Bond valence prediction

Detailed comparison with observed crystal structures requires both accurate structures and the development of parameters appropriate for bonds to nitrides, neither of which are generally available at present. However the important point is to recognize that the expected bond valences predict bond lengths which are different fi-om those predicted by the ionic radius approach. Thus using ionic radii for four-coordinated Li and O the predicted Li-O bond length would be that for valence 1/4 rather than 7/24, etc. 

Heteroionic bond A bond formed between a cation and an anion Homoionic bond A bond formed between two cations or between two anions Ideal bond valences Bond valences predicted for a valence compound using the network equations... 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

Valence The highest-energy electrons in an atom, which an atom loses, gains, or shares in forming a chemical bond. Valence shell electron-pair repulsion (VSEPR) A procedure based on electron repulsion in molecules that enables chemists to predict approximate bond angles. 

Fig. 5.4. Possible hydration spheres around anions showing the expected bond valences (a) around SO , (b) around (POsOH) (the predicted P-O bond lengths in pm are also shown to the left of the bond).

Fig. 8.9(b), ZnV20g is able to crystallize with the brannerite structure whose theoretical bond valences, calculated from the network equations ((3.3) and (3.4)) and shown in Fig. 8.9(b), already predict an out-of-centre distortion for the ion. ZnV20g thus adopts a bond graph that supports the electronically induced distortion. In this case the adoption of a lower symmetry bond graph is favoured because it is able to reduce the bond strain. 

Not all structures are based on close packed lattices. Ions that are large and soft often adopt structures based on a primitive or body centred cubic lattice as found in CsCl (22173) and a-AgI (200108). Others, such as perovskite, ABO3 (Fig. 10.4), are based on close packed lattices that comprise both anions and large cations. The larger and softer the ions, the more variations appear, but the lattice packing principle can still be used. Santoro et al. (1999,2000) have shown how close-packing considerations combined with the use of bond valences can give a quantitative prediction of the structure of BaRuOs (10253). 

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... 

As described in Chapter 11, bond valences can play a role in modelling but, since most crystal structures can still not be predicted ab initio, diffraction methods remain the most common and reliable technique for determining the structures of those compounds that can be prepared as single crystals large enough for study by X-ray or neutron diffraction. 

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. 

When non-bonding valence electrons are present, the VSEPR model (Gillespie and Hargittai 1991) provides a simple explanation which correctly predicts the geometries of isolated molecules, but it is less effective in describing the behaviour in solids where secondary bonds are present. Both VSEPR and the bond valence model give only a semi-quantitative treatment, but the bond valence model is able to explain under what conditions the stereoactivity of the lone electron pair will be suppressed. 

In cases where there are no electronically driven distortions, the orbital description provides no better account of the chemistry than the bond valence model. Rather it tends to make an essentially simple situation more complex. For example, consider the phosphate and nitrate anions, and NOJ. In orbital models the P atom is described as sp hybridized and the N atom as sp hybridized, but these descriptions are just representations of the spherical and cylindrical harmonics appropriate to the observed geometries. They provide no explanation for why P is four but not three coordinate, or why N is three but not four coordinate. The bond valence account given in Chapter 6 is simpler, more physical, and more predictive. The orbital description is merely a rather complicated way of saying that the ions obey the principle of maximum symmetry but implying that the constraints are related in some unspecified way to the properties of one-electron orbitals rather than to the ionic sizes. 

A closer comparison of bond valence and electron density models is not possible because of the different underlying assumptions of the models. The forces in the bond valence model act between structureless point atoms, but the forces in the electron density model are exerted by electrons on nuclei and vice versa. This basic difference makes it difficult to compare the two models in greater detail. They are best seen as complementary, the electron density model providing important information about the nature of the bonding between the atoms, the bond valence model providing a simple tool for predicting structure and properties, particularly in cases where the structure is complex. 

Rutherford, J. S. (1990). Theoretical prediction of bond-valence networks. Acta Cryst. B46, 289-92. 

Thorp, H. H. (1998). Bond valence sum analysis of metalloenzymes. 3. Predicting bond lengths in adjacent redox states using inner-sphere reorganiza-tional energies. Inorg. Chem. 37, 5690-2. 

We may predict the distances from the structure and radii. Carbon without doubt is quadrivalent, so that the iron-carbon bonds must have bond number. The sum of the iron radius 1.167 A and the carbon radius 0.772 A is 1.939 A, and with the correction of Equation 11-1 we obtain 2.04 A as the predicted Fe—C distance. This is in reasonably good agreement with the experimental value 2.01 A. Each iron atom forms a bond with bond number with each of two carbon atoins, using up 1 of its total valence of 6 and leaving 4 for the Fe—Fe bonds. The predicted bond numbers for ligancy 12 and 11 are 0.39 and 0.42, respectively, and the predicted Fe—Fe distances are 2.58 A and 2.56 A, which are approximately equal to the corresponding observed values,... 

D. (a) Find the number of rings plus double bonds in a molecule with the composition C 4H,2 and draw one plausible structure, (b) For an ion or radical, the rings + double bonds formula gives noninteger answers because the formula is based on valences in neutral molecules with all electrons paired. How many rings plus double bonds are predicted for C4Hl0NO+ Draw one structure for C4H 0NO+. 

Valence bond theory predicts the hybridization of orbitals, which occurs when an atom promotes an electron from a lower to a higher energy level in order to form more bonding pairs. You should be familiar with the five types of hybridizations (sp, sp2, sp3, dsp3, cfsp3). 

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