VALENCE MULTIPOLE ANALYSIS OF OXIDES, SULFIDES, HALIDES, TELLURIDES, AND SELENIDES

In the vectorial bond-valence model, bonds are treated as vectors in the direction from cation to anion, with magnitude equal to the bond valence. To characterize the spatial distribution of these bonds about atoms in crystal structures, we have performed multipole expansions, truncated at the quadrupole term, about each atom in thousands of oxides, sulfides, halides, tellurides, and selenides. The norm of the valence dipole moment characterizes the lopsidedness of the distribution, while the norm of the quadrupole moment characterizes deviation from spherical symmetry. These terms are predictable on the basis of the valence of the strongest bonds reaching each atom, and map out preferred distortion pathways for coordination shells in which the central atom is subject to electronic structure effects due to lone pairs and asymmetrically filled d-subshells. Our analysis demonstrates the following points. 1) If the valence vectors are normalized to the total incident bond valence, and compared to similarly normalized magnitudes of the strongest bond valences, differences in distortion pathways due to differences in oxidation state tend to disappear. 2) Particular types of electronic structure effects exhibit characteristic types of distortion pathways in valence space. 3) Valence multipole terms about different anions (which are all subject to lone-pair effects) are similar, but some differences arise because of differences in anion size, which lead to more or less ligand-ligand repulsion. When modeling this behavior, it is, as yet, unclear whether one should treat all these anions as having different preferred distortion pathways in valence space, or should treat them as having the same preferred distortion pathway in valence space, with differences arising due to ligand-ligand interactions.