In constructing the table of bond-valence balance for fl-HBO2, Zachariasen [Aeta Cryst. (1963), 16, 385-389] makes use of two empirical correlations between bond valence and bond length: one for B-O bonds and one for hydrogen bonds, whose bond valence he apportions to O-H and H. • • O on the basis of the O-O distance. The root-mean-square deviation Avrm~ from the formal anionic charges being taken as the criterion, Zachariasen's curve compares as follows with three analytical functions proposed in the literature: 0.07 v.u. (Zachariasen, 1963); 010 [Pauling, J. Amer. Chem. Soc. (1947), 69, 542-553]; 0.09 [Donnay & Allmann, Amer. Min. (1970), 55, 1003-1015; D-A]; 0-10 [Brown & Shannon, Acta Cryst. ~1973), A28, S 107]. The D-A curves are then applied to three recently refined borate structures. The resulting Z~Vrms values [0.08 v.u. for CaB6Oa(OH)4.3H20, gowerite; 0.04 for K2BsOaOH. 2H20; 0.07 for Na2B406(OH)2.3H20, kernite] show the adequacy of the procedure. Though lacking any obvious theoretical basis, such curves are useful (at their own level of depth) in interpreting structural details through the quantitative application of Pauling's charge-neutrality principle: distorted coordination polyhedra are seen as the expression of the drive toward minimization of Avrm~.
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Donnay et al. (1973) studied this question.