Observed bond lengths

The observed bond lengths in some intermetallic compounds can be made compatible with those in the constituent metals by consideration of the possibility of distributing the d character unequally among the bond orbitals of an atom. 

Pt also have the same metallic valence, 5.78 or 6. Then in 1977 I reconsidered this question (17) with consideration of the observed enneacovalence of transition metals in some of their organometallic compounds and concluded that the metallic valence could become as large as 8.3 for Ru-Rh and Os-Ir alloys. This conclusion was reached by an argument based on the observed bond lengths that I now believe to have been misleading. 

For sphalerite and wurtzite, for example, the discussion of partial ionic character as described above for molyde-nite leads to the resultant average charges +0.67 for sulfur and—0.67 for zinc. The distribution of the sulfur atoms is calculated to be 12% S2 (quadricovalent), 50 percent S+, 32 percent S°, 6 percent S-, 0.2% S2-. The observed bond length 2.34 A with the sulfur radius 1.03 A and the Schomaker-Stevenson correction 0.05 A leads to 5 = 1.36 A for zinc (quadricovalent Zn2-). The increase by 0.05 A over the value 1.309 A for sp3 bonds of Zn° is reasonable as the result of screening of the nucleus by the extra electrons. 

Bond type X Covalent radii"-4 (A) AEN Schomaker and Stevenson Blom and Haaland Observed bond lengths (A)... 

So each bond has a bond order of 1.5, which is consistent with the observed bond length. These two resonance structures are often called Kekule structures because they were first proposed in 1865 by Kekule, who imagined that the molecule converted very rapidly from one form to the other. This, however, is not the case the molecule never has either of the Kekule structures but only a single structure, which is intermediate between these two hypothetical structures and is approximately represented as follows ... 

Table 2.6 Comparison of Observed Bond Lengths and Bond Lengths Calculated from the Sum of Covalent Radii...

The X-ray structure of lithium l-(dimethylamido)boratabenzene, reported in 1993, provided the first crystallographic characterization of a transition metal-free boratabenzene (Scheme 13).18a The observed bond lengths are consistent with a delocalized anion and with significant B—N double-bond character. In a separate study, the B—N rotational barrier of [C5H5B—NMeBnjLi has been determined to be 10.1 kcal/mol, and it has been shown that TT-complexation to a transition metal can increase this barrier (e.g., 17.5 kcal/mol for (C5H5B-N(i-Pr)2)Mn(CO)3).24... 

The previous literature on the effects of partial covalence on interatomic distances is contradictory. Pauling (1960) cites the examples of CuF, BeO, AIN, and SiC where observed bond lengths are shorter than the sum of the covalent radii. He attributes these differences to partial ionic character and thus implies that partial ionic character shortens covalent bonds. This conclusion is in accord with the Schoemaker— Stevenson (1941) rule Dab = a + pb—C nx— b where > interatomic distance between A and B, rx and r = covalent radii of A and B, a and xb = electronegativity of A and B and C = constant. 

A single S-O bond has a length of approximately 150 pm, but as a result of the multiple bonding between sulfur and oxygen, the observed bond length in S02 where the bond order is 1.5 is 143 pm. 

Bond lengths are also useful when deciding contributions from resonance structures. Structure I shows a double bond between N and O, while structure II shows the N-O bond as a single bond. If the structures contribute equally, the experimental N-O bond length should be approximately half way between the values for N-O and N=0, which is the case. Thus, we have an additional piece of evidence that indicates structures I and II contribute about equally to the actual structure. The observed bond lengths in the N20 molecule are shown below (in picometers). 

In the compound ONF3, the O-N bond length is 116 pm. The N-O single bond length is 121 pm. Draw resonance structures for ONF3 and explain the short observed bond length. 

Figure 40c and d, account for the observed bond length distribution and serve to delocalize the positive charges onto all Te atoms. 

By writing about complexes containing triple bonds between phosphorus and transition metals, one has to take into account the triple-bond character of phosphinidene complexes which are in a nearly linear coordination mode (type C) in contrast to the usual bent coordination mode D possessing typical double-bond features. Due to the additional r-donation bonding ability of the PR moiety to the metal atom in type C and the observed bond lengths, this type of complexes has to be included into the classes of metal-phosphorus triple bond compounds. Thus, at the end of this review will appear a chapter highlighting the appropriate compounds of type C. 

In many compounds, the experimental bond valences, S, and the theoretical bond valences, s, are both found to be equal to the bond fluxes, <1>, within the limits of experimental uncertainty. This is an empirical observation that is not required by any theory. For this reason, and because there are occasions when the differences between them are significant and contain important information about the crystal chemistry, it is convenient to retain a different name for each of these three quantities to indicate the ways in which they have been determined. The bond flux is determined from the calculation of the Madelung field, the theoretical bond valence is calculated from the network equations (3.3) and (3.4), and the experimental bond valence is determined from the observed bond lengths using eqn (3.1) or (3.2). 

The differences in the two observed bond lengths for Ca-F 1 bonds can be attributed to steric effects discussed in Section 12.3.5. 

In cases where the experimental and theoretical bond valences are different, the bond capacitances do not cancel, but the experimental bond valences continue to give a good estimate of the bond flux (Preiser et al. 1999). In these cases, discussed in Chapters 8 and 12, the theoretical bond valences can be used to determine a reference bond length against which the sizes of the strains in the observed bond lengths can be measured. 

The bond strain in this chapter, as in most other places in this book, is defined as the difference between the observed bond lengths and the bond lengths calculated from the theoretical bond valences. A bond strain index that measures this strain is defined in eqn (12.1). 

These parameters are found by fitting the bond valence to experimentally observed bond lengths. It is this empirical fitting that gives the model its robustness, since the fitted parameters automatically compensate for a number of systematic effects. As an example, suppose that the true charge, q, of a cation differs from the formal charge, V, by a factor k as given by eqn (9.1) ... 

---