Valence bond model

V. S. Urusov, I. P. Orlov, State-of-the-art and perspectives of the bond-valence model in inorganic chemistry. Crystallogr. Rep. 44 (1999) 686. 

Typical Ni—L bond lengths have been extracted from the Cambridge Structure Database (CSD) and listed in tabular form.321 Also, Ni11—L bond lengths from the CSD have been analyzed by the BDBO technique, which is related to the bond valence model (BVM) where the total bond order is equal to the oxidation state of any atom.322 Selected mean Ni—L distances from the CSD source are collected in Table 2. 

Thus, this simple equation implies the relation between the H- -H distance and the H-F bond length, which is shown in Figure 8.5. Here squares represent the data obtained at the MP2/6-311-H-G and triangles show the MP2/6-31G data. The solid line is obtained via eqs. 8.7 and 8.5 using the B and ro constants given by Dunitz [16]. This line reflects the validity of the bond valence model. 

Brown, I. D. (1987). Recent developments in the bond valence model of inorganic bonding. Phys. Chem. Miner. 15, 30-34. 

Theoretical aspects of the bond valence model have been discussed by Jansen and Block (1991), Jansen et al. (1992), Burdett and Hawthorne (1993), and Urusov (1995). Recently Preiser et al. (1999) have shown that the rules of the bond valence model can be derived theoretically using the same assumptions as those made for the ionic model. The Coulomb field of an ionic crystal naturally partitions itself into localized chemical bonds whose valence is equal to the flux linking the cation to the anion (Chapter 2). The bond valence model is thus an alternative representation of the ionic model, one based on the electrostatic field rather than energy. The two descriptions are thus equivalent and complementary but, as shown in Section 2.3 and discussed further in Section 14.1.1, both apply equally well to all types of acid-base bonds, covalent as well as ionic. 

This book is divided into four parts. Part I provides a theoretical derivation of the bond valence model. The concept of a localized ionic bond appears naturally in this development which can be used to derive many of its properties. The remaining properties, those dependent on quantum mechanics, are, as in the traditional ionic model, fitted empirically. Part II describes how the model provides a natural approach to understanding inorganic chemistry while Part 111 shows how the limitations of three-dimensional space lead to new and unexpected properties appearing in the inorganic chemistry of solids. Finally, Part IV explores applications of the model in disciplines as different as condensed matter physics and biology. The final chapter examines the relationship between the bond valence model and other models of chemical bonding. 

The ionic model divides the forces acting on atoms into an electrostatic component that can be calculated using classical electrostatic theory and a short-range component that is determined empirically. The previous chapter explored the properties of the classical electrostatic field. This chapter explores the properties of the empirically determined short-range force which is represented in the electrostatic model by the bond capacitance, C,y, defined in eqn (2.8). Rather than try to determine the values of Cy directly, it is better to step back and look at the way in which the bond valence model developed historically. Its connection with the electrostatic model of Chapter 2 will then become apparent. 

Surprisingly, therefore, the same topological equations (3.3) and (3.4), provide a description of both ionic and covalent bonding. It does not therefore matter whether a bond is considered to be ionic or covalent in character since both have the same bond valence description. This leads to the important corollary the bond valence model cannot distinguish between ionic and covalent bonding. Within the model, the terms ionic bond and covalent bond are without any formal significance. 

In Chapter 2 it was shown that the Madelung field of a crystal is equivalent to a capacitive electric circuit which can be solved using a set of Kirchhoff equations. In Sections 3.1 and 3.2 it was shown that for unstrained structures the capacitances are all equal and that there is a simple relationship between the bond flux (or experimental bond valence) and the bond length. These ideas are brought together here in a summary of the three basic rules of the bond valence model, Rules 3.3, 3.4, and 3.5. 

First, however, it is appropriate to introduce the Principle of maximum symmetry, an important heuristic that underlies the bond valence model and... 

While the principle of maximum symmetry is a heuristic with wide scientific application, Rules 3.3 to 3.5 define the bond valence model. They have each been discussed before but are brought together here for convenience. 

The correlation between bond length and bond valence corresponds to the third rule of the bond valence model. 

However, we do not need to abandon the bond valence model for those few inorganic compounds which contain homoionic bonds since there are a number of ways of adapting the model depending on the nature of the structure. If the two cations or two anions that form the bond are equivalent by symmetry, as the two Hg cations are, for example, in the tetragonal crystals of Hg2Cl2 (65441, Fig. 3.4), the normal rules still apply. In this compound the two Hg ... 

However, if the atoms are not related by symmetry, the normal rules break down. The homoionic N-N bond in the hydrazinium ion is an electron pair bond, but one in which N1 contributes 1.25 and N2 0.75 electrons. How can we apply the bond valence model in such cases where no solution to the network equations is possible One approach is to isolate the non-bipartite portion of the graph into a complex pseudo-atom. Thus in the hydrazinium ion the homoionic bond and its two terminating N atoms are treated as a single pseudo-anion which forms six bonds with a valence sum equal to the formal charge of —4. 

While this definition is arbitrary it is appropriate because it is based on chemical as well as geometric considerations and, like other definitions, it agrees with the conventional assignment in cases where there is no dispute. The definition can be justified for use with the bond valence model since any true bond that is excluded by this definition contributes at most only 4 per cent to the cation bond valence sum, and generally much less given that eqn (3.1) tends to overestimate the valence of weak bonds. 

The first rule is the Principle of electroneutrality (Rule 11.1) which restricts the chemical composition of inorganic compounds to those in which the net charge is zero. In the context of the bond valence model this rule can be stated as ... 

The bond valence model may also be used to refine the structure since it is based on the same assumptions as the two-body potential method. The network equations (3.3) and (3.4), can be used to predict the theoretical bond valences as soon as the bond graph is known. From these one can determine the expected bond... 

Bond valences can be used in conjunction with other techniques, particularly powder diffraction where, for example, light atoms are difficult to refine in the presence of heavy atoms. Adding the chemical constraints of the bond valence model can stabilize the refinement, particularly in the case of superstructures that have high pseudo-symmetry (Thompson et al. 1999). 

The previous chapters have described the bond valence model and shown how it can be used to understand many aspects of the crystal chemistry of inorganic compounds, but the model has found application in many other fields ranging from metals to proteins. This chapter does not pretend to be a comprehensive review of the uses to which bond valences have been put. Rather it is intended to give a flavour of the wide range of problems that can be treated using the model, presented from the point of view of the scientific issues that need to be addressed rather than from the point of view of the model itself It is apparent that these applications extend well beyond the inorganic systems within which the model was developed, but the common feature is that all involve some form of acid-base bonding. 

O Keeffe (1991Z)) has used bond valences to model the coherent interface that occurs between the semiconductors Si and MSi2 with M = Ni or Co (27139). Although these systems contain Si-Si bonds and therefore do not obey the assumptions of the bond valence model (condition 3.2), the mathematical formalism of the model still works because of the high symmetry. As both Si-Si and Si-Ni bonds are found in NiSi2, the cubic structure is strained (cf. BaTiOs in Section 13.3.2) and this strain affects the structure of the interface. Of the six possible interfacial structures examined, the two with the lowest BSI eqn (12.1) are those that are believed to occur in NiSi2 and CoSi2 respectively, and in both cases the strain introduced at the interface is correctly predicted. 

Most transition-metal cations can adopt several different oxidation states depending on the method of preparation and the compound in which they find themselves, but which oxidation state they adopt in a particular compound is not always clear from the chemical formula or from the nature of the bonding environment. Providing that the oxidation state is not zero, the bond valence model can help because the metal ligand bond can usually be described as an... 

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