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ION–SOLVENT INTERACTIONS 155

all the particles in the system is worked out, an impractical task without computers.
The foundation of such an approach is knowledge of the intermolecular energy of
interaction between a pair of particles. The validity, and particularly the integrity, of
the calculations is dependent upon the extent to which the parameters in the equations
representing attraction and repulsion can be obtained independently of the facts that
the computation is to calculate. Thus, if the energy for the interaction of a particle
with its surroundings is known, then is the force on the particle and hence the
acceleration and final velocity can be calculated [e.g., every femtosecond
With the appropriate use of the equations of statistical mechanics, the properties of a
system (particularly the dynamic ones such as diffusion coefficients and the residence
times of water molecules) can then be calculated.
In spite of these confident statements, the computation of the properties of ionic
solutions is truly difficult. This is partly because of the general limitations of molecular
dynamics. Because it is based on classical mechanics, MD cannot deal with situations
in which 1, i.e., quantal situations (e.g., molecular vibrations). Again, MD
depends on potential and kinetic energy (as does quantum mechanics), but it does not
account for entropy, which is an important characteristic of equilibrium conditions in
systems.
Another problem is that long-range Coulombic forces, which are the principal
actors in solvation, have to be subjected in practice to a cutoff procedure (thus, they
tend to continue to be significant outside the volume of the few hundred particles in
the system considered), and the effect of the cutoff on the accuracy of the final
calculation is sometimes unclear. For these reasons, much of the computational work
on solvation has been carried out with gas-phase clusters, where the essence of the
solvational situation is retained but the complexities of liquids are avoided.

2.17.4. Basic Equations Used in Molecular Dynamics Calculations
The basis of MD calculations in solvation is pairwise interaction equations
between the ion and the water molecule. The form of these equations depends greatly
upon the water molecule model chosen; there are several possibilities.
For example, suppose one can choose a rigid three-point-charge model of water
with an internal geometry of and 100 pm for the HOH angle and OH distance,
respectively. The interaction energy involves a “Lennard-Jones” 6–12 potential for
electrostatic interactions between water–water and ion–water pairs, U pair; a nonaddi-
tive polarization energy, and a term that includes exchange repulsion for
ion–water and water–water pairs,

The pair additive potential is