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Refined bond length-bond valence relationships for M−O bonds have been applied to isopolyoxometalate and some oxide structures (M=MoVI, WVI, VV, NbV, TaV). The M−O bond valences and the distribution of the (negative) ionic charge over the different types of oxygen atoms have thus been obtained. Additional negative charge and an equivalent positive charge were found to exist on certain types of oxygen atoms. The reasons for the observed distribution of the bond lengths and bond valences in the M−O frameworks and of the charge over the oxygen atoms have been analyzed. The main factors determining the distribution are the stabilization of the polymeric structures by strengthening of the inner M−O bonds of the M−O frameworks through acceptance of the negative charge by the terminal oxygen atoms and of the positive charge by (approximately) linearly bridging oxygen atoms and/or (angularly) bridging OH groups and coordinated H2O molecules. Both charge situations are restricted by the necessity to fulfill simultaneously the geometrical conditions of the M−O frameworks (interdependence of the M−O bond lengths), the bond length-bond valence relationships of the M−O bonds, and the valence sum rule for the M and O atoms and by avoidance, as far as possible, of very high negative charge on terminal oxygen atoms. Similar but much less detailed calculations and analyses were undertaken by some authors to locate the positions of OH groups and coordinated H2O molecules as well as to elucidate the hydrogen bridge system of polyoxometalates. Other authors have attempted to define, among other features, the charge distributions and basicities of the oxygen atoms in polyoxometalate ions. Our results differ considerably from those of the second group of authors, and reasons for the differences are discussed. Additionally, a number of general questions are treated in detail: the conditions for the extension of the coordination sphere of the protonated tetrahedral monometalate ions and the reasons for the occurrence of distorted MO6 octahedra (MOk polyhedra); the question of the coordination number of the addenda elements M in special cases; the amphoteric character of the species; the protonation sites; the relationship between charge distribution and basicity (as defined by the protonation constants) of polyoxometalate ions; the strength of the integration of the different types of MO6 octahedra (MOk polyhedra) within the M−O frameworks (kinetic inertness of the structures); the stabilization of the polymeric character of the different M−O frameworks by the "meshing effect" and by "normal" bonding; the question of a "trans influence"; the question of ions (guests) encapsulated by (uncharged or charged) M−O frameworks (hosts); and others. In summary, the bond valence model, which is strictly fulfilled within the accuracy of the bond lengths for polyoxo species, proves to be a powerful tool for studying bonding questions and yields a fascinating picture of the polyoxometalate structures. [ABSTRACT FROM AUTHOR]

The literature relating to the bonding in polyoxometalate ions is reviewed. The author's opinions are presented and expanded to give a bond model for polyoxometalate ions of the early transition elements (groups V and VI) composed of MO6 octahedra (MOk polyhedra with k>4). This bond model concerns in particular the bond valence (bond lengths) and charge distribution in the polyoxometalate ions and the factors modifying them. It is based on the following commonly used concepts and principles as applied to polyoxometalate ions:Lewis's octet rule, extended to the decet and dodecet rule for MV and MVI;pπ-dπ M=O double bond and the coordinate bond (dative bond);the resonance concept;the resonance bond number (or the bond valence concept and the valence sum rule);polydentate ligands and the chelate effect;the larger space requirements of unshared electron pairs (cf. the VSEPR model);the model of multicenter pπ-dπ multiple bonds for certain μ-oxo bridges between metal atoms;Brønsted's acid/base concept and acid/base equilibria;Pauling's rules for the acid/base strength of (monomeric) oxoacids/oxoanions;the law of mass action (Le Chatelier's principle), and others. The result is a set of resonance structures for polyoxometalate species in which three types of resonance can be distinguished. These, in turn, explain:the cohesion of the strongly distorted tetrahedral MO4 building units in the structures by formation of MO6 octahedra and hence the enhanced stability of the polyoxometalate ions;the distribution of the formal ionic charge over (nearly) all types of oxygen atoms, but preferably the terminal ones;the occurrence of positively charged oxygen atoms, caused by charge separation processes;the enhanced basicity of polyoxometalate ions; and further features. A "meshing effect" defines the increase of the bond valence in inner (bridging) M−O bonds and hence the stabilization of the structures due to extension of the coordination spheres of MO4 tetrahedra. Thus, the bond lengths of the different structure types are governed by a maximization of the bond valence of the inner, bridging (or minimization of the bond valence of the outer, terminal, in contrast to frequent statements in the literature) M−O bonds. The limits of the maximization of the inner bond valences of the polyoxometalate ions are determinedby minimum stoichiometric requirements for corresponding resonance formulae (inevitability of charge on bridging oxygen atoms);by the necessity to fulfill simultaneously the geometrical relationships of the M−O bond lengths (as defined by their interdependence in the M−O frameworks) and the valence sum rule for M and O atoms which are interrelated through the bond length-bond valence function;by (for the solid state) the packing of (poly)anions, cations, and molecules of water of crystallization with respect to the requirements of their size, shape, and charge;and/or by the capacity of the terminal oxygen atoms for the acceptance of unshared electron pairs in relation to that of the bridging oxygen atoms. The principle of the stabilization of polymeric species by maximization of their inner bond valence, which is simultaneously connected with an increase of the basicity of the species, is, however, only valid for a certain range of acidification of the oxometalate solution from which or in which the species form. The overlying principle is ultimately the consumption of H+ ions in the MO4w−/H+ systems, thus fulfilling the requirements of Le Chatelier's principle. [ABSTRACT FROM AUTHOR]

Bond length-bond valence relationships have been investigated fundamentally with emplasis on the M-O bonds in polyoxo compounds (M=MoVI, WVI, VV, NbV, TaV). 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. [ABSTRACT FROM AUTHOR]