Novel approach to the concept of bond-valence vectors.

A new approach to the old idea of deriving a bond-valence vector from the well-known bond-valence concept has been proposed. The foundation of the proposal is the previous electrostatic model in which bond valences are interpreted as electric fluxes. The outcome of this approach is actual vectorial quantities whose magnitudes are strictly but nonlinearly related to the scalar bond valences and are directed along the bond lines. It has been proved that the sum of all these bond-valence vectors drawn from a coordination center to its ligating atoms will be close to zero for the complete coordination sphere. Therefore, unlike the scalar bond valences, the obtained vectors provide information about the spatial arrangement of ligands. The geometrical consequences of the proposed bond-valence vector (BVV) model are analyzed for the geometries of the carbonates, phosphates, and five-coordinated organoaluminum compounds with CO3, PO4, and AlCO4 skeletons, respectively, retrieved from the Cambridge Structural Database. For acyclic carbonates this BVV model allows one to predict the O-C-O angles with a mean absolute error of 1.0 degrees using the empirical C-O distances only. Furthermore, this BVV model is able to quantitatively describe the strains in cyclic carbonates. The preliminary studies for NO2E, PO3E, and SO3E systems with a strongly stereoactive lone electron pair (E) show that the model may serve as a quantitative description of the lone electron pair effect on the coordination sphere. A great advantage of the presented BVV approach is that the derived relation between a bond-valence vector, bond valence, and bond length is given by an uncomplicated equation allowing quick and simple computations, thus providing a new analytical tool for describing the geometry of a coordination sphere that may be applied for structure validation.