**5. Orientation of the solvent molecules in the first coordination shell**

Orientation of the molecules around the ion can be characterised by an angle between the vector connecting the ion with the oxygen and the dipole moment of the solvent molecule. The angular distribution functions are shown in Figure 6.

Fig. 6. Distribution functions of angular orientation of the nearest neighbours of Na+ (solid), Mg2+(dashed), Ca2+ () and Cl- (dotted) in water (a), methanol (c) and equimolar mixture (b, d). The angle defined in the inset.

Distribution functions of the angular orientation of the water molecules in the primary shells of Na+, Mg2+ and Ca2+ ions show the peak centred at cos = -1. This indicates that the

Interactions of the chloride ions with methanol and water are weaker than those of cations.

the bulk solvent. The chloride ions favour methanol molecules in their coordination shells. This preference is observed in solutions of NaCl, CaCl2 and MgCl2, over the whole range of the composition of the mixed solvent. The preferential solvation of Cl- by methanol has been postulated from self-diffusion coefficients. The diffusion experiments have shown that in methanol rich solvents translations of the chloride ions and methanol molecules are strongly

Orientation of the molecules around the ion can be characterised by an angle between the vector connecting the ion with the oxygen and the dipole moment of the solvent molecule.

Fig. 6. Distribution functions of angular orientation of the nearest neighbours of Na+ (solid),

Distribution functions of the angular orientation of the water molecules in the primary shells of Na+, Mg2+ and Ca2+ ions show the peak centred at cos = -1. This indicates that the

(dotted) in water (a), methanol (c) and equimolar mixture

despite very similar binding energies of the anion with the solvent components.

**5. Orientation of the solvent molecules in the first coordination shell** 

The angular distribution functions are shown in Figure 6.

is flexible, but its composition differs significantly from that of

ion favours the methanol molecules in its primary shell

The coordination shell of Cl-

correlated (Hawlicka, 1986). The Cl-

Mg2+(dashed), Ca2+ () and Cl-

(b, d). The angle defined in the inset.

antidipole orientation of the water molecules in the cation shells dominates. The distribution of the angle for Mg2+ is narrower than those for Na+ and Ca2+. This is not surprising that the water molecules are better oriented in the field of Mg2+, which is stronger than the fields of Na+ and Ca2+. The primary shell of Ca2+ contains more water molecules than the shells of the six-coordinated Na+ and Mg2+ions, therefore the angular distribution for Ca2+ shows a shoulder for cos -0.7. This means that the dipole moments of a few water molecules in the Ca2+ shell are tilted, by about 45o, from the antidipole orientation. This 'improper' orientation vanishes in equimolar mixture when the coordination number decreases from 10 to 7. This suggests that the coordination shell of Ca2+ is compact.

The antidipole orientation of the methanol molecules is also observed in the Na+ and Mg2+ shells. A different orientation has been noticed for the methanol molecules in the Ca2+ shell. The distribution of the O-Ca2+O angles, shows the dominant peak at cos =-0.9. Thus the dipole moments of the methanol molecules in the Ca2+vicinity are tilted by about 25o.

As might be expected the orientation of the solvent molecules in the vicinity of chloride ions is different. The distance from the anion to oxygen is longer than that to hydrogen. This suggests a hydrogen bond between the anion and the nearest solvent molecules. In aqueous and methanolic solutions the dominant peaks of the angular distributions are centred at cos=0.68. This confirms that H-bond between the anion and solvent molecules is almost linear. As might be expected the orientation of the solvent molecules in the anion shell for all studied solutions is independent of the solvent composition.

To describe a geometrical arrangement of the solvent molecules in the solvation shells two angles can be defined. The angle is the angle between two vectors pointing from the ion to the nearest oxygens. The angle, which is the angle between the three oxygens, permits to deduce a difference between the order of the water molecules in the coordination shells and the tetrahedral structure of water. The distributions of the angles have been computed without any distinction between oxygens belonging to water and methanol molecules. The results are displayed in Figure 7.

Fig. 7. Distribution of angles, for the water (a) and methanol (b) molecules in the primary shells of Na+ (solid), Mg2+(dashed), Ca2+() and Cl- (dotted).

The distribution of angles computed for the coordination shells of the Na+ and Mg2+ ions is independent of the solvent composition. Two peaks, centred at 90o and 180o, indicate that the water and methanol molecules form an octahedron around the cation. The distribution

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 415

1 ps, afterward, independently of the time interval, they reach a constant value close to 0.95. This means that about 95% of the solvent molecules do not leave the coordination shells of the cations during the whole simulation time. The coordination shells of the divalent cations are very stable, with the lifetime remarkably exceeding 150 ps, and being independent of the solvent composition. The long lifetime of the primary hydration shells has been reported previously for Ca2+, about 700 ps, and Mg2+ , about 422 ps (Konesham et al., 1998). The long residence time of the solvent molecules has been expected, because the hydrodynamic radii of both cations noticeably exceed the ion radii in crystal (Hawlicka, 1995). This means that the cations move with their coordination shells together, because the ion filed controls the

The R(t) functions for the Na+ and Cl- ions decrease monotonously and they can be fitted to

1 2

( ) exp( ) exp( ) *t t Rt A <sup>A</sup>* 

The first term describes an escape of the solvent molecules located close to the border of the coordination shell, whereas the second term concerns the persistence of the shell. Parameters A1 and A2 reflect fractions of the solvent molecules involved in both processes. The first process is rather fast and its characteristic time 1 is shorter than 1 ps. The residence time 2 of the solvent molecules in the Cl- shell and the methanol molecules in the Na+ shell

Fig. 8. Influence of the time interval t. on the residence time 2 of the methanol molecules in

As seen the residence time reaches the constant value when t is not shorter than 0.2ps. Thus the 2 values discussed below were computed for t=0.2 ps. This means that the solvent molecules leaving the ion shell for the time longer than 0.2 ps were neglected in

In aqueous solution the lifetime of the coordination shell of Na+ is long, more than 170 ps, but in methanolic solution this time is much shorter, about 45 ps. Therefore is not surprising

that the lifetime of the Na+ shell decreases when the methanol content increases.

increase with the time interval t. Such dependence it is shown in Figure 8.

1 2

(8)

translations of all nearest neighbours.

a second-order exponential decay:

the Cl- shell.

further calculations.

of the angles between three oxygens of the solvent molecules in the Na+ and Mg2+ shells shows two peaks at 60 and 90o, respectively. This confirms the octahedral arrangement of the coordination shells.

The Ca2+ shell, which contains more molecules, does not show any symmetry. As seen from Figure 7 in aqueous solution the distribution of O-Ca2+-O angles exhibits two peaks, around 67o and 135o, respectively. The former angle is close to the value, which can be expected for tetrahedral or hexahedral symmetry, but the latter angle cannot be correlated with any of the polyhedra. This means that the Ca2+ shell is irregular. When the coordination number of Ca2+ decreases with the increasing methanol content, the most probable O-Ca2+-O angle increases. In methanolic solution the distribution of angles shows two peaks around 75o or 145o, respectively. This means that the cation shell remains irregular. The distribution of the O-O-O angles confirms a lack of symmetry of the Ca2+ shell, because in all studied solutions these angles are either 55o or 107o.

The O-Cl- -O angles, computed for the solutions of NaCl, MgCl2 and CaCl2, are very similar. As seen from Figure 7 the distribution of the O-Cl- -O angle is almost uniform. This means that the coordination shell does not show any symmetrical arrangement. A lack of the symmetry of the Cl- shell causes that in aqueous solution the distribution of the O-O-O angles is almost uniform, except a small peak at about 54o. It is worthy to notice that such peak is believed to be a distinctive feature of the tetrahedral arrangement of pure water (Gallanger & Sharp, 2003). This means that in the coordination shell of Cl the water structure partially remains.
