Why Use MO Theory?

While Lewis structures and Valence Bond Theory are useful, they oversimplify chemical bonding and can’t explain everything. Molecular Orbital (MO) Theory is more complex, but it can account for cases that simpler models can’t explain.

Consider the [H₂]⁺ ion, for example. Lewis structures can’t handle a “half bond.” How do you draw a Lewis structure for a bond with just one electron? MO theory shows that bonding is about overlapping wavefunctions, which is not always easy to show on a Lewis Structure. A single electron can still form a bond, even if it’s weaker.

Or consider oxygen, O₂. Lewis structures predict it should be diamagnetic (no unpaired electrons), yet liquid oxygen is attracted to magnets (it’s paramagnetic). MO theory explains this by showing that O₂ has unpaired electrons in its antibonding orbitals. 

Orbitals as Waves

MO theory treats electrons as waves. When atoms approach one another, their atomic orbitals interact, just like how waves can interfere constructively or destructively.

Constructive interference increases electron density between nuclei which creates a bonding molecular orbital. This stabilizes the molecule, like a glue holding the atoms together. When this overlap occurs along the internuclear axis, it forms a σ (sigma) bond.

Destructive interference creates a node (a region of zero electron density) and leads to an antibonding orbital, denoted σ*. Electrons in this orbital reduce the bond’s strength and can even prevent bonding altogether.

For every bonding orbital formed, there is a corresponding antibonding orbital. Bonding orbitals are lower in energy, while antibonding orbitals are higher in energy.

Bond Order

The overall stability of a molecule depends on how many electrons go into bonding versus antibonding orbitals. This is summed up using bond order:

$$\text{Bond Order} = \frac{\text{(Electrons in bonding orbitals)} – \text{(Electrons in antibonding orbitals)}}{2}$$

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• Bond Order = 1 → a single bond

• Bond Order = 2 → a double bond

• Bond Order = 0 → no bond forms

For example, in He₂, both bonding and antibonding orbitals are filled with two electrons each:

$$\text{Bond Order} = \frac{2 – 2}{2} = 0$$

So, He₂ doesn’t exist as a stable molecule. But if one electron is removed, as in [He₂]⁺, the bond order becomes 0.5, which shows a weak but real bonding interaction.

The Frontier Orbitals

Two molecular orbitals are especially important for understanding chemical reactivity:

HOMO (Highest Occupied Molecular Orbital) Is where the most reactive, loosely held electrons live. These are the ones most likely to be donated in reactions.

LUMO (Lowest Unoccupied Molecular Orbital) Is the first place electrons go when accepted. Molecules with a low-energy LUMO are good at accepting electrons.

Color and Conjugation

In conjugated molecules (like polyenes or dyes), electrons are delocalized across several atoms. This reduces the HOMO-LUMO gap, meaning these molecules absorb light at longer wavelengths.

That’s why some organic compounds appear colourful. If a molecule absorbs blue light, it might appear orange or red. If you add more conjugation, and the absorption becomes a longer wavelength (lower energy). This explains why even small changes in molecular structure can change a molecule’s colour.