1.3- Diaxial interaction, substituted cyclohexanes

Determination of the relative stability of many other substituted cyclohexane stereoisomers can be done in a similar manner. However, examples in which there are complications due to 1,3-diaxial interactions between groups or examples in which the rings are substituted with polar groups, whose dipoles interact, are much more complicated. Recently, computer programs have been developed that enable the most stable conformation of many molecules, cyclic and noncyclic, to be determined. These molecular mechanics calculations can provide the most stable shape of even quite complex molecules. 

Ye have chosen these substitution patterns since they must have axial substituents in any chair conformation, and 1,3 diaxial substituent-hydrogen interactions are expected to be the strongest van der Waals interaction in cyclohexane. We have excluded 1,1,2,2-tetrasubstituted cyclohexanes, since 1,2 interactions are presumably the principal factors in these molecules. 

Again, the E selectivity of the rearrangement of B depends on the tendency of the R1 substituents to occupy pseudoequatorial positions, which is enforced by bulkier groups X due to 1,3-diaxial interactions. Based on an observed quantitative relationship between ZjE ratios of Claisen rearrangement products and axial/equatorial ratios in cyclohexanes it has been suggested that ZjE ratios in Claisen products can be predicted from AG + values for axial/equatorial equilibria of substituted cyclohexanes28 ... 

Figure 6.13 Traditional explanations of equatorial preference of alkyl-substituted cyclohexanes based on the 1,3-diaxial repulsive interactions or the presence of gauche interactions.

Substitution of a methyl group at C(3) or C(4) of cyclohexene is opposed by one less 1,3-diaxial interaction than in cyclohexane. Accordingly, the preference for the equatorial orientation of a methyl group in cyclohexene is somewhat less than in cyclohexane. A value of 1 kcal/mol has been suggested for the conformational energy of the methyl group in 4-methylcyclohexene based on epoxidation rates. ... 

The more stable chair conformation of a substituted cyclohexane is the one that minimizes diaxial steric interactions and therefore has large groups equatorial. 

To predict the more stable conformer of a more highly substituted cyclohexane, the cumulative effect of placing substituents either axially or equatorially must be considered, in addition to their potential mutual 1,3-diaxial or 1,2-gauche (Section 2-9) interactions. For... 

Introducing one or more sp carbon atoms into the six-membered ring introduces more strain, since these atoms require 120 ° angles. Any addition reaction that converts the system to a saturated cyclohexane will tend to be more favorable than for a comparable acyclic system. Thus, cyclohexanone is a little more susceptible to addition reactions than acetone. However, in cyclohexanone, two 1,3-diaxial interactions are removed (7.31, 7.32), This means that for substituted cyclohexanones, the axial conformation is less unfavorable than for a related cyclohexane. As noted earlier, the difference in energy between axial and equatorial conformations for methyl cyclohexane is 7.5 kj mol", and there is only about 5 % of the axial conformer at equilibrium. For 3-methylcyclohexanone, the energy difference is only 2.9 kJ mol", and at equilibrium, there is 25 % of the axial isomer (7.33). 

In substituted cyclohexanes, the chair conformation with the most and the largest substituents equatorial is the most stable this is attributed to gauche and 1,3-diaxial interactions. The difference in energy between axial and equatorially substituted forms is dependent mainly on the size of the substituent. 

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