Do two atoms 'participating' in a single covalent bond rotate in only one direction, without rotating the entire molecule?

Question

A Biology textbook stated that, "single bonds allow the atoms they join to rotate freely about the bond axis".

This definition is not clear enough for me to answer the question, "do two atoms 'participating' in a single covalent bond rotate in only one direction, without rotating the entire molecule?", like this:

I think I have read that single bonds permit rotation, because the overlap between two atoms' orbitals, participating in a single bond, does not change with rotation in one direction, whereas, in double bonds, another pair of orbitals is shared between the two atoms, therefore, rotation of one atom, in any direction, independent of the other, would cause one of these orbital pairs to cease overlap.

So, I take it this is the reason why atoms participating in single bonds, rotate independently of one another, in a specific direction, whereas, atoms participating in double bonds rotate with one another, unitedly, regardless of the direction of rotation.

Moving on, let us say we have an atom single covalently bonded to two atoms, such as our good old friend H2O, let us assume it is linear (which it is not in reality):

H — O — H

If we rotate the single oxygen atom 'sideways' (in line with the hydrogen atoms), I would assume the single bonds between the hydrogen atoms and oxygen atom, would rotate with the oxygen atom to maintain the overlap between the two hydrogens' orbitals and the oxygen's orbitals.

In reality H2O looks more like this:

Therefore, I would assume that rotating the oxygen atom in any direction (up, down, left and right), would result in the orbitals of the hydrogen and oxygen atoms losing their overlap with one another and to maintain overlap, the single bonds would rotate with the oxygen atom.

Thus, why I think atoms in a single covalent bond can only rotate in one direction, without rotating the entire molecule.

Answer 1

Rather than thinking of rotation of the atoms, it makes more sense to think of a rotation of the groups that are attached to the atom - similar to the first figure you showed. This phenomenon is called internal rotation and in principle is not completely free. When you take an ethane molecule and start to rotate the two methyl groups around the connecting CC bond, you will find that the potential energy that you have to overcome is sinusoidal with maxima and minima corresponding to the eclipsed and staggered positions, respectively (see the figure below). You can calculate this profile with QM software, but qualitatively, it emerges from the interplay between Pauli repulsion and orbital overlap. For single bonds, the barrier is on the order of a few kcol/mol, much less than the thermal energy typically available to a molecule at room temperature and the two groups can more or less rotate freely. For double bonds, the barriers are so high that the molecule cannot overcome the potential hill and no rotation is observed.

Note that, in terms of degrees of freedom, internal rotation corresponds to a vibration mode rather than a rotation because the atoms of the molecule move with respect to each other.

Figure source.

Answer 2

Assuming that the molecule is stable and well-behaved, molecular rotations happen along single covalent bonds, in whatever direction, because that is the only thing that the molecule has enough energy to do.

Silly example: The energy cost of turning your car wheel to the left or the right isn't too bad, but attempting to rotate it in other directions (say upwards or downwards) would require more strength than most people could muster. Also, it would wreck your car. In the same way, a molecule ripping itself apart spontaneously is certainly possible, however, the likelihood is incredibly small.

Lastly, in a void, the rotation of the entire molecule has no effect on the overall energy of the molecule and therefore we don't typically care about it too much.