CO2 MO-scheme

If you talk about MO schemes you don't get to talk about exciting molecules. But CO₂ is interesting because a simple correlation consideration shows you things that the Lewis structure doesn't.

The bonding energy of CO₂ (1 816 kJ/mol) is 176 kJ/mol higher than twice the C=O bonding energy (820 kJ/mol) known from ketones. The reason is just another kind of delocalisation [1]. Let's see where it comes from.

What does the MO scheme look like? We have 3 sets of 4 valence orbitals and 16 valence electrons. That means (with a minimal LCAO base) there will be 12 orbitals, 8 of them populated .

CO₂ is of the D_∞h point group. But I don't think you need to know that. It basically means that you have Σ and Π symmetry races, in other words there are σ- and π-orbitals.

The first three orbitals can be considered the bonding, non-bonding and anti-bonding combination of the s-orbitals. p_z-orbitals are mixing in wherever it fits, mainly at the C in the second one and at the O's in the third one.

The next one is a (twice degenerate) bonding π-MO. Then comes a σ-MO which is mainly made of p_z-orbitals and a little bit of s. Again the bonding pσ-MO is higher in energy than the bonding pπ-MO. This is because of the s mixing in just as we had it in diatomic molecules. The HOMO is a twice degenerate non-bonding π-orbital. You can also see the unoccupied MOs with more nodal planes.

The interesting thing about CO₂ is its delocalised π-system. It has to be described as a 4-electron-3-center-MO. In both the xz- and the yz-plane there is a bonding and a non-bonding occupied π-MO which is delocalised over the whole molecule. This is totally different to allene even though it has the same Lewis structure. Allene has two localised two-center π-MOs perpendicular two each other. CO₂ has the same formal bond order as allene but the bonding MOs are much lower in energy because they are 3-centered MOs. This causes the high bonding energy in CO₂ and it is just a special case of delocalisation.

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This is the electrostatic potential. You can clearly see that the carbon atom attracts a negative charge. Besides that the LUMO is big at the C, so a nucleophilic attack will also work as far as orbitals are concerned (if we assume that this simple approach is good enough).

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[1] The reason why delocalisation causes lowering of the energy is not as simple as it seems. The first explanation would be that delocalisation means lower kinetic energy. Explain it with Heisenberg (higher position uncertainty means lower momentum uncertainty and therefore lower momentum in a stationary state) or with Schrödinger (delocalisation means less curvature). But that's only part of the truth because the virial theorem has to hold. I mentioned that a while ago.