Empirical bond-strength-bond-length curves for oxides

Bond-strength-bond-length relationships for bonds between oxygen and H⁺, Li⁺, Be²⁺, B³⁺, Na⁺, Mg²⁺, Al³⁺, Si⁴⁺, P⁵⁺, S⁶⁺, K⁺, Ca²⁺, Sc³⁺, Ti⁴⁺, V⁵⁺, Cr⁶⁺, Mn²⁺, Fe³⁺, Fe²⁺, Co²⁺, Cu²⁺, Zn²⁺, Ga³⁺, Ge₄₊ and As⁵⁺ have been derived by requiring that the sums of the bond strengths around the cations be equal to their valence in 417 crystals whose structures have been accurately determined. The relationship is of the form s = (R/R₀)^-N where s = bond strength, R = bond length and R₀ and N are fitted constants. It is further shown that all ions with an isoelectronic core can be fitted by a single pair of parameters, R₀ and N, that are independent of the ionic character of the bond and the coordination number of the cation. The resulting bond strengths have the property that they are directly related to the covalent character of the bond and that their sum around each atom is, on average, within about 5% of its valence. The bond-strength-bond-length curves are particularly useful in accounting for bonding in cases where the coordination is very distorted (e.g. Na⁺, Cu²⁺ and V⁵⁺). They can also be used to predict the positions of hydrogen atoms, to analyze for different oxidation states and site occupancies, to calculate ionic radii and to provide an indication of the correctness of crystal structure determinations.