Rotation, free or restricted, is a property of single bonds. Because the electron density in a sigma bond is cylindrically symmetrical, it is not altered by rotation around the bond. The situation is dramatically different in the case of double bonds. Here, in addition to the sigma bond, there is a pi bond, and the electron density in the pi bond is concentrated above and below the sigma bonded framework. Rotation around a double bond twists the p orbitals out of alignment, thereby reducing orbital overlap and raising the potential energy of the pi electrons. Figure 1 illustrates this idea.
Sorry, That's a No No
In order to rotate around the double bond in structure 1, it is necessary to break the pi bond. In structure 2 the p orbitals are perpendicular (orthogonal) to each other and their overlap is zero. Typical C-C pi bond strengths are approximately 65 kcal/mol. In other words, the potential energy barrier to rotation about a double bond in alkenes is at least 65 kcal/mol. Recall from our discussion of Molecular Motions that the barrier to rotation around C-C bonds in alkanes is approximately 3-5 kcal/mol. Since the thermal energy available at room temperature is significantly less than 65 kcal/mol, rotation around a double bond does not occur. The lack of rotation gives rise to the possibility of geometric isomers.
The simplest hydrocarbon in which geometric isomerism is possible has the molecular formula C4H8. One isomer is called cis-2-butene while the other is called trans-2-butene. Figure 2 shows the structures of these two compounds.
Geometric Isomers Exemplified
Notice that geometric isomers have different physical properties. In fact, geometric isomers are diastereomers, i.e. they are stereoisomers that are not enantiomers. The prefixes cis and trans refer to the relative dispositions of the substituents attached to the doubly bonded carbon atoms. In the cis diastereomer the hydrogen atom attached to one carbon is on the same side of the double bond as the hydrogen attached to the other carbon. In the trans stereoisomer they are on opposite sides.
Exercise 1 What is the name of the following compound? (Hint: It helps to like old time cowboy movies.)
Exercise 2 Draw complete Lewis structures for each of the following formulas. Indicate whether or not geometic isomers are possible.
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It's not always the case that there are two identical groups attached to the doubly bonded carbon atoms. In such instances the meaning of cis and trans becomes murky if not meaningless. In order to identify diastereomeric alkenes unambiguously, chemists have devised a convention based upon the Cahn-Ingold-Prelog rules. The convention works as follows:
- Prioritize the two groups attached to one of the doubly bonded carbon atoms according to the Cahn-Ingold-Prelog rules.
- Prioritize the two groups attached to the other doubly bonded carbon atom according to the Cahn-Ingold-Prelog rules.
- The stereoisomer in which the two groups with the same priority are on the same side of the double bond is designated with the prefix "Z".
- The stereoisomer in which the two groups with the same priority are on the opposite sides of the double bond is designated with the prefix "E".
Figure 3 demonstrates the application of these rules to specify the two diastereomers of 1-fluoro-2-chloropropene.
Exercise 3 Select the correct stereochemistry for each of the following alkenes.
Some Relevant Examples
An interesting example of the importance of geometric isomerism is found in the structures of fats and oils. Unsaturated fats and oils contain double bonds. Figure 4 shows the structure of a typical "polyunsaturated" fat that might be obtained from an oil such as corn oil. The word polyunsaturated simply means that the fat or oil contains more than one double bond. What's interesting about this structure is that all the double bonds have the Z-configuration. This bit of information offers some insight into the nature of fatty acid biosynthesis since the Z-configuration is inherently less stable than the E arrangement.
Now You're Cookin'
In contrast to the structure shown in Figure 4, most of the double bonds in vitamin A have the E-configuration as shown in Figure 5.
Your RDA of Vitamin A
Exercise 4 What is the molecular formula of vitamin A? What is the index of hydrogen deficiency of vitamin A? What is the degree of unsaturation of vitamin A?
Isomerization of Alkenes
Although the pi bond prevents rotation about a double bond, it is possible to interconvert cis and trans isomers photochemically. To understand how this happens, consider the changes in the molecular orbital diagram of the pi bond of an alkene shown in Figure 6.
A Pi Bond: HOMO and LUMO
Irradiation of a cis-alkene with light of the appropriate wavelength excites an electron from the p to the p* orbital. This breaks the pi bond. If rotation around the sigma bond occurs very fast, the substituent attached to one of the carbons will end up on the opposite side of the pi bond when the excited electron returns to its lower energy state and the pi bond is reformed. The formation of the trans-isomer is favored because it is more stable.
The photochemical isomerization of cis alkenes to their trans diastereomers plays an important role in the chemistry of vision. Figure 7 illustrates the isomerization of 11-cis-retinal to the trans -isomer. This transformation is a complex, multi-step process that occurs in your eye under the control of an enzyme called opsin.
Oh Say Can You See