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ION–SOLVENT INTERACTIONS 203

many times, the numerical values have not changed by more than one percent. The
method involves an application of the known differences of quadrupole interactions
of ions which have the same size but different signs.

2.27.2. Transition-Metal Ions

Our overview of hydration so far is based upon ions which are simple, mostly
those from groups IA and IIA. We haven’t yet said anything about the ions with more
complex electronic structures, for example, the transition-metal ions, two-valent and
three-valent entities. There are many who would expect such ions to have valence-
force interactions (orbital bond formation) with water molecules, but in fact they don’t.
It is possible to interpret their hydration heats in terms of electrostatic interactions with
water, but one has to be more sophisticated and no longer regard the ions as simple
spheres but take into account the shape and direction of their molecular orbitals and
how these affect the electrostatics of the interactions with water molecules.
It turns out that the splitting of electron levels in the ions caused by the water
molecules changes the electrostatic interaction of the ions with the waters. This in turn
makes the course of a plot of individual hydration of transition-metal ions against the
radii of the ions no longer a continuous one, which one would expect from
first-approximation electrostatic studies, but takes into account some irregularities that
can be quite reasonably accounted for. Now, there is also lurking among the literature
on ion hydration in the gas phase the surprising (but clearly explainable) fact that the
second water molecule sometimes has a larger heat of hydration than the first.

2.27.3. Molecular Dynamics Simulations

The last part of our treatment of the central aspects of the chapter concerned
molecular dynamics. We showed the power of molecular dynamics simulations in
ionic solutions and what excellent agreement can be obtained between, say, the
distribution function of water molecules around an ion calculated from molecular
dynamics simulation and that measured by neutron diffraction.
However, there has been in the past some semantic confusion in these calculations.
Most of them are about distribution functions. Some of the workers concerned assumed
that they were calculating hydration numbers when in fact they were calculating
time-averaged coordination numbers. Nevertheless, a few groups have indeed been able
to calculate the rate at which water molecules react when an ion is brought near them and
the lifetime of the water molecules near the ion as it moves. From this, they have calculated
hydration numbers that are in fair agreement with those determined experimentally.

2.27.4. Functions of Hydration

The rest of this chapter has been concerned with phenomena and effects that are
connected with hydration. The first one (salting out) concerns the solubility of
nonelectrolytes as affected by the addition of ions to the solution. Here two effects are