March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 1. Localized Chemical Bonding

1.J. Bond Distances⁵⁵

The distances between atoms in a molecule are characteristic properties of the molecule and can give information if compared with the same bond in different molecules. The chief methods of determining bond distances and angles are X-ray diffraction (only for solids), electron diffraction (only for gases), and spectroscopic methods, especially microwave spectroscopy. The distance between the atoms of a bond is not constant, since the molecule is always vibrating; the measurements obtained are therefore average values, so that different methods give different results.56 However, this must be taken into account only when fine distinctions are made.

Measurements vary in accuracy, but indications are that similar bonds have fairly constant lengths from one molecule to the next. While exceptions are known,57 the variation is generally < 1%. Table 1.4 shows distances for single bonds between two sp³ carbons.⁵⁸–⁶⁵ However, an analysis of C–OR bond distances in >2000 ethers and carboxylic esters (all with sp³ carbon) shows that this distance increases with increasing electron withdrawal in the R group and as the C changes from primary to secondary to tertiary.⁶⁶ For these compounds, mean bond lengths of the various types ranged from 1.418 to 1.475 Å. Certain substituents can also influence bond length. The presence of a silyl substituent β⁻ to a C–O (ester) linkage can lengthen the C–O, thereby weakening it.⁶⁷ This finding is believed to result from σ–σ∗ interactions in which the C–Si σ bonding orbital acts as the donor and the C–O σ∗ orbitals acts as the receptor.

Table 1.4 Bond Lengths between sp³ Carbons in Some Compounds.

C–C Bond in

Reference

Bond Length (Å)

Diamond

⁵⁸

1.544

C₂H₆

59

1.5324 ± 0.0011

C₂H₅Cl

60⁵⁸

1.5495 ± 0.0005

C₃H₈

1.532 ± 0.003

Cyclohexane

⁶⁰

1.540 ± 0.015

tert-Butyl chloride

⁶¹

1.532

n-Butane to n-heptane

⁶²

1.531–1.534

Isobutane

⁶³

1.535 ± 0.001

Bond distances for some important bond types are given in Table 1.5.⁶⁸ Although a typical carbon–carbon single bond has a bond length of ~1.54 Å, certain molecules are known that have significantly longer bond lengths.⁶⁹Calculations have been done for unstable molecules that showed them to have long bond lengths, and an analysis of the X-ray structure for a photoisomer (4) of [2.2]-tetrabenzoparacyclophane, 3A (also see Sec. 2.G), showed a C–C bond length of 1.77 Å.⁶⁹,⁷⁰ Note that 3A is shown as the molecular model 3B for comparison with photoisomer 4, which has the two four-membered ring moieties. Long bond lengths have been observed in stable molecules (e.g., benzocyclobutane derivatives).⁷¹ A bond length of 1.729 Å was reliably measured in 1,1-di-tert-butyl-2,2-diphenyl-3,8-dichlorocyclobutan[b]naphthalene, 5.⁷² X-ray analysis of several of these derivations confirmed the presence of long C–C bonds, with 6 having a confirmed bond length of 1.734 Å.⁷³

Table 1.5 Bond Distancesa

^aThe values given are average lengths and do not necessarily apply exactly to the compounds mentioned.⁸⁰ [Reproduced from Allen F.H.; Kennard, O.; Watson, D.G.; Brammer, L.; Orpen, A.G.; Taylor R. J. Chem. Soc. Perkin Trans. 2 1987, S1–S19 with permission from the Royal Society of Chemistry.]

A theoretical study has been reported, using computer simulation to apply encapsulation, strapping back, and stiffening to “squeeze” C–C bonds, leading to shorter bonds than would be observed if hybridization and conjugative effects operated alone.⁷⁴ The additional strain caused by threefold symmetric geometry constraints is believed responsible for this effect rather than changes in hybridization alone, as postulated by others.75–⁸²

There are indications that a C–D bond is slightly shorter than a corresponding C–H bond. Thus, electron-diffraction measurements of C₂H₆ and C₂D₆ showed a C–H bond distance of 1.1122 ± 0.0012 Å and a C–D distance of 1.1071 ± 0.0012 Å.⁵⁹

As seen in Table 1.5, carbon bonds are shortened by increasing s character. This is most often explained by the fact that, as the percentage of s character in a hybrid orbital increases, the orbital becomes more like an s orbital and hence is held more tightly by the nucleus than an orbital with less s character. However, other explanations have also been offered (see Sec. 2.C), and the matter is not completely settled. In general, molecules with one π bond (X=X) have shorter bond distances when compared to single bonds, X–X, and molecules with two π bonds (XX) have even shorter bond lengths. Indeed, the bond length clearly decreases in the molecules H₃C–CH₃, H₂C=CH₂, and HCCH: C–C bond lengths of 1.538, 1.338, and 1.203 Å.⁸³ There is work that suggests the absence of σ bonds may play a role in producing short bond distances in molecules that contain only π bonds.⁸⁴ This suggests that σ bonds prevent π bonds from adopting their optimal shorter distances. Such bonds occur in some organometallic compounds.