Bent bond

Hirshfeld (1964) pointed out that bond bending not only occurs in ring systems, but also results from steric repulsions between two atoms two bonds apart, referred to as 1-3 interactions. The effect is illustrated in Fig. 12.3. The atoms labeled A and A are displaced from the orbital axes, indicated by the broken lines, because of 1-3 repulsion. As a result, the bonds defined by the orbital axes are bent inwards relative to the internuclear vectors. When one of the substituents is a methyl group, as in methanol [Fig. 12.3(b)], the methyl-carbon-atom hybrid reorients such as to maximize overlap in the X—C bond. This results in noncolinearity of the X—C internuclear vector and the three-fold symmetry axis of the methyl group. Structural evidence for such bond bending in acyclic molecules is abundant. Similarly, in phenols such as p-nitrophenol (Hirshfeld 

the exocyclic C—O bond is bent by C - -H repulsion, leading to unequal C—C—O bond angles. 

The first charge density observation of bond bending in cyclopropane was from the experimental charge densities of cts-l,2,3-tricyanocyclopropane (Hartman and Hirshfeld 1966) and 2,5-dimethyl-7,7-dicyanonorcaradiene (Fritchie 1966). It has been confirmed by a considerable number of other studies, including one on 

1994) and diazirine (N=NC) rings (Kwiatkowski et al. 1994). Density-based evidence for the bending in acyclic molecules caused by intramolecular nonbonded repulsions is available from experimental studies on 2-cyanoguanidine (Hirshfeld and Hope 1980) and theoretical analysis of 2-cyanoguanidine, hydrazoic acid, cyanogen azide, formic acid, and diimide (Eisenstein and Hirshfeld 1979). The results have abundantly confirmed Hirshfeld s earlier conclusions based on molecular geometry. 

That bond-bending strain is not confined to three-membered rings is evident from charge density studies on cyclobutane (Stein et al. 1992), cyclobutadiene 

---

FIGURE 3 10 Bent bonds in cyclopropane (a) The orbitals involved in carbon-carbon bond formation overlap in a region that is displaced from the internuclear axis (b) The three areas of greatest negative electrostatic potential (red) correspond to those predicted by the bent bond description... 

In keeping with the bent bond de scription of Figure 3 10 the carbon-carbon bond distance in cycio propane (151 pm) is slightly shorter than that of ethane (153 pm) and cyclohexane (154 pm) The calculated val ues from molecular models (see Learning By Modeling) reproduce these experimen tal values... 

Cyclobutane has less angle strain than cyclopropane (only 19.5°). It is also believed to have some bent-bond character associated with the carbon-carbon bonds. The molecule exists in a nonplanar conformation in order to minimize hydrogen-hydrogen eclipsing strain. 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

The concept of hybrid orbitals is deeply ingrained in the thinking of organic chemists, as widely reflected in texts and the research literature. However, Pauling and others recognized that there was a different conceptual starting point in which multiple bonds can be represented as bent bonds. ... 

It has been shown that description of bonding based on the bent-bond concept can be just as successful in describing molecular structure as the hybridization concept. We will, however, use the hybridization terminology. 

The alkyl-bridged structures can also be described as comer-protonated cyclopropanes, since if the bridging C—C bonds are considered to be fully formed, there is an extra proton on the bridging carbon. In another possible type of structure, called edge-protonated cyclopropanes, the carbon-carbon bonds are depicted as fully formed, with the extra proton associated with one of the bent bonds. MO calculations, structural studies under stable-ion conditions, and product and mechanistic studies of reactions in solution have all been applied to understanding the nature of the intermediates involved in carbocation rearrangements. 

Strong sp -sp a bonds are not possible for cyclopropane, because the 60° bond angles of the ring do not permit the orbitals to be properly aligned for effective overlap (Figure 3.10). The less effective overlap that does occur leads to what chemists refer to as bent bonds. The electron density in the carbon-carbon bonds of cyclopropane does not lie along the internuclear- axis but is distr-ibuted along an arc between the two carbon atoms. The r-ing bonds of cyclopropane are weaker than other carbon-carbon a bonds. 

Organic chemists usually think of a double bond as the combination of a a bond and a 7i bond. An alternative is to consider a double bond as made up of two equivalent bent bonds (these bonds point above and below the intemuclear axis). 

Apply the bent-bond model to the preferred conformations of acetaldehyde and propene. Do bent-bonds maintain or remove eclipsing interactions in the equilibrium structures of the two molecules Formulate a simple rule based on the bent-bond model for predicting conformational preferences in systems containing trigonal atoms. 

Bent bonds (Section 4.4) The bonds in small rings such as cyclopropane that bend away from the internuclear line and overlap at a slight angle, rather than head-on. Bent bonds are highly strained and highly reactive. 

Cyclopentenones. from 1.4-diketones. 886-887 Cyclopropane, angle strain in, 115 bent bonds in. 115 from alkenes. 227-229 molecular model of, 111. 115 strain energy of, 114 torsional strain in, 115 Cystathionine, cysteine from. 1177 Cysteine, biosynthesis of, 1177 disulfide bridges from, 1029 structure and properties of, 1018 Cytosine, electrostatic potential map of, 1104... 

The double bond can also be pictured as consisting of two equivalent orbitals, where the centers of electron density point away from the C—C axis. This is the bent-bond or banana-bond picture. Support for this view is found in Pauling, L. Theoretical Organic Chemistry, The Kekule Symposium Butterworth London, 1959, p. 2 Palke, W.E. J, Am. Chem. Soc., 1986,108, 6543. However, most of the literature of organic chemistry is written in terms of the a-7t picture, and in this book we will use it. 

Multiple bonds can be treated as ring structures with bent bonds. The distortions dealt with in the preceding paragraph must be taken into account. For example, in ethylene every C atom is surrounded tetrahedrally by four electron pairs two pairs mediate the double bond between the C atoms via two bent bonds. The tension in the bent bonds reduces the angle between them and decreases their repulsion toward the C-H bonds, and the HCH bond angle is therefore bigger than 109.5°. 

This alternative description follows from classical ideas and from a VB description utilizing hybrid orbitals. According to this description, a double bond is described as consisting of two bent bonds, sometimes called r bonds or banana bonds, formed by the overlap of... 

Figure 3.19 Bent-bond representation of the double bond in ethene. The overlap of sp3 orbitals on each carbon atom produces to bend bond (r) orbitals.

Figure 3.20 (a) The cr-ir model of the C=C double bond, (b) Taking the sum and difference of these orbitals produces two bent bond (r) orbitals. 

The bent-bond model can be expressed in orbital terms by assuming that the two components of the double bond are formed from sp3 hybrids on the carbon atoms (Figure 3.19) That this model and the ct-tt model are alternative and approximate, but equivalent, descriptions of the same total electron density distribution can be shown by converting one into the other by taking linear combinations of the orbitals, as shown in Figure 3.20. But neither form of the orbital model can predict the observed deviations from the ideal angles of 109° and 120°. 

---