By James Ashenhurst
The Pi Molecular Orbitals of Cyclobutadiene
Last updated: March 2nd, 2019
Previously, we’ve seen what the molecular orbitals of benzene look like, and that the fact that they are partially duplexed (or to use the proper nomenclature, “degenerate“) helps to explain benzene’s unusual stability.
Let’s flip the coin. What about cyclobutadiene, a molecule we usually class as antiaromatic. Why is it so unusually unstable?
Again, examining the pi molecular orbitals will give us some useful clues.
Today, let’s build up the orbitals of cyclobutadiene using the principles we’ve discussed in previous posts and see if we can gain some useful insights.
Cyclobutadiene has a pi system comprised of 4 individual atomic p orbitals and thus should have a total of 4 pi molecular orbitals.
Following our “apartment building” analogy from last time, the lowest-energy molecular orbital (the “ground floor” of cyclobutadiene, if you will) should have all phases of the p-orbitals aligned and zero nodal planes, like this:
Conversely, the highest-energy pi orbitals (the “penthouse”) will have all phases alternating, and thus have two nodal planes. (As we said last time, the “penthouse” is not exactly desirable real estate for electrons)
That leaves us with the intermediate pi orbitals, which each have a single nodal plane. As with benzene, there are two ways to place a single nodal plane on cyclobutadiene, either through the bonds, or through the atoms:
That gives us our four molecular orbitals. Now lets populate them with the “tenants”: the pi electrons.
Cyclobutadiene has a total of 4 pi electrons. So ranking all the pi molecular orbitals by energy, and populating the orbitals according to Hunds rule, we get the following picture:
Can you see why cyclobutadiene might be unstable?
- First, the highest-occupied molecular orbitals of cyclobutadiene are non-bonding orbitals, intermediate in energy between the lowest (π1, bonding) and highest (π4, antibonding) energy orbitals. “Non-bonding” implies that filling these orbitals with electrons does not result in any stabilization of the molecule.
- Second, note that each of the non-bonding orbitals are singly occupied. Therefore this orbital picture predicts that cyclobutadiene should have a diradical nature. We’re used to thinking of free-radicals as highly reactive intermediates… so you can imagine that a species containing two free radicals is even more reactive! [Note ]
The bottom line here is that the pi molecular orbital picture of cyclobutadiene is in agreement with our observations that cyclobutadiene is unusually unstable. (As previously noted, cyclobutadiene has only ever been isolated as a “matrix-isolated species” – that is, a species frozen in an inert gas at extremely low temperatures. Warming to a balmy –80° results in self-destruction. Note )
Hopefully these two posts have helped to show that molecular orbital diagrams can provide extremely useful clues about molecular stability!
In the next post we’ll cover a very convenient short-cut that will help us quickly draw molecular orbital diagrams in seconds (yes, really!) called Frost Circles. Or, more blandly, the Polygon method.
1. More advanced calculations, far beyond what we will discuss, predict that cyclobutadiene distorts to a rectangular shape which results in the two singly-occupied orbitals resolving into two orbitals of slightly different energy, one doubly-occupied and the other empty. The bond lengths of cyclobutadiene have been measured, confirming the rectangular shape.
Note that the pi electrons are not “delocalized” like they are in benzene.
3. If benzene is about 36 kcal/mol more stable than (theoretical) cyclohexatriene, exactly how unstable is cyclobutadiene? The negative resonance energy of cyclobutadiene is calculated to be –54.7 kcal/mol, relative to 1,3-butadiene. In addition, 30.7 kcal/mol of strain is found, giving a total destabilization of 85.4 kcal/mol. [Ref]