THE VALENCE QUADRUPOLE MOMENT FOR DESCRIBING ELECTRONIC STRUCTURE EFFECTS IN TRANSITION METALS

A number of workers have suggested using vectorial bond-valence sums to describe the spatial distribution of bonds about atoms in crystal structures. A bond-valence vector points from cation to anion, and its magnitude is equal to the bond valence. The sum of the bond-valence vectors about an atom describes the lopsidedness of the distribution, and so are essentially dipole moments of the valence distribution. These can be used to characterize non-centrosymmetric distortions, but cannot characterize centrosymmetric distortions such as would be caused by asymmetrically filled d-subshells (e.g., the first-order Jahn-Teller effect). However, such distortions can be described by valence quadrupole moments, which describe deviations from spherical symmetry. Here we develop the mathematical formulation of the valence quadrupole moment, and show how it can be used to predict distortion pathways of transition metals subject to electronic structure effects caused by asymmetrically filled d-subshells.