Cyclohexanes destabilization energies

Corey and Feiner have developed a computer program (LHASA) for conformational analysis and for determining the destabilization energies (Ep) in substituted cyclohexane derivatives. In the following discussion, we will adopt their A, G and U designations and use the corresponding values for evaluating steric interactions. 

Figure 6 Incremental calculation scheme to predict destabilization energies ED in monoaxial substituted (a), 1,2-diequatorial substituted (b), and 1,3-diaxial substituted (c) cyclohexane chair conformations in the LHASA program.

Substituents larger than H prefer to be equatorial on a cyclohexane ring. Larger substituents have a smaller amount of the conformation with the substituent axial present at equilibrium than smaller substituents. Therefore, compare the axial strain energies (see Table 6.2) of the substituents. The one with the smaller axial destabilization energy will have a larger amount of the conformation with the substituent in the axial position present at equilibrium. 

The simplest isolable species that fits this description is piperazine (27) with an enthalpy of formation44 of 29.4 kJ mol-1. Can we reliably estimate this value in terms of the conceptually simpler acyclic amines, acyclic polyamines, alicyclic amines or other heterocycles One may estimate it simply as the sum of the enthalpy of formation of cyclohexane (2, n = 6) and twice the exchange energy, S5. The predicted value is 21 kJmol-1, suggestive of at least 7 kJmol-1 of strain. Do not forget that 27 should enjoy stabilization as befits its being a vie-diamine. This destabilization is twice that of piperidine (3, n = 6) as relatedly defined by its measured enthalpy of formation and that estimated by summing the enthalpy of formation of cyclohexane and 1 -85. Equivalently, disproportionation reaction 30 is found to be thermoneutral. 

Spherical polar coordinates are used for conformational representation of pyranose rings in the C-P system. Unlike the free pseudorotation of cyclopentane, the stable conformations of cyclohexane conformers are in deeper energy wells. Even simong the (less stable) equatorial (6 = 90 ) forms, pseudorotation is somewhat hindered. Substitutions of heteroatoms in the ring and additions of hydroxylic or other exocyclic substituents further stabilize or destabilize other conformers compared to cyclohexane. A conformational analysis of an iduronate ring has been reported based on variation of < ) and 0 (28), and a study of the glucopyranose ring... 

Axial strain energy (Section 6.7) The amount of destabilization caused by a group in the axial position in the chair conformation of cyclohexane. 

In monosubstituted cyclohexanes, the substituent prefers to be equatorial to an extent that is greater the larger the substituent. The substituent experiences destabilizing 1,3-diaxial interactions when axial, and so by ring inversion assumes the equatorial position (see Chapter 1). This inversion is an equilibrium process and the equilibrium ratios, of course, can be expressed as a free energy difference in the present context they are known as A values1 and these are collected in Table 6.2. 

Some perspective is necessary here. As indicated in Chapter 7, Section 4.1 on the Cope rearrangement, the free energy for formation of a cyclohexane-1,4-diyl is 50-53 kcal/mol and that for formation of two allyl radicals is roughly 57 kcal/mol. However, in the current system, the diyl is destabilized by roughly 20 kcal/mol due to the bicyclo[2.2.1]ring system that must be generated. Such a species is kinetically inaccessible due, in part, to a substantial negative entropy despite the fact that the activation enthalpy for its formation would appear to be 50-55 kcal/mol. 

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