[chiralSPO (OP)]

I teach chemistry at both the undergraduate and graduate levels (and general public level as well occasionally), so I am no stranger to explaining the same phenomena in different ways that are not necessarily in good agreement (undergraduate level often being oversimplified dramatically for ease of understanding). But every so often I find myself trying to figure out whether undergraduate "facts" are valid and hold up to scrutiny of more complex models... this is one of those times.

Undergraduate level understanding of single and multiple bonds:
• A single bond is always a sigma bond, while a double bond is one sigma bond and one pi bond, and a triple bond is one sigma bond and two pi bonds.
• This explains why single bonds are free to rotate while double bonds cannot (rotating a bond with pi symmetry would require breaking the bond.)

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Advanced level:
• We have to look at the molecular orbitals to accurately describe the electronic structure.
• For example, the molecular orbital diagram of B₂ predicts a Bond Order of 1 (4 electrons in bonding orbitals and 2 electrons in antibonding orbitals) And because the filled sigma bonding and filled sigma antibonding orbitals cancel, and the unbalanced bonding electrons are in pi bonding orbitals, the single bond must be a pi bond.


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What I'm struggling with now, is trying to think if there is some actual experimentally verifiable consequence of this (like restricted bond rotation). Unfortunately, bond rotation is meaningless for the linear B₂ molecule, but perhaps someone who hasn't been overthinking this can suggest another molecule that appears to have a single bond with pi symmetry, and would have other bonds that could be used to define rotations.

Other probing questions welcome--anything to break myself out of this current and useless perspective... thanks!

[Kryptid]

I think, in the case of S₂N₂, a single pi bond stretching across the ring is a component of the resonance structure. Look at the bottom two resonance contributors: https://ars.els-cdn.com/content/image/1-s2.0-S0010854506002669-sc6.gif

[chiralSPO (OP)]

Interesting... the plot thickens... thanks Kryptid!

[JazzHandsMafia]

I am not sure if I parsed the question properly, but it seems to be matter of atomic/molecular orbital theory.

However, the sigma vs. pi bonding bit can get a bit mixed up; this is because students tend to get turned around with the terminology.
The sigma  bonds of course do not actually correspond to s orbitals, but only to the geometry of the bond. Thus, pi orbitals can be used in both sigma bonds and pi bonds between atoms.

Let us now address symmetry. Remember that molecular orbitals are either bonding , non-bonding, or anti-bonding. Either bonding or anti-bonding can be used to hold electrons, but anti-bonding orbitals are the result of a waveform that contributes no electron density between the two atoms: A nodal plane.

This difference in energy, and therefore stability, is key.
The bond energy is tied to the bonding orbitals, and gives us an approach to qualitatively assess them.

The branch of chemistry that comes to mind is photochemistry.
Most courses will completely ignore this field. Probably because most professors dislike dealing with radical chemistry.

Of particular interest is photoisomerization. Light is absorbed (say, by the electrons in the pi-bond of a molecule). The excited electrons move out of the ground state and into a new orbital; perhaps anti-bonding orbitals.
 
This changes the electronic map of the molecule, and opens a brief window for rotation to occur around the bond. When the electrons drop back into ground configuration, some fraction of the molecules being excited will have changed isomer configuration (say, from trans- to -cis or the reverse).

In fact, this pathway is the key to human vision; the photoisomerisation of a cis bond in retinal to the corresponding trans form is the initial key to a major signaling pathway.

In the above picture, note how some wavelength of light is absorbed, changing isomer configuration or retinal.

For a nice example molecule smaller than retinal,
I recommend 1,2-Dichloroethene ; CAS 156-59-2 (cis, or Z isomer)
156-60-5 (trans, or E isomer)