Page 264 - MODERN ELECTROCHEMISTRY

200 CHAPTER 2

energies of interaction obtained by solving it are then quantized. Such an approach
was begun for ion–water interactions by Clementi in the 1970s.
A quantum mechanical approach to ion–water interactions has the up side that it
is the kind of development one might think of as inevitable. On the other hand, there
is a fundamental difficulty that attends all quantum mechanical approaches to reactions
in chemistry. It is that they concern potential energy and do not account for the entropic
aspects of the situation. The importance of the latter (cf. the basic thermodynamic
equation depends on temperature, so that at T = 0, the change in
entropy in a reaction, has no effect. However, in calculations of solvation at
ordinary temperatures, the increase in order brought about by the effect of the ion on
the water molecules is an essential feature of the situation. Thus, a quantum mechanical
approach to solvation can provide information on the energy of individual ion–water
interactions (clusters in the gas phase have also been calculated), but one has to ask
whether it is relevant to solution chemistry.
Another problem in the quantal approach is that ions in solution are not stationary
as pictured in the quantum mechanical calculations. Depending on the time scale
considered, they can be seen as darting about or shuffling around. At any rate, they
move and therefore the reorientation time of the water when an ion approaches is of vital
concern and affects what is a solvation number (waters moving with the ion) and what is
a coordination number (Fig. 2.23). However, the Clementi calculations concerned station-
ary models and cannot have much to do with dynamic solvation numbers.
Finally, Con way points out that the values of the energies obtained by solving the
Schrodinger equation and by electrostatics are about the same. But this should be! The
quantum mechanical calculations do not infer that the electrostatic ones (Section
2.15.11) are wrong. Indeed, the Schrödinger equations solved by Clementi involved
the same energy that was used in the electrostatic method. It is a matter of whether the
sophistication of quantization gives increasing insight into the behavior of a real
system in solution. The answer in the 1990s is: not yet.
However, science evolves! More will be seen of the quantum mechanical ap-
proach to solvation and in particular in nonaqueous solutions when there is more
chance of interactions involving overlap of the orbitals of transition-metal ions and
those of organic solvent molecules. Covalent bond formation enters little into the
aqueous calculations because the bonding orbitals in water are taken up in the bonds
to hydrogen. With organic solvents, the quantum mechanical approach to bonding may
be essential.
The trend pointing to the future is the molecular dynamics technique, and
treatments of this kind were discussed in Section 2.17. The leaders here are Heinzinger
and Palinkas (in the 1990’s), and the major thing to note is that the technique provides
needed information on the number of waters in the first shell. The MD method does
this by calculating the distribution function (Section 2.17.2) and may also provide
information on a second layer, lifetimes of the solvent molecules in the hydration
sheath, and so on.