Bent bond orbitals

FIGURE 7. Forster-Coulson-Moffltt bent bond orbitals of cyclopropane. Reprinted from E. Honegger, E. Heilbronner and A. Schmelzer, Nouv. J. Chim., 6,519 (1982) by permission of Gauthier-Villars Publishers... 

The results of the Coulson-Moffitt model have been verified many times using different energy minimization criteria for obtaining the best hybridization ratios (n and m) and determining angles between bent bond orbitals. Some results are summarized in Table i7-23-31-45- 7... 

Since ethylene oxide has a plane of symmetry bisecting the CC bond [marked by a dotted line in (81)], its MOs must be either symmetric or antisymmetric with respect to reflection in this plane. The MOs in the 7r-complex representation (78) satisfy this criterion but the bent-bond orbitals in (80) do not. We can, however, construct from the two bent-bond orbitals and 02 two linear combinations 0i + 02 02 which is... 

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... 

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. ... 

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. 

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. 

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°. 

On a more qualitative level, the bonding in the more stable isomer lb can be explained on the basis of the general molecular orbital scheme for bent (C2v) metallocenes containing 14 valence electrons, as shown in Fig. 5. The localization of three electron pairs in bonding orbitals (lal, 2 i, 2b2) is primarily responsible for the Si-Cp interaction the absence of a silicon orbital of a2 symmetry imposes the presence of a ligand-based non-bonding orbital. Structural adjustment from D5d (ferrocene type) to C2v... 

The bent structure, increases the difference in energy of non-bonding orbitals and is likely to be formed for the singlet ground configuration whereas the excited configurations are likely in a linear or nearly linear structures. 

---