Page 218 - MODERN ELECTROCHEMISTRY

154 CHAPTER 2

brief account will be given of how far this approach has gone in improving our
understanding of ionic solvation.

2.17.2. An Early Molecular Dynamics Attempt at Calculating Solvation
Number

Palinkas et al. were the first (1972) to calculate the expression:

where is the mean density of water molecules, and is the radial pair distribution
function for the pair ion–oxygen. A plot of against r leads to a series of maxima,
the first much greater than the second, and the number of waters “under” this peak is
the number in the first shell nearest to the ion.
These sophisticated calculations are impressive but they err in representing their
results as solvation numbers. They are, rather, coordination numbers and grow larger
with an increase in the size of the ion (in contrast to the behavior of the hydration
numbers, which decrease as the ion size increases).

2.17.3. Computational Approaches to Ionic Solvation
In considering various computational approaches to solvation, it must first be
understood that the ion–water association alone offers a great range of behavior as far
as the residence time of water in a hydration shell is concerned. Certain ions form
hydrates with lifetimes of months. However, for the ions that are nearly always the
goal of computation (ions of groups IA and IIA in the Periodic Table and halide ions),
the lifetime may be fractions of a nanosecond.
As indicated earlier in this chapter (see Section 2.3), there are three approaches
to calculating solvation-related phenomena in solution: Quantum mechanical, Monte
Carlo, and molecular dynamics.
The quantum mechanical approach, which at first seems the most fundamental,
has major difficulties. It is basically a K approach, neglecting aspects of ordering
and entropy. It is suited to dealing with the formation of molecular bonds and reactivity
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by the formation in terms of electron density maps. However, ionic solutions are
systems in which order and entropy, its converse, are paramount considerations.
The most fruitful of the three approaches, and the one likely to grow most in the
future, is the molecular dynamics approach (Section 2.3.2). Here, a limited system of
ions and molecules is considered and the Newtonian mechanics of the movement of

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There is a more fundamental difficulty: the great time such calculations take. If they have to deal with
more than ten electrons, ab initio calculations in quantum mechanics may not be practical.