Correlation with bond-length

This section considers recent attempts to extrapolate from observed structures to the experimentally unattainable transition state structures for bond making and breaking reactions. (Transition state structures for conformational changes are experimentally observable in the crystal in favourable cases, as described in Section 3, pages 135-136.) The approach builds on the regular correlations between structure and reactivity, particularly the linear correlations with bond length described in the previous section. 

In summary, the previous example shows that bond dissociation enthalpies should not be correlated with bond lengths unless the relaxation energies of the fragments are comparable. On the other hand, when two bonds between the same pairs of atoms have identical bond lengths, it is sensible to assume that they have similar bond enthalpy contributions. Hence, in this case, a bond enthalpy contribution can be transferred from one molecule to another. 

In most of these cases the homoionic bond can be assigned a valence, but this does not always correlate with bond length as the examples of the trifluoroacetate ion and S-bonded dmso show. However, a correlation is expected for Cu(N02)g and has been found for Hg-Hg bonds. In addition to the well-known mercurous ion (Hg ), cations such as ngj" ", Hg4+, (Hg +) (infinite chains), and (Hg ) (infinite sheets) are also known. The Hg-Hg bonds in these cations show a considerable variation in length which correlates well with the bond valence, as shown in Fig. 3.8 (Brown et al. 1984). 

Kaliaperumal, R., Sears, R. E. J., Ni, Q. W., and Furst, J. E., Proton chemical shifts in some hydrogen bonded solids and a correlation with bond lengths, J. Chem. Phys. 91,7387-7391 (1989). 

Eq. (69) besides giving an excellent possibility for enumerating P ° shows that bond orders are a function of molecular topology only. Since bond orders can be correlated with bond lengths 85,102-104) molecular topology also determines molecular geometry. 

The usefulness of bond valence lies in its correlation with bond length. For each pair of ions that form a bond, there is a correlation between Sy and the bond length, Ry, similar to that shown in Fig. 2.3. Weaker bonds, i.e. those with smaller valence, are longer and those with higher valence are shorter. Thus a knowledge of the valence of a bond leads to a prediction of its length and vice versa. 

Historically, bonding interatomic distances in crystals were first discussed in terms of atomic or ionic radii however the concept of bond valence and its correlation with bond length has now come to the fore, largely because of the work of W. H. Zachariasen and of I. D. Brown. A brief summary of the reasons for preferring the latter approach is given first. In fact a case will be made for abandoning the concept of ionic (or atomic) radii as currently applied in that area of crystal chemistry (oxides and similar materials) that is the main concern here. 

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