A Simple Molecular Orbital Treatment of the Barrier to Internal Rotation in the Ethane Molecule

The origin of the barrier to internal rotation in the ethane molecule is explored in terms of elementary molecular orbital (MO) considerations. Emphasis is placed on the antibonding effect, i.e. the result that an antibonding MO is more destabilized than its bonding counterpart is stabilized, relative to the parent atomic orbitals (AOs). It is shown that, in the case of two equivalent AOs, this effect is approximately proportional to the square of the overlap integral. By constructing the ethane Mos from those of two methyl fragments, it is shown that the most important orbital energy changes consequent upon rotation about the C-C bond can be expressed in terms of the antibonding effect arising from the filled twofold-degenerate p-bonding and -antibonding MOs. This can be reduced to the dependence on the rotation angle of the vicinal H-H overlap integrals, which are calculated explicitly, showing that the antibonding effect is minimised in the staggered conformation.