Bond valences ideal

Fig. 9.1. Structures of the acetate ion showing bond valences (above the bond) and bond lengths (in pm below the bond) (a) the ideal structure of the isolated ion (b) the structure normally observed in the solid state (c) the structure observed when bonded to a strong cation (Si) (d) the structure observed for the diprotonated acetate ion (e) the structure of the trifluoroacetate ion normally observed in the solid state.

This has a number of interesting consequences. One is that the oxidation state of Nb is lowered from the ideal value of -1-3.5 to +3.425. A second consequence is that each Eu ion at the surface of the (EuS)3 layer has a different environment since each sees a different part of the NbS2 layer. Some Eu + ions lie directly over an ion and form a very short Eu S bond, while others lie between the ions and form two or more longer bonds. Not surprisingly, the bond valence sums around the Eu ions, as well as around the ions of the NbS2 layer, show considerable variation depending on the relative positions of the layers at any given point in the crystal. 

The experimental crystal structure determination showed that this molecule has bond distances with unexpected values, which were not consistent with classically localized bond-valence forms in particular, the C-9=N-4 and C-12=N-6 bonds, which are both formally double bonds, and not of equal length. In addition, the N-l-N-2, N-3-N-4, and N-5-N-6 bonds were expected to be shorter than the C-N single bonds, C-l-N-3, C-2-N-3, and C-ll-N-5. In fact, none of the former three is shorter than any other of the latter three. They are shorter than the C-12-C-10 bond in the ring system. The bond distances in C-ll-S-l-C-1 fragment are normal for their types. These two C-S bonds have effectively ideal lengths and are in the normal range. 

Fig. 10.11. Structures of the acetate ion and the water molecule. Numbers given are bond valences and (in parentheses) bond lengths in pm for the C-C and C-0 bonds, a The traditional ideal structure of the acetate ion in which all bonds are assigned integral bond orders...

One should strictly make a distinction between ideal bond valence defined theoretically from the bond graph in Section 10.3.2 and experimental bond valence determined from the observed bond lengths using Equations 10.1 or 10.2. Except in the situations described in Section 10.6, tbe two differ only by the experimental uncertainty... 

Ideal M-O distances were calculated from bond valences. 

Since the valence V, is known for aU the atoms, this set of m equations can be solved to give S,y for each of the m bonds. This calculation is implemented in the program BONDVAL [18]. The bond valences calculated from these network equations are known as ideal bond valences. If they are the same as the experimental values, the assumptions of the bond valence theory are validated [17], but if they are different, they indicate that one of the additional constraints described above is present. In principle it should be possible to model these constraints by choosing suitable bond capacitances, but in practice the capacitances themselves often depend on the context in ways that are not always transparent [19]. 

If an atom finds itself in a cavity that is too large for its bonds to adopt their ideal length, the bonds must be stretched. According to the distortion theorem (5), the environment of the atom will distort in such a way as to make the bond lengths unequal in order that the bond valence sums becomes equal to the atomic valences. As mentioned in Sect. 7.4.1, this contributes to the distortion around titanium(IV) in BaTiOs. In many cases, such distortions are found in compounds where electronic distortions are also expected, the two effects being mutually supportive. 

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