Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 771
interpret crystallographic metal-oxygen distances in terms of the sum of the vdW radius of
oxygen and the ionic radius of the metal. It should b emphasized, however, that the division
of bond lengths into “cation” and “anion” components is entirely arbitrary. If the ionic radius
is retained, the task remains to seek a connection to the Born radius, an issue that has a
long-standing history beginning with the work of Voet. 172 Of course, any addition to the
ionic radius necessary to obtain good results from the Born equation needs a physical explanation.
This is typically done in terms of the water radius, in addition to other correction
terms such as a dipolar correlation length in the MSA (mean spherical approximation). 181-183
In this case, however, proceeding from the first RDF peak, the size of the water moiety is
implicated twice.
It has been shown 82 that the puzzle is unraveled if the covalent (atomic) radius of oxygen
is subtracted from the experimental first peak position of the cation-oxygen radial distribution
curve (strictly, the upper limits instead of the averages). The values of r aq so
obtained are very close to the Born radius,
d(cation-O) - r cov(O) = r aq ≈ r B [13.1.31]
Similarly, for the case of the anions, the water radius, taken as 1.40 Å, is implicated,
d(anion-O) - r(water) = r aq ≈ r B [13.1.32]
Furthermore, also the metallic radii (Table 13.1.7) are similar to values of r aq. This correspondence
suggests that the positive ion core dimension in a metal tends to coincide with
that of the corresponding rare gas cation. The (minor) differences between r aq and r metal for
the alkaline earth metals may be attributed, among other things, to the different coordination
numbers (CN) in the metallic state and the solution state. The involvement of the CN is apparent
in the similarity of the metallic radii of strontium and barium which is obviously a result
of cancellation of the increase in the intrinsic size in going from Sr to Ba and the
decrease in CN from 12 to 8.
Along these lines a variety of radii are brought under one umbrella, noting however a
wide discrepancy to the traditional ionic radii. Cation radii larger than the traditional ionic
radii would imply smaller anion radii so as to meet the (approximate) additivity rule. In fact,
the large anion radii of the traditional sets give rise to at least two severe inconsistencies: (i)
The dramatic differences on the order of 1 Å between the covalent radii and the anion radii
are hardly conceivable in view of the otherwise complete parallelism displayed between
ionic and covalent bonds. 184 (ii) It is implausible that non-bonded radii 185 should be smaller
than ionic radii. For example, the ionic radius of oxygen of 1.40 Å implies that oxygen ions
should not approach each other closer than 2.80 Å. However, non-bonding oxygen-oxygen
distances as short as 2.15 Å have been observed in a variety of crystalline environments.
“(Traditional) ionic radii most likely do not correspond to any physical reality,” Baur
notes. 186 It should be remarked that the scheme of reducing the size of the anion at the expense
of that of the cation has been initiated by Gourary and Adrian, based on the electron
density contours in crystals. 187
The close correspondence seen between r B and r aq supports the idea that the Born radius
(in aqueous solution) is predominantly a distance parameter without containing dielectric,
i.e., solvent structure, contributions. This result could well be the outcome of a
cancellation of dielectric saturation and electrostriction effects as suggested recently from