Distinguish molecular orbitals with sigma and pi symmetry
The labels σ and π describe how a molecular orbital behaves around the internuclear axis. They do not tell you whether the orbital is bonding or antibonding.
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The core idea
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Learning objectives
- Distinguish molecular orbitals with sigma and pi symmetry
Use the bond axis as your reference
The labels σ and π describe how a molecular orbital behaves around the internuclear axis. They do not tell you whether the orbital is bonding or antibonding.
Imagine rotating the orbital about the bond axis. This simple symmetry test is more reliable than judging whether a sketch happens to look like an s or p orbital.
σ and π symmetry
A σ molecular orbital is unchanged by rotation about the internuclear axis. Its electron density is arranged symmetrically around that axis.
A π molecular orbital has one nodal plane that contains the internuclear axis. Rotation by 180° about the axis changes the sign of the wavefunction, although the electron-density picture may look unchanged.
Symmetry is separate from bonding character
End-on overlap along the bond axis usually gives σ and σ* orbitals. Side-on overlap of two parallel p orbitals perpendicular to the axis usually gives π and π* orbitals.
Both σ and π orbitals can be bonding or antibonding. The σ/π label comes from rotational symmetry; the presence or absence of an asterisk comes from phase between adjacent atoms and the resulting internuclear node.
For a π orbital, the nodal plane through the bond axis is present in both π and π*. The antibonding π* orbital has an additional node between the nuclei.
Worked example: the two 2p overlaps
Two 2p orbitals pointing along the internuclear axis overlap end-on. Their in-phase combination is σ(2p), while their out-of-phase combination is σ*(2p).
Two parallel 2p orbitals perpendicular to the axis overlap side-on. Their in-phase combination is π(2p), while the out-of-phase combination is π*(2p).
A molecular orbital has a nodal plane containing the bond axis but no node between the nuclei. Give both its symmetry and bonding character.
Check your answer
It has π symmetry because of the nodal plane through the axis, and it is bonding because there is no additional internuclear node.
Try the rotation test
First mark the bond axis. Then imagine a small rotation about it: a σ wavefunction retains its sign pattern, whereas a π wavefunction does not.
Only after assigning σ or π should you inspect adjacent phases and internuclear nodes to add bonding or antibonding.
An orbital has cylindrical density around the bond axis and a node halfway between the nuclei. Classify it fully.
Check your answer
It is σ* antibonding: cylindrical symmetry gives σ, while the internuclear node gives antibonding.
Separate the two labels
A good exam answer may need two independent decisions: symmetry and bonding character. Writing only ‘π’ does not say whether the orbital is π or π*.
State the visible evidence rather than relying on the orbital name alone.
Why is ‘all π orbitals are bonding’ incorrect?
Check your answer
π only describes symmetry. In-phase side-on overlap gives bonding π, while out-of-phase side-on overlap gives antibonding π*.
Common mistake: counting every nodal plane as antibonding
The nodal plane that contains the internuclear axis is required by π symmetry; it does not by itself make a π orbital antibonding.
Antibonding character requires the additional destructive interaction between the atoms, seen as a node in the internuclear direction.
Correct: ‘A π orbital is always antibonding because it has a nodal plane.’
Check your answer
The axial nodal plane defines π symmetry. A bonding π orbital has continuous side-on density between atoms; π* has an additional internuclear node.
Check your understanding
For every sketch, mark the bond axis, apply the rotation or nodal-plane test, then determine bonding character separately.
Next, place these orbitals on discrete energy levels and use electron-filling rules correctly.
Give the shortest accurate test that distinguishes σ from π symmetry.
Check your answer
A σ wavefunction is unchanged by rotation about the internuclear axis; a π wavefunction has a nodal plane containing that axis.
Distinguish molecular orbitals with sigma and pi symmetry scientific representation
Text alternative: The σ or π label is independent of whether the orbital is bonding or antibonding. Symmetry is assigned from behaviour in space, not from the orbital's energy ranking.
About 5 minutes
Symmetry and bonding character are independent labels
- σ/π describes spatial symmetry; * describes antibonding
Sigma and pi spatial symmetry
- nodal plane contains internuclear axis
Text alternative: The σ or π label is independent of whether the orbital is bonding or antibonding. Symmetry is assigned from behaviour in space, not from the orbital's energy ranking.