The bond valence approach

The use of empirical correlations between the bond length and strength of chemical bonds in crystal chemistry dates back to the work of Byström & Wilhelmi (1951) and Zachariasen (1954), who generalized Pauling's electrostatic valence principle to extract estimates for the different bond strengths, e.g. in the asymmetric  coordination polyhedra of transition metals. Donnay & Allmann (1970) developed these ideas into the concept of bond valence (BV). It is one of the major advantages of the BV concept that it does not require an a priori distinction between covalent and ionic types of bonding. Thus, the terms `cation' and `anion' in this context simply classify the particles according to their electronegativity and are equivalent to Lewis acids and bases. The monotonic decrease of the bond valence sA-X with bond length RA-X  between a cation A and an anion X may be approximated as

Some of the early investigations preferred the power law ansatz

mostly because of the slightly reduced computational effort. The empirical parameters R0 and b (or R0 and N) are chosen to ensure that the expectancy value for the bond-valence sum V(A) of the cation A for bonds to all its coordinating anions X

equals the formal valence Videal(A). A detailed introduction into the bond-valence model as well as a stringent formal deduction from a set of axioms can be found in the work of Brown (1992, 1997). Empirical bond-valence parameters for numerous atom pairs can be found in the literature (e.g. Brese & O'Keeffe, 1991; Brown, 1996); for a compilation of data from earlier literature see e.g. Brown (1981). Over the last decades bond-valence sum calculations have become a valuable tool in crystal structure determinations for the localization of light atoms from X-ray data, the distinction of isoelectronic ions (such as Al(III) from Si(IV)) or as a quick check for the plausibility of a structure solution (see e.g. Waltersson, 1978; Adams et al., 1993; Withers et al., 1998) The predictive power of the bond-valence approach stimulated considerable efforts to elucidate its equivalence to the established concepts of bonding in inorganic solids, especially to the borderline cases of purely ionic (cf. Brown, 1992; Preiser et al., 1999) or covalent bonding (cf. Burdett & Hawthorne, 1993; Hawthorne, 1994; Urusov, 1995; Mohri, 2000).

Nevertheless, one should be aware that the refinement of bond-valence parameters from bond lengths of reference crystal structures is based on simplifying assumptions which in some cases limit their applicability. One of these assumptions that shall be addressed in this work is the hypothesis that the bond-valence parameter b may be treated as a universal constant. As for numerous cation-anion pairs only a limited number of reliable structure determinations were available, a significant refinement of the two highly correlated BV parameters b and R0 was generally hard to achieve and often impossible. Thus, Brown & Altermatt (1985) suggested keeping b to the universal value of 0.37Å and to refine R0 only.

Based on that simplification Brese & O'Keeffe (1991) could also determine R0 values for less common cation-anion pairs in their comprehensive bond-valence parameter tables. Following a suggestion by Ray et al. (1979), these authors interpreted the values of R0(ij) as the sum of atomic radii of the atoms i and j modified by an electronegativity related correction term

Thereby it became possible to estimate R0 even for atom pairs, where no experimental data were available. Brese and O'Keeffe employed their own electronegativity scale (O'Keeffe & Brese, 1991), which except for the charge-dependent electronegativity of hydrogen is closely related to the widely accepted scale of Allred & Rochow (1958). As will be shown further below, the question whether this simplification is justified is intimately linked to the more fundamental question what is the maximum cation-anion distance that should be assumed to contribute to a chemical bond.

Goto chapter 2: Influence of bond softness on bond valence