Bond valences parameters

This section discusses the determination of the bond valence parameters used in eqns (3.1) and (3.2) though the principles can be applied to the other expressions discussed in Section A1.3. Since there is no exact theoretical derivation of the correlation between bond valence and bond length, the bond valence 

Mostly taken from Brown and Altermatt (1985) and Brese and O Keeffe (1991). (A complete set is available at http //www.ccpl4.ac.uk/ccp/web-mirrors/i d brown/bond valence parm/) 

In principle the bond valence parameters could be obtained by comparing the experimental bond valences, S, determined using an initial set of bond valence parameters, against the theoretical bond valences, s, calculated using the network eqns (3.3) and (3.4). These initial values could then be refined to minimize the differences given by the expression (Al.l)  

This method has not so far been used but should work well providing that only structures with unstrained bonds are used. 

The normal procedure is to refine the bond valence parameters by minimizing the difference between the atomic valence and the sum of the bond valences 

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For unstrained compounds the quantum mechanical component of the ionic model is described entirely by the empirical bond valence parameters, Rq and B, and an explicit knowledge of the bond capacitances is not needed. 

A second problem is the widespread occurrence of compounds in which several different anionic elements bond to the metal (heteroleptic compounds). Most inorganic compounds have homoleptic coordination, i.e. the cation is bonded to only one kind of anion, making the determination of the bond valence parameters relatively simple (Appendix 1). Flomoleptic coordination is much less common among the transition-metal complexes. As described in Appendix 1, bond valence parameters for a variety of transition metals to O, N, C, Cl, S, and P have been determined using heteroleptic systems although the values obtained are often less reliable than those obtained from homoleptic systems. 

In spite of these difficulties, there have been a number of determinations of bond valence parameters for use in transition-metal complexes. In most cases the bond valence parameters determined for oxides work well with transition-metal complexes, but care is needed when the metal can be found in different spin states or the ligand allows different degrees of tt bonding. 

The robustness of the bond valence model derives, therefore, from two factors the independence of the bond valences from the location of the bonding electrons, and the use of fitted values for the bond valence parameters which automatically compensates for systematic changes in the bond length produced by other effects. 

The advantage of this method is that it can be easily used with any number of cation coordination spheres whose bond distances are available. Even one coordination sphere is sufficient to give a trial value though the more that are used the more confidence one can have in the value of Rq. One needs to exercise a little care if only a few coordination spheres are known, since the oxidation state may be unstable except in the presence of strained bonds which could lead to a false value of Rq. There are a number of potential pitfalls in determining bond valence parameters. For example, the inclusion of poorly determined structures in the sample tends to increase the value (and uncertainty) of B with a corresponding decrease in Rq. A critique of these problems has been given by Tytko (1999). 

The above procedure was used by Brown and Altermatt (1985) to produce an extensive table of bond valence parameters, mostly of bonds to. They based... 

In a series of papers Palenik and his coworkers (Palenik 1997a,6,c Kanowitz and Palenik 1998 Wood and Palenik 1998, 1999a,6 Wood et al. 2000) have determined bond valence parameters for transition metals. Some of these have been chosen to be independent of oxidation state in an attempt to provide values of Rq that can be used when the oxidation state of the cation is not known. While these parameters are not as accurate as those that take the oxidation state into account, they can be used to make an approximate determination of the oxidation state, after which the correct value of Rq can be substituted. 

The values of are not determined from the theory but, like other bond valence parameters, are fitted to observed bond lengths in the manner described in Section A1.2. The parameters that Valach reports for Cu-0 and Cu-N bonds give zero valence at finite bond lengths, but the valences calculated for very short bonds are probably too low. 

Brese, N. E. and O Keeffe, M. (1991). Bond valence parameters for solids. Acta Cryst. B47, 192-7. 

Brown, I. D. and Altermatt, D. (1985). Bond-valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database. Acta Cryst. B41, 244-7. 

Garcia-Rodriguez, L., Rute-Perez, A., Ramon-Pinero, J., and Gonzalez-Silgo, C. (2000). Bond valence parameters for ammonium-anion interactions. Acta Cryst. B56, 565-9. 

TABLE 3.7. Bond-Valence Parameters for Some Halides, Nitrides, Oxides, Phosphides, and Sulfides... 

Table 1 Selected bond valence parameters Rq (B = 0.37 A)5 (mostly taken from references 4 and 6) and crystal radii from reference 8 ...

Brown and Altermatt have reported the bond valence parameters from bond lengths for 750 atom pairs using the Inorganic Crystal Structnre Database. Also Brese and O Keefe" have supplemented these data for 969 pairs of atoms by critically examining reported strnctnres in the literatnre. 

For each crystal structure where a central atom is snrronnded by the same kind of atoms, the bond valence parameter is obtained from Eqnation 22.3 by Eqnation 22.4 ... 

The bond-valence approach [28] has proven to be a powerful tool for the prediction and interpretation of bond lengths in solids. Bums et al. [19] presented revised bond-valence parameters derived from uranyl polyhedra in well-refined stmctures. These parameters facilitate calculations in the case of as previously proposed parameters generally performed poorly. Bums et al. [19] provided bond valence parameters that were optimized over all uranyl polyhedra, as well as those that are coordination specific. The coordination specific parameters for six-coordinated are = 2.074 A, b = 0.554 A for seven-coordinated Rij = 2.045 A, b = 0.510 A for eight-coordinated Rij = 2.042 A, b = 0.506 A. Optimal parameters for all types of polyhedra are = 2.051 A, ft = 0.519 A. 

Bond valence sum is calculated using interatomic distances and empirical bond valence parameters tabulated for each type of the bond. The analysis was conducted using VaList software [A.S. Wills and I.D. Brown, VaList, CEA, France (1999)], available from ftp //ftp.ill.fr/pub/dif/valist/. 

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