Page 97 - MODERN ELECTROCHEMISTRY

40 CHAPTER 2

random movements of ions in the solution (and the waters near them) are tested by
calculating the energy changes they would bring about were they to occur. The ones
that happen with the lowest energy (with a negative free-energy change) are those
taken to be occurring in reality.
The molecular dynamics (MD) calculations are different from the Monte Carlo
ones. Instead of using assumptions about random movements of the ions and solvent
molecules and calculating which of the movements is good (lowers energy) or bad
(raises it), the molecular dynamics approach works out the potential energy of the
molecular entities as they interact with each other. Then, by differentiating these
energies with respect to distance, one can derive the force exerted on a given particle
at each of the small time intervals (mostly on a femtosecond scale). As a result of such
computations, the dynamics of each particle, and hence the distribution function and
eventually the properties of the system, can be calculated. The critical quantities to
know in this approach are the parameters in the equation for the intermolecular energy
of interaction. To compensate for the fact that only interactions between nearest
neighbors are taken into account (no exact calculations can be made of multibody
problems), these parameters are not calculated from independent data, but an assump-
tion is made that the two-body-problem type of interaction is acceptable and the
parameters are computed by using a case for which the answer is known. The
parameters thus obtained are used to calculate cases in which the answer is unknown.
The ability of these computational approaches to predict reality is good. A
limitation is the cost of the software, which may amount to many thousands of dollars.
However, some properties of solutions can be calculated more cheaply than they can
be determined experimentally (Section 2.5). Increasing computer power and a lower-
ing of the cost of the hardware indicates a clear trend toward the ability to calculate
chemical events.

2.3.3. Spectroscopic Approaches

In the latter half of this century physicochemical approaches have increasingly
become spectroscopic ones. Infrared (IR), Raman, and nuclear magnetic resonance
(NMR) spectroscopic approaches can be used to register spectra characteristic of the
ion–solvent complex. The interpretation of what molecular structures give these
spectra then suggests structural features in the complex. On the other hand, the
spectroscopic technique does not work well in dilute solutions where the strength of
the signal emitted by the ion–solvent interaction is too small for significant determi-
nation. This limits the spectroscopic approach to the study of solvation because it is
only in dilute solutions that the cations and anions are sufficiently far apart to exert
their properties independently. Thus, spectroscopic methods are still only a partial help
when applied to solvation. Spectroscopic and solution property approaches are sum-
marized in Table 2.2.
Two other points must be made here: