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ION–SOLVENT INTERACTIONS 163

2.19. SOLVENT DYNAMIC SIMULATIONS FOR AQUEOUS SOLUTIONS

Of the models of water chosen as practical for MD simulation work, the central
force model is the best because the effect of ions on intramolecular frequencies can be
studied. Heinzinger and Palinkas first used such a model in 1982 to calculate the
ion–water pair potentials as a function of the ion–water distance and orientations as
shown in Fig. 2.64. Such computations were carried out using 200 water molecules,
8 cations, and 8 anions in a 2.2 M solution. The side of the cube in the computation
was 2000 pm.
The time-average positions for and can be seen in Fig. 2.64. For
the arrangement is octahedral but for there is only a small preference for
octahedral coordination. On the other hand, and are firmly octahedral. As one
goes outward past 400 pm, the preferential orientation is gone except for and this
seems to form a second shell. It must be again stressed that the numbers are all
time-averaged (coordination) numbers and have only a tenuous relation to the time-
dependent hydration numbers.
It is possible to calculate diffusion coefficients by computing the mean square
displacement distance and dividing by 6t. [The basic relation here is the Einstein–
Smoluchowski equation (Section 4.2.6)]. The values are surprisingly good and are
shown in Table 2.26.
Both transition times, reorientation of water near the ion and translation, can be
calculated. The value for the reorientation time of is ps; this is a low value
because of the weak field in the water arising from the large size of . The hindered