Bond valence parameters determination

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. 

Practical Steps of Bond Valence Parameter Determination. 114... 

In the course of the discussion of bond valence parameter determination we will also link the energy of an atom M in a given structural environment to deviations of its bond valence sum V A) from the absolute value of its oxidation state and to a (also bond valence-based) penalty function AFevr that penalizes deviations in the bond arrangement from the equal valence rule ... 

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. 

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... 

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) ... 

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). 

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. 

Thus values of Rijcan be determined for pairs of atoms in a variety of coordinations in experimental crystal structures, and are generally found to be nearly constant for a given pair. Particularly in the case of oxides, for which a large data base exists, Rjj values are known rather accurately (Brown Altermatt, 1985). Bond valence parameters for a wide variety of cation - anion bonds were subsequently determined by Brese O Keeffe (1991) using an interpolation technique. Parameters for anion-anion bonds in solids have also been determined (O Keeffe Brese, 1992). 

Bond valence sums can be very useful in determining atom valences in crystals in cases where there is ambiguity. A simple example (O Keeffe, 1989) to illustrate the point is afforded by the structure of ilmenite which may be formulated Fe(ll)Ti(IV)03 or Fe(lll)Ti(lll)03. From the observed bond lengths and known bond valence parameters... 

The fitted constants N, Rq and B depend only on the nature of the bonded atoms (i,j) and are given in the literature [585,586] or may be calculated by the computer code VALENCE [587] designed to calculate bond valences from bond lengths and vice versa. This code allows also calculation of bond-valence sums and average bond lengths, and can determine bond-valence parameters from the bonding environments of different cations. 

Practical Considerations in Determining Bond Valence Parameters. 91... 

Before turning to the practical determination of bond valence parameters, it appears appropriate to briefly discuss connections between experimentally observable quantities and the bmid valence parameters. Qualitatively, it is obvious that the closer two atoms of opposite charge approach each other, the more electron density will be found in the bonding region and the stronger their interaction will be. So it appears natural to link bmid valence to the electron density, p(f), and several such approaches can be found in the literature. 

Still it should have become obvious from the above discussion that there is a close functional relationship between bond valence and electron density at the bond critical point (and in the same way between bond valence and the Laplacian of V Pbcp) and that this correlation involves a scaling based on the principal quantum number (row number) of the atoms involved or a closely correlated quantity, and at least for the case of the Laplacian to a measure of atomic polarizability (such as the atomic hardness or its inverse the atomic sofmess). This fundamental correlation should thus be taken into account when fine-tuning approaches to determine bond valence parameters and BV-related forcefields. 

As briefly mentioned in Sect. 2.2, the bond valence parameter b represents the compliance of a bond to external forces. Approximating by a universal value therefore eliminates the crystal-chemical information on elastic behavior from bond valence parameters (or more precisely reduces the information from an approximation that takes into account structure type and atomic properties to a crude estimate solely based on the coordination type). Whether such information is relevant for a given application purpose and available for specific cation-anion pair may depend on individual circumstances. Here it will be assumed that retaining this information available is desired, and thus it is necessary to elaborate suitable procedures to systematically determine the respective b values. 

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