Methylcyclohexane energy difference

The more stable diastereomer in each case is the one having both methyl groups equatorial. The free-energy difference favoring the diequatorial isomer is about the same for each case (about 1.9 kcal/mol) and is close to the — A(j value of the methyl group (1.8 kcal/mol). This implies that there are no important interactions present that are not also present in methylcyclohexane. This is reasonable since in each case the axial methyl group interacts only with the 3,5-diaxial hydrogens, just as in methylcyclohexane. 

CHa-ring interactions might also be expected to control the conformational preferences of dimethylcylohexanes. It might even be anticipated that the energy differences between a diequatorial conformer and a diaxial conformer will be twice the equatorial-axial energy difference in methylcyclohexane. 

The two conformations of methylcyclohexane are rapidly interconverting— they are in equilibrium. The conformer with the methyl equatorial is more stable than the conformer with the methyl axial, so the equatorial conformer is present in a larger amount in the equilibrium mixture. The axial strain energy is actually the free energy difference between the conformations and can be used to calculate the equilibrium constant for the process by using the equation A G° = —RT In K. Using the value of —1.7 kcal/mol (—7.1 kJ/mol) for AG°, the equilibrium constant is calculated to be 18 at room temperature. Therefore, at any instant, 95% of methylcyclohexane molecules have the methyl group equatorial, and only 5% have the methyl axial. 

The two chair conformations of methylcyclohexane interconvert at room temperature, so the one that is lower in energy predominates. Careful measurements have shown that the chair with the methyl group in an equatorial position is the most stable conformation. It is about 7.6 kJ/mol (1.8 kcal/mol) lower in energy than the conformation with the methyl group in an axial position. Both of these chair conformations are lower in energy than any boat conformation. We can show how the 7.6 kJ energy difference between the axial and equatorial positions arises by examining molecular models and Newman projections of the two conformations. First, make a model of methylcyclohexane and use it to follow this discussion. 

You might recall from your general chemistry course that it s possible to calculate the percentages of two isomers at equilibrium using the equation AE = -RT In K, where AE is the energy difference between isomers, R is the gas constant 18.315 J/(K moDl, T is the Kelvin temperature, and K is the equilibrium constant between isomers. For example, an energy difference of 7.6 kJ/mol means that about 95% of methylcyclohexane... 

Use SpartanBuild to construct models of axial and equatorial conformations of methylcyclohexane and (er/-butylcyclohexane. Minimize each structure, and use the energy differences to predict the relative conformational preferences of methyl and tert-butyl groups. 

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. 

Figure 3 Absolute errors (kcal/mol) for the axial-equatorial energy difference in methylcyclohexane (solid bars) and phenylcyclohexane (striped bars).

For example, in methylcyclohexane (X=CH3), the conformer with the methyl group axial is 7.3 kJ mol i higher in energy than the conformer with the methyl group equatorial. This energy difference corresponds to a 20 1 ratio of equatoriahaxial conformers at 25 °C. 

A map of the photoisomerization potential energy surface for tetraphenylethylene in alkane solvents was prepared using a fluorescence and picosecond optical calorimetry (Figure 3.4) [21]. Line shapes of the vertical and relaxed exdted-state emissions at 294 K in methylcyclohexane were obtained from the steady-state emission spec-tmm, the wavelength dependence of the time-resolved fluorescence decays, the temperature dependences of the vertical and relaxed state emission quantum yields, and of the time-resolved fluorescence decays. Analysis of these data in conjunction with values of the twisted exdted-state energy provided values for the energies of the vertical, conformationally relaxed, and twisted exdted states on the photoisomerization surface, as well as the barriers to their interconversion. The energy difference between the last two states is found to be 1.76 0.15 kcal/mol in methylcyclohexane. 

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... 

Given that two isomers of methylcyclohexane exist, our next job is to determine which is more stable. As it turns out, we can even make a reasonable guess at the magnitude of the difference in energy between the two diastereomers. First of all, notice that axial and equatorial methylcyclohexane are interconverted by a chair flip (Fig. 5.26). What turns out to be the crucial factor in creating the energy difference... 

PROBLEM 5.15 Use the data in Table 5.3 to calculate the energy difference between the possible isomers of 1-isopropyl-l-methylcyclohexane. 

WORKED PROBLEM 5.20 Use the data of Table 5.3 (p. 202) to estimate the energy difference between (a) the two chair forms of cM-l-isopropyl-2-methylcyclohexane and (b) the two chair forms of ira i-l-isopropyl-2-methylcyclopropane. 

Show by a calculation (using the formula AG° = -/iTln that a free-energy difference of 7.6 kJ moF between the axial and equatorial forms of methylcyclohexane at 25°C (with the equatorial form being more stable) does correlate with an equilibrium mixture in which the concentration of the equatorial form is approximately 95%. 

We saw in Problem 4.20 that cis-decalin is less stable than frons-decalin. Assume that the 1,3-diaxial interactions in cis-decalin are similar to those in axial methylcyclohexane [that is, one CH2 H interaction costs 3.8 kJ/mol (0.9 kcal/mol)], and calculate the magnitude of the energy difference between cis- and frans-decalin. 

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