[ryhan]

I have drawn the molecular orbital diagram for NO below

I have two questions, firstly my friend and I are debating as to whether a HOMO orbital can be a pi* orbital, he believes that it can not be which raised my doubts as to what the HOMO orbital actually is, I labelled what i believe to be the HOMO orbital in the picture provided.

I was also in doubts as to what the LUMO would be considered to be, would it be the empty p orbital to the right of the pi* orbital that is singly occupied or would it be the sigma* orbital that is above the two pi* orbitals. the reason I ask is because i have an itch in my brain telling me that perhaps the p orbitals are treated as one? sorry if that sounds completely ludicrous.

[Corribus]

HOMO and LUMO designations are most useful for bookkeeping in spectroscopy and electronchemistry applications (as well as molecular electronics), where the orbital energies are one of the most important determiners of physical properties. As such, degenerate orbitals are typically considered "the same" when determining what the HOMO and LUMO is.

The case you identified is kind of the chemical equivalent of the glass half empty or glass half full problem. The π* orbital in this case is certainly the highest occupied orbital but it could also be viewed as the lowest energy orbital to which an electron could be promoted/added, so in that sense it could be designated as the LUMO as well. Due to this ambiguity, half-filled orbitals are usually designated SOMO, or singly-occupied molecular orbital.

http://goldbook.iupac.org/S05765.html

[ryhan]

Thank you so much for clarifying this!