Studies on bond and atomic valences. I. correlation between bond valence and bond angles in Sb^III chalcogen compounds: the influence of lone-electron pairs

In the present bond-valence concept the bond-valence parameter r_o is treated as constant for a given pair of atoms, and it is assumed that the bond valence s_ij is a function of the corresponding bond length D_ij, and that the atomic valence is an integer equal to the formal oxidation number ^forV_i derived from stoichiometry. However, from a statistical analysis of 76 [Sb^IIIS_n] and 14 [Sb^IIISe_n] polyhedra in experimentally determined structures, it is shown that for Sb^III—X bonds (X = S, Se), r_o is correlated with _i, the average of the X—Sb—X angles between the three shortest Sb—X bonds. This is interpreted as a consequence of a progressive retraction of the 5s lone-electron pair from the Sb^III nucleus, which can be considered as continuous change of the actual atomic valence ^actV_i of Sb from +3 towards +5. A procedure is derived to calculate an effective atomic valence ^effV_i of Sb^III from the geometry, _i and D_ij, of the [Sb^IIIX_n] polyhedra, which approximates ^actV_i and is a better description of the actual valence state of Sb^III than the formal valence ^forV_i. Calculated ^effV_Sb^III are found to vary between +2.88 and +3.80 v.u. for [Sb^IIIS_n] and between +2.98 and +3.88 v.u. for [Sb^IIISe_n] polyhedra. It is suggested that a corresponding modification of the present bond-valence concept is also required for other cations with lone-electron pairs.