.241 nm [8], respectively. That difference is not very significant and can be due to lower concentration of the simulated system, 0.55 M, than those investigated experimentally, 1.0 M [7] and 4.0 M [8], respectively. Although the Ca2+ hydration structure does not change dramatically with concentration, the neutron scattering experiments have shown a decrease of the Ca2+ – H distance with the increasing salt concentration. The discrepancy between
results of MD simulation and scattering experiments may be also due to an inadequate potential applied for ion interactions. We have noticed [17] that Lennard – Jones potentials slightly underestimate interactions of ions with BJH water and PHH methanol and in consequence they overestimate average distances between ions and sites of both solvents. We have however found that the kind of potential does not affect a composition of the ion coordination shell. In aqueous solution the sharp maximum of g CaH(r) function is observed at 0.34 nm and this distance is also about 10% larger as compared with the neutron scattering results [8]. However, the difference of the positions of the g CaO(r) and
gCa2+OM(r)
150
100
50
0 0.0
0.2
0.4
0.2
0.4
0.6
0.8
0.6
0.8
gCa2+OW(r)
10
5
0 0.0
r, nm Fig. 2. Ca2+ – methanol oxygen (upper) and Ca2+ – water oxygen (bottom) radial distribution functions in aqueous solution (dotted) and aqueous methanol, 5 mol% (dashed) and 10 mol% (solid).
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K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
Table 2 Characteristic parameters of the ion – oxygen radial distribution functions xM
Ion
Site
R M1
g(R M)
nj
0.0
Ca+ 2
OW H OW
0.267 0.340 0.365 (0.319) 0.267 (0.262) 0.267 0.340 0.270 0.325 0.360 0.265 0.375 0.282 0.267 0.340 0.270 0.330 0.360 (0.352) 0.267 (0.265) 0.365 (0.352) 0.270 (0.260)
10.3 4.09 2.87 (3.06) 1.88 (2.24) 4.55 1.58 130.0 41.9 3.01 2.03 1.89 1.17 4.34 1.37 71.7 27.2 3.06 (2.59) 3.22 (1.84) 0.99 (10.48) 1.37 (15.68)
8.5 17.3 16.7 (12.3) 6.5 (7.2) 3.4 6.7 4.7 5.2 11.3 6.4 0.3 0.1 3.1 6.3 5.6 6.2 6.3 (7.7) 6.3 (4.9) 0.2 (2.8) 0.2 (4.90)
Cl
HW 0.05
Ca+ 2
Cl
0.1
Ca+ 2
Cl
OW H OM HM OW HW OM HM OW H OM H OW HW OM HM
characterized by the angle / between two vectors; one of them is the vector connecting the ion and the oxygen atom of the solvent molecule, and the second is the dipole moment. Distributions of the angles have been calculated for water and methanol molecules independently and the results are presented in Fig. 3. In aqueous solution the angular distribution function exhibits a maximum at / ; 165-. This confirms that water molecules prefer almost anti-dipole orientation. In aqueous solution the g CaO(r) function shows also a broad peak at 0.505 T 0.005 nm. This represents the second coordination shell of calcium ions and its position agrees reasonably with the X-ray scattering result, 0.455 nm [7]. Although the fitting of the experimental structure functions gives this distance shorter of about 10%, one should notice that the resolution of the broad peak in the range 0.4 and 0.55 nm is not easy. This peak contains contributions of interactions of ions in solvent separated pairs and oxygen atoms in the coordination shells of ions. The most important feature seems to be the contribution of the solvent separated ion pairs, which are formed when a chloride ion replaces the water molecule in the second coordination shell of the calcium ion [5]. Thus in more concentrated CaCl2 solutions the second coordination hydration shell of Ca2+ may be partially distorted and the Ca2+ –O distance may be slightly shorter. The first coordination shell of Ca2+ consists of either 8 or 9 water molecules (n(r min) = 8.6). Usually the calcium ion is assumed to be eight-coordinated, but such slightly higher coordination number is in good agreement with results of other simulations [4,8,11]. Integration of the second peak of g CaO(r) gives 20 – 21 water molecules, whereas the fitting procedure of the experimental structure functions [7] leads to noticeably smaller numbers. It is worth stressing that the number of second neighbours depends on concentration and decreases from about 13 to 5 molecules when the concentration increases from 1 to 5 M [7]. In more concentrated solutions two chloride
x shell M
0.58 0.43
0.02 0.015
0.64 0.50
0.03 (0.26) 0.03 (0.50)
R max denotes the distance, where radial distribution function has a maximum of is the methanol the height g ij (R max), n j is the coordination number and x shell M mole fraction in the first co-ordination shell. Results for NaCl solution [17] are given in parentheses.
n (φ)
g CaH(r) peaks, about 0.073 nm (see Table 2), is in excellent agreement with the experimental results [8]. That difference suggests the water molecules in the coordination shell of Ca2+ prefer the anti-dipole orientation. The orientation of the solvent molecules in the coordination shell of the ion is usually
45
90
135
180
0
45
90
135
180
n (φ)
0
Fig. 3. Distribution functions of the angular orientation around Ca+ 2 of the nearest methanol (upper) and water (bottom) molecules in aqueous solution (solid) and in aqueous methanol solutions: 5 mol% of methanol (dashed) and 10 mol% of methanol (dotted). / is the angle between the dipole moment of the solvent molecule and the vector connecting Ca2+ and oxygen.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
ions (1.8 T 0.2 [9]) enter the second coordination shell of Ca2+ and a solvent shared ion pair is formed. An arrangement of such coordination shell must be changed, thus the number of water molecules in the second coordination shell decreases. Recent results of X-ray diffraction [7] have shown similar arrangement of methanol molecules around Ca2+ ions, although the average distance of Ca2+ –OM is slightly shorter than that of Ca2+ – OW. This similarity causes a difficulty to investigate a preferential solvation of ions in methanol –water mixtures [19] and the only measure of an eventual effect can be the location of methyl groups. But they are not coordinated by cations. Characteristic parameters of radial distribution functions listed in Table 2 confirm that the average distance between Ca2+ and oxygen of either methanol or water is almost the same. Similar feature is observed for Na+ ions [17]. However, the solvation of Na+ and Ca2+ in aqueous methanol shows a qualitative difference. As seen from Fig. 2 small amounts of methanol, 5 and 10 mol%, do not affect the position of the Ca2+ OW peak, but reduces the peak height of more than 50%. Integration of g(r) function shows a dramatic reduction of the number of water molecules coordinated by Ca2+. This number decreases from more than eight to less than four water molecules. The total number of solvent molecules coordinated by the calcium ion remains, however, unchanged, because methanol molecules enter the nearest environment of the cation. This peak of the Ca2+ OM radial distribution function at 0.27 nm, is very high and is followed by a broad second peak at 0.4 – 0.55 nm. The coordination numbers listed in Table 2 show that Ca2+ ions are preferentially solvated by methanol. The content of methanol in the coordination shells is very high, much higher than in bulk solution. The high concentration of methanol in the first coordination shell of Ca2+ causes some of the molecules not to show anti-dipole orientation, as it can be deduced from Fig. 3. A detailed analysis of the particle
155
configurations suggests that methanol molecules aggregate around Ca2+. Most of them can be found either in the first or the second coordination shell. Such behaviour was not expected, because interactions of Ca2+ with water and methanol are similar (see Fig. 1). A comparison of the characteristic parameters of the radial distribution functions for chloride ions in CaCl2 solutions with those for NaCl solutions [17] shows that a change of the counter-ion does not affect the Cl oxygen distance. In aqueous solution of CaCl2 the first maximum (see Fig. 4) is, however, lower but broader and the following maximum is very poorly defined. This indicates a rather fast exchange of the water molecules between the first coordination shell and bulk water. Integration of the first g ClO(r) peak gives more than 16 water molecules. This unreasonable high value results from the poorly defined position of the first minimum and suggests that interactions of the anion with water molecules are rather weak. The g ClH(r) function better describes the coordination shell of Cl. Its first maximum at 0.267 nm is sharper and is followed by a better defined minimum. As expected the Cl HW distance is shorter and indicates the OH bond orientation of water molecules in the Cl shell. The angular distribution function, shown in Fig. 5, with the maximum at / ; 50-, followed by a broad maximum at / ; 90- indicates that only some of the water molecules exhibit the OH bond orientation. The angular distribution function has been calculated independently for two different spheres around the anion. Their radii have corresponded to the minima the of g ClO(r) and g ClH(r) functions, respectively. As seen from Fig. 5 the angular distribution function, calculated for molecules in the smaller sphere, with the radius defined by the position of the g ClH(r) minimum, shows sharper maximum at / ; 50-, which represents OH oriented molecules. This means that the g ClH(r) function better represents the coordinated water molecule and
gCl-W(r)
4
2
0 0.0
0.2
0.4
0.2
0.4
0.6
0.8
0.6
0.8
gCl-OM(r)
2
1
0 0.0
r, nm Fig. 4. Cl water oxygen (upper) and Cl methanol oxygen (bottom) radial distribution functions in aqueous solution (dotted) and aqueous methanol 5 mol% (dashed) and 10 mol% (solid). Crosses in upper panel represent Cl HW radial distribution function.
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
n (φ)
156
0
45
90 φ
135
180
Fig. 5. Distribution functions of the angular orientation of the water molecules in the coordination shell of Cl in aqueous solution (solid) and aqueous methanol 5 mol% (dashed) and 10 mol% (dotted). Angular orientation of water molecules within a small sphere (see text) in aqueous solution (?). / is the angle between the dipole moment of the solvent molecule and the vector connecting Cl and oxygen.
gCa2+Ca2+(r)
integration of this function gives a more reliable value of the coordination number. The result, n(r min) = 6.5, is in very good agreement with coordination number 6, extracted from X-ray diffraction in 1 M solution [7]. Addition of methanol does not affect the position of the g ClH(r) maximum but slightly reduces the Cl OW distance. With increasing methanol content the Cl OW first peak becomes slightly higher but sharper. Consequently the coordination number calculated by integration of g ClO(r) peak decreases. The first maximum of the Cl –HW function also increases with increasing methanol concentration, but the
number of hydrogen atoms in the vicinity of anion remains unchanged. When the methanol content reaches 10 mol% the coordination numbers calculated from both peaks, of the g ClO(r) and g ClH(r) functions, are the same. This suggests that addition of methanol stabilizes the H-bonded water molecules in the shell of chloride ions. In methanol –water solution of CaCl2 the chloride ion is preferentially hydrated and methanol molecules do not even enter the vicinity of the anion. Such feature is unexpected, because in NaCl solutions in methanol –water mixtures the strong preferential solvation of Cl by methanol molecules has
30 20 10 0
0.2
0.4
0.6
0.8
gCa2+Cl-(r)
15 10 5 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
gCl-Cl-(r)
2 1 0
0.2
0.4
0.6
0.8
r, nm Fig. 6. Radial distribution functions of ions: Ca2+ – Ca2+(upper), Ca2+ – Cl (middle) and Cl – Cl (bottom) in aqueous solution (solid line), 5% methanol (dashed line) and 10% methanol (dotted line).
K. Bujnicka, E. Hawlicka / Journal of Molecular Liquids 125 (2006) 151 – 157
been observed [17]. A detailed analysis shows that a broad, very poorly defined maximum of Cl OM maximum (see Fig. 2), does not represent the methanol molecules coordinated by Cl. These molecules are coordinated by the Ca2+ ions, engaged in the solvent separated pairs. Radial distribution functions of ions are shown in Fig. 6. In aqueous solution, unlike ions associate and the g CaCl(r) function exhibits the sharp maximum, located at 0.305 nm. This can be attributed to contact ion pairs [5,7]. The g CaCl(r) function can be used to compute the association constant K A [20]: Z rmin KA ¼ 4kINA I103 gþ ðrÞIr2 dr ð5Þ aþ þa
where (a + + a ) denotes the sum of the ionic radii in the crystal and r min is the position of the first minimum. In aqueous solution the association of unlike ions is negligible, because K A < 10. In aqueous methanol a decrease of the g CaCl(r) peak is accompanied by a rise of a new broad maximum at 0.55 –0.6 nm and a of peak the g CaCa(r) function (see Fig. 6), which suggests an aggregation of the cations. In aqueous solution the Ca2+ – Ca2+ function does not show any peak (see Fig. 6) and a detailed analysis of the positions of all particles confirms that the distribution of Ca2+ ions is random. Addition of methanol induces aggregation of Ca2+ ions. The well-defined g CaCa(r) peak, at about 0.7 nm is observed when the methanol content is very low, 5 mol%. When the methanol concentration increases two broad peaks are observed, at about 0.5 and 0.75 nm. A detailed analysis of the positions of all ions shows that the peak positions correspond to the distances between calcium ions in the big ion cluster [(Ca2+)4(Cl)5 – 6]. This cluster is preferentially solvated by methanol molecules and contains about 60% of all methanol molecules. This phenomenon may be considered as a nucleus of phase separation. It is worth to notice that formation of the cluster has been observed in all performed simulations, independently on the initial placement of particles in the cubic box.
ions results from a competition between ion – solvent interactions and a tendency of the solvent to preserve its H-bonded network. In aqueous methanol the cation seems to be selectively solvated by methanol, despite very similar interactions of the Ca2+ ion with water and methanol. One may suppose that both the coordination shell of Ca2+ consisting of 8 or more water molecules, and methanol molecules with a bulky methyl group, do not fit three dimensional water network. In consequence both, ions and methanol molecules are Fexcluded_ from the water structure. They aggregate and become a nucleus of a phase separation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
4. Conclusions Results presented above confirm our previous hypothesis [17] that in highly associated solvents, a selective solvation of
157
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