Cyclohexane gauche interactions

A torsion angle of 60 between C-C bonds represents a gauche interaction and so an axial methyl substituents experiences two gauche interactions with the cyclohexane ring whereas the equatorial methyl substituents experiences none. Due to this, the latter chair conformation is preferred and about 95 per cent of methylcyclohexane molecules are in this conformation at any point of time, compared to 5 per cent in the other conformation. 

What is the reason for this apparent discrepancy It is a solvent effect. In aqueous solution (Figure 9.6), the OH group at the anomeric C atom of the glucose becomes so voluminous due to hydration that it strives for the position in which the steric interactions are as weak as possible. Thus, it moves into the equatorial position—with a AG° value of approximately -1.6 kcal/mol—to avoid a gauche interaction with the six-membered ring skeleton. (Remember that axially oriented substituents on the chair conformer of cyclohexane are subject to two gauche interactions with the two next-to-nearest C. —C bonds. They therefore have a... 

The increment of energy due to the skew-butane or gauche interaction is variously assigned values of about 0.7 to 1.2 kcal/mole. The value used throughout this contribution is 1.0 kcal. This is a very important parameter because, as will be seen, it permits conformational analysis not only of the cyclohexanes but of the decalins and methyldecalins as well. 

The validity of the computed equilibria is substantiated by the experimental cis/trans ratios for the three positional isomers of dimethyl-cyclohexane, measured at ambient temperature by Roebuck and Evering (42) and at 175° by Boelhouwer et al. (43). The experimental results, presented in Table II, are in excellent agreement with theoretical equilibria that were computed on the basis of 1.0 kcal per gauche interaction. 

The stable chair-chair conformation of gauche interactions compared to one in the chair form of frans-1,2-dimethyl-cyclohexane and three in the chair conformations of cis-decalin and cis-l,2-dimethylcyclohexane. The various factors affecting cis-trans equilibrium of the decalins are given in Table III. Both isomers have an... 

Consider tmns-1,2-di methylcyclohexane 6. In the conformer 6a, the two equatorial methyl groups are gauche to each other, which will raise the energy by 0.9 kcal mol-1. In the conformer 6b, the product of chair inversion of 6a, each axial methyl group is engaged in two butane gauche interactions. This will raise the energy by 2 x (2 x 0.9) = 3.6 kcal mol-1. The conformer 6a, therefore, is more stable than 6b by 3.6 - 0.9 = 2.7 kcal mol-1. Thus, trans- 1,2-disubstituted cyclohexane must prefer the conformer in which both the substituents occupy equatorial positions. 

Each conformer of cis-1,4-dimethylcyclohexane, 11a or lib, has one methyl group axial and the other equatorial. The axial methyl group is engaged in two gauche interactions as shown, raising the energy of the system by 2 x 0.9 =1.8 kcal mol-1. In comparison, the more stable conformer of tram-1.4-dimethyl-cyclohexane. 10b, is more stable than cis -1,4-dimethyIcycloh ex an e 11 by 1.8 kcal mol-1. 

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.

Schleyer, P. v. R. Williams, J. E. Blanchard, K.R.J.Am. Chem. Soc. 1970,92,2377concluded that the gauche interactions in the cyclohexane skeleton are not comparable to those of gauche butane because the nonbonded hydrogen-hydrogen interactions are minimized in cyclohexane. 

The decalin (bicyclo[4.4.0]decane) ring system provides another important system for study of conformational effects in cyclohexane rings. The energy difference can be analyzed by noting that the cis isomer has three more gaucfce-butane interactions than does the irons isomer. Assigning a value of 0.8 kcal/mol to the gauche interaction would predict an enthalpy difference of 2.4 kcal/mol between the two isomers. Equilibration of the cis and irons isomers shows that the irons isomer is favored by about 2.7-3.0 kcal/mol. 

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