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120 CHAPTER 2

or

where and are the dipole moment, quadrupole moment, and polarizability
of the water molecule. The ion-water distance is symbolized by where
is crystallographic ionic radius and is the radius of the water molecule. The sign
in the ion–quadrupole term refers to cation and anion, respectively.
Using values of esu cm, and
–1
molecule for and respectively, the term can be rewritten as

2.15.11.2. When there will be two interaction
energies: (1) the interaction energy of a solvationally coordinated water with the ion,
and (2) the interaction energy of nonsolvationally coordinated water
(NSCW) with the ion, . The energy is given by Eq. (2.65). An
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NSCW does not give any average preferred orientation. Before it has time to orient
toward the ion, the latter has left the site. Thus, NSCW is still a part of the water
structure, but on the average has an H-bonding position blocked by the ion. Thus, its
net ion–dipole interaction energy is zero. The interaction energy of an NSCW with
the ion arises from the ion–induced dipole, the ion quadrupole, and the dispersion
interactions.
Thus,

and

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Of course, in reality, there will not only be these two positions but also all possible intermediate positions,
in which the ion-solvent interaction is given for one solvent molecule by The value of
is zero for a dipole oriented directly to the ion (cos 0° = 1); and 90° for a distant water molecule (cos
90° = 0). However, there will be all different values of in between, and the model presented here does
not deal with them. As a simplification; it takes the two extreme situations (all oriented and not at all
oriented) and pretends any water molecule belongs to one group or the other.