Acyclic Systems—Torsional Potential Surfaces

Left Torsional itinerary for ethane, showing the three-fold nature of the barrier and the eclipsed and staggered forms. Right Torsional itinerary for butane. The anti-gauche interconversion crosses a barrier of ca. 3.4 kcal / mol, while the direct gauche-gauche barrier is 5-6 kcal/mol. 

The staggered form of ethane is more stable than the eclipsed. The energy difference between the two—the rotation barrier, E ot—is 3 kcal/mol. Thus, rotation about even the simplest C-C bond is not free . Instead, it is hindered by a barrier of 3 kcal / mol. However, the barrier is so small that the rotations are very fast, as shown in the next Going Deeper highlight. 

Remember, the eclipsed form is a transition state the staggered conformation is the only stable form. Interconversion between one staggered form and another is a torsional motion, where the methyls twist relative to each other. When the torsional vibration achieves enough energy to traverse the transition state, the staggered conformers interconvert. 

What does it physically mean when we state that the staggered form is 3 kcal/mol 

How Big is 3 kcal/mol As an activation barrier, 3 kcal/mol is quite small. Let s calculate how fast the bond in ethane is rotating. As in the final Going Deeper highlight of Section 2.1.3, we use the Arrhenius equation with an A value of 10 . The rate constant at 298 K for a 3 kcal / mol barrier is 6X10 s . This corresponds to a half-life of 10 picoseconds. Rotation about simple C-C bonds is extremely rapid  

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We also covered the fact that molecular structures are dynamic, not static. Multiple degrees of vibrational freedom exist—namely, stretches, bends, torsions, etc. Each is quantized and the motions are constrained by a potential surface. For most organic chemistry purposes, only the quantization of bond stretches becomes relevant. The torsional degrees of freedom, when possessing enough energy, lead to the interconversion of conformers, both in acyclic and cyclic systems. The study of these interconversions is called conformational analysis. 

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