# What exactly are the frontier orbitals in diradical species like O2?

I read about frontier orbitals, namely HOMO, LUMO. But what's exactly HOMO/LUMO? I know HOMO stands for highest occupied molecular orbital and LUMO stands for lowest unoccupied molecular orbital.

But I am not getting which orbital is to be tagged as HOMO, and which as LUMO. Consider the example of $$\ce{O2}$$, highest occupied MO is $$\pi^*_\mathrm{2p}$$ and lowest unoccupied MO is also $$\pi^*_\mathrm{2p}$$. Which orbital is HOMO/LUMO? Is $$\pi_\mathrm{2p}$$ the HOMO and $$\pi^*_\mathrm{2p}$$ the LUMO? If so, why? There is a similar case with $$\ce{B2}$$.

• O2 is a bad example to consider. As for the bonding/nonbonding part: typically yes, but not always. – Ivan Neretin Mar 4 '20 at 18:19
• It's important, that these labels only work within the framework of MO theory. There they are straight forward. The orbital highest in energy which is occupied is the HOMO and it does not matter how many fold the degeneracy is. The immediately following orbital would be the LUMO, which is unfortunately not always well defined. The case of bonding and antibonding is another story, when you venture out to more than two atoms one orbital can be both. Frontier Molecular Orbital Theory is a very helpful approximation, but it is quite crude. – Martin - マーチン Mar 4 '20 at 19:07
• For O2 and other radicals, it may be wise to use the term SOMO (singly-occupied molecular orbital), instead of HOMO/LUMO – Tan Yong Boon Mar 5 '20 at 1:46
• Truthfully, there are two questions here which are not very closely related and could stand as separate Q + A's. The first is how are the HOMO/LUMO defined in the case of a diradical like O2. The second is their bonding / antibonding character. – orthocresol May 2 '20 at 16:50
• That isn't really that surprising. The concept of bonding and anti-bonding orbitals is independent from the concept of HOMO and LUMO. It does - especially in Organic Chemistry - often get mixed up and non-bonding orbitals are introduced, too, but that's too much for the comments. I'll have to think about the Question, and we should continue conversations in Chemistry Chat. – Martin - マーチン May 5 '20 at 8:59