Bond length-bond valence relationships with particular reference to polyoxometalate chemistry

Abstract

Bond length-bond valence relationships have been investigated fundamentally with emplasis on the M-O bonds in polyoxo compounds (M=Mo^VI, W^VI, V^V, Nb^V, Ta^V). A large number of errors of different types has been made in the derivation of practically all of the published functions and/or of the relevant parameters. Considering all sources of errors, bond length-bond valence functions and the relevant parameters have been derived which represent more shallow curves than most of the functions in the literature. The relationships have been applied classically for identifying O atoms of an OH group or a coordinated H₂O molecle, to elucidate hydrogen bridge systems, to determine the oxidation numbers of M atoms (and to distinguish between different elements via the oxidation numbers), and to verify the coordination numbers assigned to the M atoms, etc. The most important application of the relationship. however, is the calculation of accurate bond valences and in particular the determination of the distribution of the charge over the O atoms of the species. These data can be used to elucidate the relatonships between structure, bonding, stability and basicity of the species. However, most functions and/or the relevant parameters stated in the literature produce errors which are most evident in the calculated formal ionic charges of the species and can involve several charge units. Even the best functions and parameters give unreliable results. A first important reason for this is the unsatisfactory identification of erroneous structural data with large random and/or systematic errors in the bond lengths and their rejection from the set of reference structures used for the derivation of the bond length-bond valence parameters B and d₀ or N and d₀ of the commonly used exponential or power functions. This makes the correct determination of B or N difficult. A second important reason is connected with the—at present—unfounded practice of using ‘universal’ B or N parameters which leads to errors for the proportion in the bond valencies of the inner (bridging) relative to those in the outer (terminal) M-O bounds of the species and for the charge separations. These quantities affect the stability of the species. A third significant reason, which is independent of and hence present even for correctly derived bond length-bond valence parameters, is a small (and inevitable) systematic error in the bond lengths of each structure determination which leads to larger errors for the formal ionic charge. This error can be completely compensated by individual fitting of the d₀ bond length-bond valence parameter for each structural determination.