Draw a molecular orbital diagram for the neutral C2 molecule

Draw a molecular orbital diagram for the neutral C2 molecule. Label all atomic orbitals and molecular orbitals. Plausible Lewis structures are :C=C: and •C≡C•. Use your molecular orbital diagram to explain which Lewis structure is a better representation.

The correct answer and explanation is :

Molecular Orbital Diagram for the C₂ Molecule

Step 1: Atomic Orbitals of Carbon
Each carbon atom has 6 electrons:

• 1s²
• 2s²
• 2p²

So for two carbon atoms, we have a total of 12 electrons to place in molecular orbitals.

Step 2: Molecular Orbital Energy Levels for C₂
For elements up to oxygen in the periodic table, the 2p orbital ordering is as follows due to s-p mixing:

CopyEditσ1s < σ1s* < σ2s < σ2s* < π2p < σ2p < π2p* < σ2p*

Step 3: Electron Configuration in Molecular Orbitals

1. σ1s (2 electrons)
2. σ1s* (2 electrons)
3. σ2s (2 electrons)
4. σ2s* (2 electrons)
5. π2p (4 electrons)
6. σ2p (0 electrons)

So the molecular orbital filling is:

markdownCopyEditσ1s² σ1s*² σ2s² σ2s*² π2p⁴

Bond Order Calculation:
Bond order = ½ [(number of bonding electrons) – (number of antibonding electrons)]
= ½ [(2 + 2 + 4) – (2 + 2)]
= ½ [8 – 4]
= 2

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Which Lewis Structure Is More Accurate?

There are two plausible Lewis structures:

1. :C=C: (double bond between carbons)
2. •C≡C• (triple bond with one unpaired electron on each carbon)

From the MO diagram, we find:

• The bond order is 2, not 3.
• All electrons are paired in the diagram—no unpaired electrons.
• Therefore, C₂ is a diamagnetic molecule, not paramagnetic.

This rules out the structure with unpaired electrons (•C≡C•). The more accurate representation is:

:C=C:

This agrees with the bond order of 2 from the MO diagram and shows no unpaired electrons. While it might seem odd that two π bonds (from π2p orbitals) form before a σ2p bond, this is consistent with molecular orbital theory for lighter diatomic molecules like C₂.