CoreChem:7.4 Orbital Descriptions of Multiple Bonds
From ChemEd Collaborative
7.4 ORBITAL DESCRIPTIONS OF MULTIPLE BONDS
The association of four sp3 hybrid orbitals with an octet can be applied to multiple bonds as well as single bonds. A simple example is ethene (ethylene), C2H4. The Lewis structure for this molecule is
As shown in Fig. 7.8, we can look at the double bond as being formed by two overlaps of sp3 hybrid orbitals, one above the plane of the molecule and one below.
Since the orbitals which overlap are not pointing directly at each other, each of these bonds is referred to as a bent bond or (more frivolously) as a banana bond.
In ball-and-stick models of molecules, a double bond is usually represented by two springs or by curved sticks (shown in Fig. 7.9) joining the two atoms together. In making such a model, it is necessary to bend the springs a fair amount in order to fit them into the appropriate holes in the balls. The ability to bend or stretch is characteristic of all chemical bonds—not just those between doubly bonded atoms. Thus each atom can vibrate about its most stable position. Perhaps ball-and-spring models would be more appropriate than ball-and-stick models in all cases.
The bent-bond picture makes it easy to explain several characteristics of double bonds. As we have noted in the previous chapter, the distance between two atomic nuclei connected by a double bond is shorter than if they were connected by a single bond. In the case of carbon-carbon bonds, for example, the 
distance is 133 pm, while the C—C distance is 156 pm. This makes sense when we realize that each bent bond extends along a curved path. The distance between the ends of such a path (the C nuclei) is necessarily shorter than the path itself.
Another characteristic of double bonds is that they make it difficult to twist one end of a molecule relative to the other. This phenomenon usually is called a barrier to rotation. Such a barrier accounts for the fact that it is possible to prepare three different compounds with the formula C2H2F2. Their structures are shown in Fig. 7.9. Structure (a) is unique because both F atoms are attached to the same C atom, but (b) and (c) differ only by a 180° flip of the right-hand 
group. If there were no barrier to rotation around the double bond, structures (b) and (c) could interconvert very rapidly whenever they collided with other molecules. It would then be impossible to prepare a sample containing only type (b) molecules or only type (c) molecules.
Since they have the same molecular formula, (a), (b) and (c) are isomers. Structure (b) in which the two F atoms are on opposite sides of the double bond is called the trans isomer, while structure (c) in which two like atoms are on the same side is called the cis isomer. It is easy to explain why there is a barrier to rotation preventing the interconversion of these cis and trans isomers in terms of our bent-bond model. Rotation of one part of the molecule about the line through the C atoms will cause one of the bent-bond electron clouds to twist around the other. Unless one-half of the double bond breaks, it is impossible to twist the molecule through a very large angle.
Sigma and Pi Bonds
An alternative, somewhat more complex, description of the double bond is the sigma-pi model shown in Fig. 7.10. In this case only two of the p orbitals on each C atom are involved in the formation of hybrids. Consequently sp2 hybrids are formed, separated by an angle of 120°. Two of these hybrids from each C atom overlap with H 1s orbitals, while the third overlaps with an sp2 hybrid on the other C atom. This overlap directly between the two C atoms is called a sigma bond, and is abbreviated by the Greek letter σ.
A second carbon-carbon bond is formed by the overlap of the remaining p orbital on one C atom with that on the other. This is called a pi bond, Greek letter π. The pi bond (π bond) has two halves—one above the plane of the molecule, and the other below it. Each electron in the pi bond (π bond) spends half its time in the top part and the other half its time in the bottom part. Overall this sigma-pi picture of the double bond is reminiscent of a hot dog in a bun. The sigma bond (σ bond) corresponds to the wiener, while the pi bond corresponds to the bun on either side of it.
Although the sigma-pi picture is more complex than the bent-bond picture of the double bond, it is much used by organic chemists (those chemists interested in carbon compounds). The sigma-pi model is especially helpful in understanding what happens when visible light or other radiation is absorbed by a molecule. We will discuss this subject in some detail in Chap. 21.
In actual fact the difference between the two models of the double bond is more apparent than real. They are related to each other in much the same way as s and p orbitals are related to sp hybrids. Figure 7.11 shows two dot-density diagrams for a carbon-carbon double bond in a plane through both carbon nuclei but at right angles to the plane of the molecule. Figure 7.11a corresponds to a sigma-pi model with the sigma bond (σ bond) in color and the pi bond in gray. Figure 7.11b shows two bent bonds. Careful inspection reveals that both diagrams are dot-for-dot the same. Only the color coding of the dots is different. Thus the bent-bond and sigma-pi models of the double bond are just two different ways of dividing up the same overall electron density.
A similar situation applies to triple bonds, such as that found in a molecule of ethyne (acetylene), 
. As shown in Fig. 7.12a,we can regard this triple bond as being the result of three overlaps of sp3 hybrids on different carbon atoms forming three bent bonds. Alternatively we can regard it as being composed of one sigma bond and two pi bonds, the sigma bond being due to the overlap of an sp hybrid from each carbon atom. Again both pictures of the bond correspond to the same overall electron density, and hence both are describing the same physical reality. We can use whichever one seems more convenient for the problem under consideration.
