Cyclohexane chair—twist equilibrium

At 25°C, the cyclohexane molecules mainly have the chair form. The equilibrium concentration of the isomeric twist form is —10 " mol dm On ionization, the solvent cation-radicals in the chair form are predominant. Electron transfer between the chair form of the cyclohexane cation-radicals and the chair-shaped surrounding cyclohexane (neutral) molecules is very fast, since it requires minimum reorganization energy. However, the chair-form cation-radical sometimes approaches a minor part of the neutral molecules in the twisted form. Because the twisted cyclohexane has lower IP, the twist-shaped molecules scavenge the cation-radicals in the chair form. 

A substituent on a cyclohexane ring (in the chair conformation) can occupy either an axial or an equatorial position. In many cases, the reactivity of the substituent depends on whether its position is axial or equatorial. The two possible chair conformations for methylcyclohexane are shown in Figure 3-23. These conformations are in equilibrium because they interconvert at room temperature. The boat (actually the twist boat) serves... 

A. The chair conformation is shown in 74. One consequence of a chair conformation is that a pronounced l,3-diaxial interaction exists between a /-butyl group and a hydroxyl group. This can be avoided if the ring adopts a twist-boat conformation 75. The number of molecules that exist to any extent in the twist-boat conformation is small, and 75 has the benefit of a hydrogen-bonded interaction between the two hydroxyl groups. The twist-boat conformation is ca, 6 kJ mol 1 more stable than the boat conformation. In this work, Stolow8 claims an equilibrium between 74 and 75. Another molecule known to exist in a twist-boat conformation is cyclohexane-1,4-dione (76) (see Hoffmann and Hursthouse9). 

Two drawings are provided that appear to be different chair conformations 48B and 48F. The Cl and C4 carbon atoms are marked in both structures Cl in 48B is up whereas Cl is down in 48F. Likewise, C4 is down in 48B but up in 48F. Conformations 48B and 48F are identical in structure and shape, and they are identical in energy. Twisting the bonds (pseudorotation) in cyclohexane will interconvert 48C into 48F and back again. In other words, chair conformations 48B and 48F are in equilibrium and because they are of the same energy, the equilibrium constant (K q see Chapter 7, Section 7.10.1) is unity (K q = 1). This means that there is a 50 50 mixture of 48C and 48F. The equilibrium constant (Kgq) for this molecule is defined as K q = [48F]/[48B], where [48C] and [48F] are the molar concentrations of each conformation. 

For a more complicated case, consider the structure of cyclohexane, which exists in two conformational mimima, the chair structure of D d symmetry and the twist-boat structure of D2 symmetry. The chair conformer is stabilized with respect to the twisted boat by about 25 kJ/mole in a minimal basis. Starting at the D d equilibrium structure, the TRIM method reaches a first-order saddle point of C2 symmetry in 16 iterations and one backstep, again with no symmetry constraints applied. The activation energy is 49 kJ/mole. Minimizing from this structure, we reach the D2 twist-boat conformation in 10 second-order iterations. Thus we have been able to walk between the two stable conformers of cyclohexane in an automated manner. The uphill and downhill walks both require only a modest number of iterations, considering that they started far away in the global region. 

The chair—chair interconversion of cyclohexane passes through twist boat conformations that are in equilibrium with a boat conformation. 

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