# Orbital size of Carbon and Oxygen in Methanal

I was given an introductory question into Carbonyl chemistry today and I wanted to ask a question about Methanal.

The following picture was shown below of Methanal:

and I noted that the orbital sizes differed for both Carbon and Oxygen in the top and bottom diagrams. I thought one of these diagrams must be wrong.

I then knew that as Oxygen has more protons than Carbon, then its atomic radius is smaller, meaning the orbital size must be smaller too, so I thought that the bottom diagram represented the size of the p orbitals better both for anti bonding and bonding.

Is the diagram for $$\pi$$ bonding drawn correctly in terms of orbital size?

• You hardly ever need to worry about the shape of the bonding orbital. The HOMO is probably the one (or linear combination of the ones) that contains the lone pairs. The LUMO below does have the right size since the two factors are in the same direction. Of course the real molecular orbitals span the whole molecule, so this is just a simplified representation of what two specific contributions might look like. For example, see: quora.com/… – Zhe Apr 18 at 17:32

The orbital size in the picture shows the coefficient in the linear combination of atomic orbitals, i.e the pi bonding MO has a larger contribution from the oxygen atomic orbital, and the pi anti-bonding MO has a larger contribution from the carbon atomic orbital.

Here is another picture for a different molecule where they use the same convention, but also show the coefficients explicitly (source):

Is the diagram for π bonding drawn correctly in terms of orbital size?

An orbital is not a "thing" so it does not have a size. It is a 3-dimensional function. The picture just shows the symmetry of that function and the node (where it is zero). For a slightly more realistic depiction, you can check out molcalc.

I’ll try to keep this explanation simple- if you want a more comprehensive example, please consult books like Orbital Interactions in Chemistry.

Oxygen is more electronegative, and hence the Oxygen p orbitals experience a greater effective nuclear charge and have a lower orbital potential energy than the carbon p orbitals. As such, this is effectively analogous to the bonding situation in compounds like HF or LiH - the bonding orbital has a greater contribution from the lower-energy atomic orbital (Oxygen) while the antibonding orbital has a greater contribution from the higher-energy atomic orbital (carbon).

In the specific context of your question, in the case of such qualitative MO diagrams the individual AOs are assumed to be of the same size, and the size of the AOs in the MO “cartoon” simply represents the respective contributions. That’s why the MO diagram in your question is drawn as shown.

This is all a bit hand-wavy, so I suggest you read up on “electronegativity perturbation” if you’re interested.