Hydration extent and structural analysis

The probability distributions of the distance between halides and the water cluster center of mass, which characterize the hydration extent of the ions, are shown in Figure 3.2. The curve for F–_(H

2O)12 exhibits a peak around 1 Å which is clearly indicative of the

(a)

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Figure 3.2. Probability distributions of the distance between the halide and the water cluster center of mass, P(rcm), for clusters containing a given halide and (a) 12, (b) 24 and (c) 48 water molecules. Obtained from

DFTB3-MD simulations at 250 K.

affinity of fluoride for full hydration inside the cluster. In the case of Cl–(H2O)12, the

peak appears around 1.75 Å, a larger value relative to that for fluoride, indicating a reduced affinity of chloride for the interior regions of the water cluster. As for Br–_(H

2O)12

and I–(H2O)12, the spatial probability distributions are characterized by a peak at much

larger distances (2.5–3 Å), clearly reflecting that both bromide and iodide are asymmetrically solvated at the cluster surface. Further inspection of Figure 3.2 demonstrates that for cluster size 24, fluoride remains fully hydrated inside the cluster at around 1 Å from the cluster center of mass, while chloride continues to shift towards the

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cluster surface, with rcm values centered around 3 Å, and both bromide and iodide remain

partially solvated at the cluster surface, with rcm values around 3.75 Å. Similarly, for

cluster size 48, fluoride remains fully hydrated at around 2 Å from the cluster center, while chloride (to a slightly lesser extent), bromide and iodide preferentially locate at the cluster surface, with rcm values centered around 4–5 Å. These results unambiguously

show that fluoride prefers full hydration inside water clusters, while chloride prefers to locate in interfacial regions, especially in larger clusters, and bromide and iodide prefer partial hydration at the cluster surface. These findings confirm the results of previous investigations.28,68

The hydration extent of ions depends on the relative strengths of the ion–water and water–water interactions, as well as entropic effects, which tend to favor of interior hydration.68 According to the results presented in Table 3.1, strong hydrogen bonds between fluoride and water molecules, which are due to the relatively high charge density of fluoride, prevail over water–water interactions and force water molecules to tightly enclose the anion. However, in the case of the larger halides, weaker ion–water interactions and entropic effects are dominated by the water–water interactions which results in the preferential location of the larger halides towards the surface of a strongly hydrogen-bonded water network. In order to provide molecular details about this, the spatial probability distributions and the number of hydrogen atoms around halides in a cluster of 12 water molecules were calculated and are shown in Figure 3.3. The halide- hydrogen distance probability distributions (Figure 3.3a) exhibit two peaks for all halides. However, these peaks are very pronounced and clearly separated by a very low minimum for fluoride, while both peaks broaden, shift towards larger distances and are separated by

59 Figure 3.3. Selected structural features of X–_(H

2O)12 (X = F, Cl, Br, I) clusters. (a) Spatial probability

distributions and (b) number of hydrogen atoms (NH) around halide anions. Obtained from DFTB3-MD

simulations at 250 K.

a less pronounced minimum for the larger halides. The existence of the two peaks might be attributed to the formation of asymmetric halide–water structures with single linear hydrogen bonds.41,105 Figure 3.4 displays the potential energy profile for the interconversion of a hydrogen-bonded halide–water binary complex to its mirror-image conformer. For F–(H2O), the symmetric transition state for interconversion lies ~8

kcal/mol higher in energy than the asymmetric linear hydrogen-bonded structures. However, for larger halides, the barrier for interconversion is much reduced, down to 1 kcal/mol for I–(H2O) (cf. Figure 3.4).These observations indicate that water molecules

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Figure 3.4. Potential energy profiles for halide–water binary cluster interconversion plotted as a function of the angle (θ) between the line that connects the water oxygen to the halide and the HOH bisector. Obtained from MP2/aug-cc-pVTZ calculations.

form a rigid shell around fluoride, due to the strong fluoride–water interactions, while they are loosely bound to the larger halides.

Based on the relative strengths of the ion–water interactions listed in Table 3.1, one would expect chloride to behave like more bromide and iodide, since their cluster binding energies are much closer, and half of the fluoride–water interaction strength or less. The fact that chloride does not seem to exhibit a pronounced affinity for interfacial hydration like bromide and iodide might be surprising at first. In fact, the ion–water interactions are stronger for chloride than for bromide and iodide (even if not dramatically more so) and the chloride–water interactions compete more effectively with the water–water interactions in small clusters, resulting in a behavior closer to that of fluoride in small clusters, i.e. some affinity for the interior regions of the cluster, even if much reduced relative to fluoride. However, as cluster size increases, the cooperative

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interactions of a strongly hydrogen-bonded water network may start prevailing over the chloride–water interactions, resulting in the higher affinity for interfacial regions of the clusters.

Interestingly, according to the calculated number of hydrogen atoms around the ions, plotted as a function of distance from the halides in Figure 3.3b, the first hydration shell of all halides contains about six water molecules. Hence, the only partially hydrated larger halides have the same number of adjacent water molecules as the fully hydrated fluoride. This is not too surprising, since the first hydration shell of larger halides would presumably accommodate a larger number of water molecules due to their larger ionic radius, a feature compensated by partial hydration resulting in the same number of adjacent water molecules for all halides.