Carbocycles

Carbocycles are organic molecules that contain one or more rings, chains of atoms that loop back on themselves. The simplest cyclic molecules are the cycloalkanes, which have molecular formulas C_nH₂n. Cycloalkanes are named after their corresponding linear alkanes with the prefix -cyclo. Cycloalkanes can be drawn as regular polygons using line-angle representations.

Substituted cycloalkanes are named similarly to linear alkanes, as the following examples illustrate. The positions on the ring are numbered in such a way that substituents receive the lowest possible numberings. Since all positions on the ring are equivalent except for the attachment of substituents, numbers are only indicated in the name of the compound when more than one substituent is present.

Like alkenes, cycloalkanes are capable of cis-trans isomerism. A cycloalkane has two distinct faces, and any substituent on a ring lies toward one of two faces. When two substituents on a ring point to the same face, they are cis. When the two substituents point to opposite faces, they are trans. Like the cases of cis-trans isomerism in alkenes, these isomers have the same atomic connectivities but differ in their spatial arrangement of atoms. Hence, they are stereoisomers.

The heat of formation of a molecule is the energy change that occurs when a molecule is assembled from its component atoms. Heats of formations typically have negative signs, indicating that the molecule is more stable than its component atoms. First, consider the heats of formations of the n-alkanes, which advance regularly by -4.95 kcal/mol for each increase in chain length. Since each unbranched alkane differs from the next in the series by a methylene (-CH₂-) group, we infer that - 4.95 is the heat of formation associated with each methylene group. The cycloalkanes, which have molecular formulas of (CH₂)_n, consist of methylene groups arranged in a ring. Hence we might expect the heat of formation of any n carbon cycloalkane to be n times -4.95.

In every case except cyclohexane, the actual heat of formation is less negative than the predicted value. That is, cycloalkanes are less stable than their straight-chain counterparts due to ring strain, unfavorable energetics caused by ring formation. Rings strains can be calculated from the difference between actual and expected heats of formation. Both cyclopropane and cyclobutane have large ring strains of 27 kcal/mol and 26 kcal/mol, respectively. Cyclopentane has much less ring strain at 6.5 kcal/mol. Cyclohexane is the only cycloalkane that has no ring strain. Cycloheptane and higher cycloalkanes tend to have modest amounts of ring strain (although strain diminishes for very large rings, where the length of the ring allows atoms to arrange themselves in low-energy conformations).

Bridged ring systems are particularly rigid due to ring strain. In a bridged system, bridgehead carbons are the points at which the two cycles meet. These carbons are nearly always singly bonded, or sp³-hybridized. Forming a π bond would require sp² hybridization and a trigonal planar geometry that would be terribly strained in the context of the ring constraints. This concept is summarized by Bredt's Rule: No bridgehead alkenes.

One early explanation given for the relative lack of ring strain in cyclopentane and cyclohexane invokes the geometry of sp³-hybridized carbons. The natural bond angle at sp³-hybridized carbons is 109.5 degrees. However, in order to accommodate the geometry of cycloalkanes these bond angles are forced into other angles, resulting in angle strain. For instance, the large amount of ring strain in cyclopropane can be explain by the large deviance of the required 60 degree bond angle from 109.5. Instead of forming direct head-on overlaps, the C-C σ bonds of cyclopropane are bent out of linearity, resulting in less stable interactions.

While this simple model of angle strain explains some of the trends in ring strain, it fails to address others. For instance, the 90 degree bond angles of cyclobutane are much closer to 109.5 than the 60 degree bond angles of cyclopropane, yet its ring strain is smaller by a mere 1 kcal/mol. Most important of all, however, is that this model predicts that cyclopentane, with bond angles of 108 degrees, should be the most stable of the cycloalkanes. This is not the case. In fact, cyclohexane is the most stable of the series with no ring strain. As we'll see in the next section, the dilemma of cyclohexane can be resolved using conformational analysis.