Long-range Coulomb forces and localized bonds

The ionic model is shown to be applicable to all compounds in which the ato ms carry a net charge and their electron density is spherically symmetric r egardless of the covalent character of the bonding. By examining the electr ic field generated by an array of point charges placed at the positions of the ions in over 40 inorganic compounds, we shaw that the Coulomb field nat urally partitions itself into localized regions (bonds) which are character ized by the electric flux that links neighbouring ions of opposite charge. This flux is identified with the bond valence, and Gauss' law with the vale nce-sum rule, providing a secure theoretical foundation for the bond-valenc e model. The localization of the Coulomb field provides an unambiguous defi nition of coordination number and our calculations show that, in addition t o the expected primary coordination sphere, there are a number of weak bond s between cations and the anions in the second coordination sphere. Long-ra nge Coulomb interactions are transmitted through the crystal by the applica tion of Gauss' law at each of the intermediate atoms. Bond fluxes have also been calculated for compounds containing ions with non-spherical electron densities (e.g. cations with stereoactive lone electron pairs). In these ca ses the point-charge model continues to describe the distant field, but mul tipoles must be added to the point charges to give the correct local field.