# Rationale for assigning antibonding MOs

How do people decide if a molecular orbital (MO) is bonding or antibonding? From Wikipedia article on antibonding MO:

[...] if the antibonding interactions outnumber the bonding interactions, the molecular orbital is said to be antibonding

and vice versa.

How do we define what an "antibonding interaction" is for cyclic molecules? Does one nodal plane count as 1 or 2 antibonding interactions? For example, the π2 molecular orbital of benzene may have 1 nodal plane, but how many antibonding interactions would that MO have?

Similarly, how do we define "bonding interactions" for cyclic molecules?

## 1 Answer

There are a couple ways that people define bonding and antibonding orbitals. One of the simplest is to just look at the energy of the MOs formed compared to the AOs they were formed from: if the MO is lower in energy, it is bonding and if the MO is higher in energy, it is antibonding.

Like I said, this way of doing thing is relatively simplistic, but you will see it pretty commonly in textbooks on the matter. The method of course isn't perfect, in particular because it essentially assumes that all local bonds are affected equally by a particular orbital.

We can see this is not the case by looking at the $\pi_2$ orbital you show. While the orbital is listed as bonding, the interactions of the p-orbitals where a positive lobe is next to a negative love will locally decrease the bonding between those two atoms (ie the MO is antibonding with respect to those local bonds).

So, for a simple first approximation, you can use the energy of the MO compared to the AO, but for a more complete sense, you should look at the symmetry of the MO and see what effect it has on a given local bond.

In terms of the ordering of the MOs themselves, assuming you don't have experimental way to determine the ordering like ionization energies, you can heuristically use an approach like you suggest where you compare the number of nodes and less nodes will mean lower in energy, more nodes will be higher.

In terms of comparing to the original AOs, it can be tricky without experimental data, however there are again general qualitative ways of ordering the MOs with respect to their original AOs. For example, if you have 2 MOs formed from two overlapping AOs, one will have to be higher in energy and the other will have to be lower.

When you get more orbitals overlapping, the arrangements can vary, but the sum of the energies has to remain the same. So, for example, if you have 3 overlapping AOs, you could form 2 bonding and 1 antibonding MOs or vis versa so long as their combined energy is the same as before.

Beyond this, you really just have to read up on MO theory to get a sense of how qualitative energy ordering is done. There is a lot more to it than what I've written (or could write) and it's probably better to build your understanding of the theory from the ground up rather than getting it piecemeal.

• Hi Tyberius, I'm not sure what you mean by "look(ing) at the symmetry of the MO and see what effect it has on a given local bond". – Jonathan Smith Aug 27 '17 at 2:23
• Also, if we were to "examine the energy of the MOs formed compared to the AOs they were formed from", and compare their relative energies in order to reach a conclusion whether the MO is bonding or antibonding, this begs the question: how do we know if a particular MO is higher or lower in energy compared to the AOs it was formed from? – Jonathan Smith Aug 27 '17 at 2:27
• @JonathanSmith So that is what I'm referring to in the 2nd paragraph of my answer when I talk about the π2 orbital. If you look at the interaction between atoms that have a positive lobe next to a negative lobe, that is an antibonding interaction because those atoms won't be drawn towards each other. – Tyberius Mar 5 '18 at 20:25