Many molecules can rotate internally around one or more of their bonds so that during a full 360 degrees rotation, they will change between unstable and relatively stable conformations. Ethane is the textbook example of a molecule exhibiting such behaviour: as one of its two methyl (CH3) groups rotates once around the central carbon-carbon bond, the molecule will alternate three times between an unstable eclipsed conformation and the preferred staggered conformation. This structural preference is usually attributed to steric effects; that is, while ethane rotates towards an eclipsed structure, the electrons in C-H bonds on the different C atoms are drawing closer to each other and therefore experience increased repulsion, introducing a rotation barrier that destabilizes the eclipsed structure. Stabilization of the staggered structure through rotation-induced weakening of the central C-C bond and hyperconjugation has been considered to be involved, but evaluation of the contributions of these effects to ethane's internal rotation barrier and conformational preference remains difficult. Here we report a series of ethane structure optimizations, where successive removal of different interactions indicates that ethane's staggered conformation is the result of preferential stabilization through hyperconjugation. Removal of hyperconjugation interactions yields the eclipsed structure as the preferred conformation, whereas repulsive forces, either present or absent, have no influence on the preference for a staggered conformation.
Natural bond orbital deletion calculations show that whereas the gauche preference arises from vicinal hyperconjugative interaction between anti C-H bonds and C-F* antibonds, the cis C-H/C-F* interactions are substantial (approximately 25% of the anti interaction). The established significantly >60 degrees FCCF dihedral angle for the equilibrium conformer can then be rationalized in terms of the hyperconjugation model alone by taking into account both anti interactions that maximize near 60 degrees and the smaller cis interactions that maximize at a much larger dihedral angle. This explanation does not invoke repulsive forces to rationalize the 72 degrees equilibrium conformer angle. The relative minimum energy for the trans conformer is the consequence of a balance between decreasing hyperconjugative stabilization and decreasing steric destabilization as the FCCF torsional angle approaches 180 degrees . The torsional coordinate is predicted to be strongly contaminated by CCF bending, with the result that approximately half of the trans --> gauche stabilization energy stems from mode coupling.
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