Electronic structure effects in the vectorial bond-valence model


Crystal structure, oxide, bond valence, vectorial bond-valence model, electronegativity, lone pair, second-order Jahn-Teller effect, spherical symmetry, minimum coordination number


The vectorial bond-valence model (VBVM) describes the spatial distribution of bonds to each atom in a system in terms of the vector sum of the incident bond valences. It has been applied in the past to cations not subject to electronic structure effects (e.g., lone-pair or Jahn-Teller effects) in which case the expectation is that the vector sum will be approximately zero. Here we analyze 178 simple-oxide crystal structures and show that the vectorial bond-valence sum is a predictable function of the atomic valence (oxidation state) of each atom and the valence of the strongest bond to atoms for which second-order Jahn-Teller and lone-pair effects play a role in determining molecular geometry. Outliers are uniformly metastable or unstable under ambient conditions, suggesting that deviation from ideal vectorial bond-valence sums might be used as a proxy for some aspect of structural potential energy. These results are all strictly in harmony with the VSEPR model of molecular geometry, but may allow for more quantitative prediction.

Original Publication Citation

B. R. Bickmore, M. C. F. Wander, J. Edwards, J. Maurer, K. M. Shepherd, E. Meyer,W. J. Johansen, R. A. Frank, C. Andros, and M. Davis. “Electronic structure effects in the vectorial bond-valence model,” American Mineralogist, vol. 98, no. 2–3, p. 340–349, 2013.

Document Type

Peer-Reviewed Article

Publication Date



American Mineralogist




Ira A. Fulton College of Engineering


Civil and Environmental Engineering

University Standing at Time of Publication