Axial bonds in cyclohexane

Equatorial bonds Figure 9.8. Equatorial and axial bonds in cyclohexane. 

Larson and Cremer have explored another approach to dissecting BDE into inherent and RSE effects4 There is a relationship between C-H BDE and the vibrational frequencies of the bonds Furthermore, the vibrations can be determined for C—H bonds in speeific conformations, for example, the equatorial and axial bonds in cyclohexanes or the anti and gauche bonds in amines. 

The chemical shift of a nucleus depends in part on its spatial position in relation to a bond or a bonding system. The knowledge of such anisotropic effects is useful in structure elucidation. An example of the anisotropic effect would be the fact that axial nuclei in cyclohexane almost always show smaller H shifts than equatorial nuclei on the same C atom (illustrated in the solutions to problems 37, 47, 48, 50 and 51). The y-effect also contributes to the corresponding behaviour of C nuclei (see Section 2.3.4). 

This problem is primarily an exercise in correctly locating equatorial and axial positions in cyclohexane rings that are joined together into a steroid skeleton. Parts (a) through (e) are concerned with positions 1, 4, 7, 11, and 12 in that order. The following diagram shows the orientation of axial and equatorial bonds at each of those positions. 

The coupling constants and calculated bond lengths for axial and equatorial C-H bonds in cyclohexane (Scheme 2.10) have been interpreted as a result of the superior electron-donating capacity of C-H bonds compared with C-C bonds (see, e.g., Ref. [38] calculations (Table 2.1) do not support this idea). Thus, the axial C-H bonds are weaker and longer than equatorial C-H bonds because each of the former undergoes hyperconjugation with two axial C-H bonds. 

In contrast with the striking anisotropic effects of circulating v electrons, the a electrons of a C—C bond produce a small effect. For example, the axis of the C—C bond in cyclohexane is the axis of the deshielding cone (Figure 3.24). The observation that an equatorial proton is consistently found further to the left by 0.1-0.7 ppm than the axial proton on the same carbon atom in a rigid six-membered ring can thus be rationalized. The axial and equatorial protons on Q are oriented similarly with respect to C,—C2 and C,—C6, but the equatorial proton is within the deshielding cone of the C2—C3 bond (and C.-Q). 

Nearly all cyclohexanes are most stable in chair conformations. In the chair, all the carbon-carbon bonds are staggered, and any two adjacent carbon atoms have axial bonds in an anti-coplanar conformation, ideally oriented for the E2 reaction. (As drawn in the following figure, the axial bonds are vertical.) On any two adjacent carbon atoms, one has its axial bond pointing up and the other has its axial bond pointing down. These two bonds are trans to each other, and we refer to their geometry as trans-diaxial. 

The bonds in cyclohexane occupy two kinds of position, six hydrogens he in the plane and six hydrogens lie either above or below the plane. Those that are in the plane of the ring lie in the equatof of it, and are called the equatorial bonds. Those bonds that are above or below are pointed along the axis perpendicular to the plane and are called axial bonds. 

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