Energy difference, between axial and equatorial conformers

The energy difference between axial and equatorial conformations is due to steric strain caused by 1,3-diaxial interactions. The axial methyl group on Cl is too close to the axial hydrogens three carbons away on C3 and C5, resulting in 7.6 kj/mol of steric strain (Figure 4.13). 

Table 6.1 A Values Free-Energy Differences between Axial and Equatorial Conformations of Monosubstituted Cyclohexanes (kcal/mol)...

X Equilibrium constant, K Energy difference between axial and equatorial conformers, kJ mol-1 % with substituent equatorial... 

When cyclohexane is substituted by an ethynyl group, —C=CH, the energy difference between axial and equatorial conformations is only 1.7 kj (0.41 kcal)/mol. Compare the conformational equilibrium for methylcyclohexane with that for ethynylcyclohexane and... 

The energy differences between axial and equatorial conformers for 7.101 are given in the below table in comparison with those for the related cyclohexanes. Explain this observation. 

Now we can compare the relative stabilities of the cis and trans isomers of 1,3-dimethylcyclohexane. The most stable conformation of the cis isomer has both methyl groups in equatorial positions. Either conformation of the trans isomer places one methyl group in an axial position. The trans isomer is therefore higher in energy than the cis isomer by about 7.6 kJ/mol (1.8 kcal/mol), the energy difference between axial and equatorial methyl groups. Remember that the cis and trans isomers cannot interconvert, and there is no equilibrium between these isomers. 

Table 4.1 shows that an axial bromine causes 2 x 1.0 kJ/mol of steric strain. Thus, the energy difference between axial and equatorial bromocyclohexane is 2.0 kJ/mol. According to Figure 4.12, this energy difference corresponds approximately to a 75 25 ratio of more stable less stable conformed Thus, 75% of bromocyclohexane molecules are in the equatorial conformation, and 25% are in the axial conformation at any given moment. 

Figure 8 Calculated conformational energy differences between axial and equatorial methyl-cyclohexane in kcal/mol. The dashed line shows the experimental value.

Conformational analysis in connection with determinations of ffee-energy differences (AG°) between axial and equatorial conformers is still attracting interest. Schneider and Hoppen (114) discussed A values ( —AG°) and preferred orientations of axial substituents with lone pairs at heteroatoms directly attached to C (e.g., -OR, -NR2, and -N3), as well as of some other nonspherical substituents (X = -NC, -NCS, -CN, -C CH). Phenyl and vinyl groups were investigated by Eliel and Manoharan (277), who found A values of 2.87 0.09 kcal/mol for phenyl and 1.68 0.06 kcal/mol for vinyl. The latter value was essentially confirmed by Buchanan (196) the formyl group A = 0.84 0.08 kcal/mol) in axial position adopts a predominant (93%) conformation (305) with the plane of the axial CHO group nearly perpendicular to the plane of symmetry of the cyclohexyl residue (Scheme 71) (196). 

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). 

What is the energy difference between the axial and equatorial conformations of cyclohexanol (hydroxycyclohexanel ... 

The equilibrium free energy difference between XX and XXI is assumed to be quite small because the energy difference values between the equatorial and axial conformers for the methyl (AG = 6.3-7.9 kJ/mol) and the two methoxy (AG = 2.1-2.9 kJ/mol) substituents of the cyclohexane ring are almost equal645. 

For testing the ability of the force fields to reproduce the energy difference between an axial and equatorial substituent, methylcyclohexane and aminocyclohex-ane have been chosen as examples. The experimental value for the energy difference between the two chair conformers in methylcyclohexane is 1.75 kcal/mol [45]. All force fields correctly calculate the equatorial conformer to be the most stable one as displayed in Fig. 8. Again, the energy difference is strongly overestimated by CVFF and UFF1.1. 

For aminocyclohexane, the experimental value for the energy difference between the axial and equatorial conformer is 1.49 kcal/mol with the equatorial conformer as the most stable one [46]. In Fig. 9 it is shown that AMBER predicts the axial... 

The total energy differences that afford 100 1 selectivity are not great. For comparison, recall that AG for the cis and trans isomers of the dimethyl-cyclohexanes or between the axial and equatorial conformations of methyl-cyclohexane is 1,600-1,700 cal/mole. 

From this type of consideration, Beckett, Pitzer and Spitzer drew up energy relationships of the type shown in Table 2, which. gives the conformations (equatorial or axial) of the substituents, the number of n-butane skew interaction energies, x, the calculated energy differences between isomers, and finally the observed values. The observed and calculated values show the same trend, all hough the value for x, the n-butane shew interaction, again seems nearer to 1-0 kcal/mole. 

The A value, the free-energy difference between the two chair conformations with axial and equatorial alkyl groups, is widely used as a measure of steric size . For all alkyl groups there is less than 7% of the axial conformation present at ambient temperature and direct quantitative observation of the equilibrium is not possible. Historically, indirect examination of conformational equilibria in disubstituted cyclohexanes has been used to predict equilibria in monoalkyl compounds (assuming additivity of substituent effects), and reviews of early work in this field and of the pitfalls encountered have been given... 

It will be of interest to note at this point some facts regarding the cause or basis of the anomeric effect. There has been considerable discussion regarding this point. It is evident from Table 7.5 (and see also Table 7.6) that the value of the anomeric effect in the gas phase is substantial, with an energy difference between the most favorable axial and equatorial conformations of 1.42 kcal/mol. But also note that the value is reduced to about half (0.76 kcal/mol) at a dielectric constant of 20. This indicates that the anomeric effect contains a substantial contribution from electrostatics (i.e., dipole-dipole repulsions between the C-O bonds, and preferential solvation of the equatorial conformation). But they also show that a sizable portion of the effect is from something other than simple electrostatics. If the cause were simply electrostatics, the 1.42 kcal/mol number would be reduced to a sizable negative number, and while there is substantial energy reduction, it does not go nearly that far. 

Given the difference in strain energy between the axial and equatorial conformations of methylcyclohexane, we can calculate the ratio of the two conformations at equilibrium using the equation that relates the change in Gibbs free energy (AG°) for an equilibrium, the equilibrium constant (Al q), and the temperature (T) in kelvins. R, the universal gas constant, has the value 8.314 J (1.987 cal)-il -moD. ... 

Gibbs free energy differences between axial-substituted and equatorial-substituted chair conformations of cyclohexane were given in Table 2.4. 

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