Few authors write and illustrate as well as F. Donald Bloss, as evinced by his elegant book
Crystallography and Crystal Chemistry. His carefully crafted prose and illustrations for point and space group isometries, tensors, crystal structures, for example, render these concepts self-evident. Moreover, his application of Pauling’s second principle serves to illustrate the constraint imposed on a stable crystal structure that the sum of the bond strengths reaching each anion in a structure closely matches the magnitude of the valence of the anion. The arrangement of the atoms in such structures not only determines the electron density, ED, distribution (the Hohenberg-Kohn theorem), but it also provides a connection for Pauling’s principle, one that has a basis in well-developed power law trends that obtain between bond length, R(M-O) and the average bond strength <s> for a bonded interaction R(M-O) = 1.43 (<s>/r)
-0.21 and the value of the ED, ρ(r
c), at the bond critical point, R(M-O) = 1.41(ρ(r
c)/r)
-0.21,
where r is the periodic table row number of the M atom.
The bonded radius, rb(O), of the O atom, determined on the basis of the electron density distributions, varies directly with R(M-O) and the bond character, increasing from 0.65 Å when bonded to electronegative nitrogen to 1.40 Å when bonded to electropositive lithium. The bonded radii of the M-atoms, rb(M) increase linearly and are highly correlated with the crystal radii, rc(M), but are typically ~0.25 Å larger in several cases. The overall close agreement and the well-developed correlation between two sets of radii is a testament of the relative precision of the crystal radii. But, on the other hand, the large variation in bonded radius of the oxygen atom indicates that the derivation of the crystal radii, assuming a virtually constant radius for the atom, is problematical.
