Acta Crystallographica Section B

Structural Science

Volume 54, Part 3 (June 1998)

research papers

Acta Cryst. (1998). B54, 204-210 [ doi:10.1107/S0108768197012809 ]

Theoretical Prediction of Bond-Valence Networks. II. Comparison of the Graph-Matrix and Resonance-Bond Approaches

J. S. Rutherford

Abstract: This paper provides a common framework for the bond-valence and resonance-bond-number methods, both of which explain the principal variations in inorganic bond lengths from the sum of radii, as arising from the connectivity of the structure, and therefore may apply graph information in conjunction with the Valence-Sum Rule. Under these constraints, possible predictions are limited to specific ranges of (M - N + 1) parameters, where M and N are the size and order of a multigraph describing the crystal motif. Further restrictions on these parameters may arise from non-crystallographic graph symmetries. Convenient graph-theoretical calculation schemes are described for both approaches. As it is possible to identify the best possible prediction within the limits described, which is that most closely corresponding to the experimental result, we have a means of making a direct comparison of the effectiveness of the various methods proposed, as well as being able to evaluate them against a statistically based prediction. The resonance-bond-number method proves to be the better predictor in most cases. Examples analysed in this way comprise KVO₃ (potassium metavanadate), [alpha] -Ga₂O₃ (gallium oxide), TeI₄ [tellurium(IV) iodide], Li₂SiO₃ (lithium metasilicate), Li₂GeO₃ (lithium metagermanate) and CaCrF₅ (calcium chromium fluoride).