Sigma and Pi Bonds: MDCAT Chemistry notes

Sigma and pi bonds

A covalent bond forms when orbitals on two atoms overlap. How they overlap decides the type of bond.

Feature	Sigma (σ) bond	Pi (π) bond
Overlap	Head-on (axial), along the internuclear axis	Sideways (parallel) overlap of two p orbitals
Orbitals	s–s, s–p, p–p (end-on) or hybrid orbitals	Unhybridized p–p only
Strength	Stronger (greater overlap)	Weaker (poorer overlap)
Electron density	On the axis between the nuclei	Above and below the axis
Rotation	Free rotation possible	Rotation is restricted

A σ bond can exist on its own. A π bond forms only after a σ bond is already present between the same two atoms.

• A single bond is 1 σ.
• A double bond is 1 σ + 1 π.
• A triple bond is 1 σ + 2 π. In ethyne, the two π bonds are at right angles to each other and merge into a cylindrical cloud of electron density around the C–C σ bond.

In propene and ethene, the π bond comes from sideways overlap of the unhybridized p orbitals on the $sp^2$ carbons.

Counting bonds: worked examples

• Ethene $\mathrm{C_2H_4}$: 4 C–H + 1 C–C σ gives 5 σ and 1 π. It has 6 shared pairs, which is more than $\mathrm{N_2}$ (3), $\mathrm{CO_2}$ (4) or $\mathrm{NH_3}$ (3).
• Propene $\mathrm{C_3H_6}$: 6 C–H + 2 C–C gives 8 σ and 1 π.
• Benzene $\mathrm{C_6H_6}$: 6 C–C + 6 C–H gives 12 σ and 3 π.
• Maleic anhydride $\mathrm{C_4H_2O_3}$: the five-membered ring contains 5 σ bonds, and there are 2 exocyclic C=O and 2 C–H bonds. That gives 9 σ and 3 π (one C=C and two C=O).

Theories of bonding

Valence Bond Theory (VBT) and Molecular Orbital Theory (MOT) explain how σ and π bonds form. VSEPR only predicts shapes and says nothing about how a bond is made.

In MOT, atomic orbitals combine into molecular orbitals.

• A bonding MO is lower in energy than the atomic orbitals it came from, so it is more stable.
• An antibonding MO is higher in energy.

Key formulas

$$\text{Bond order} = \tfrac12\,(N_b - N_a)$$

Here $N_b$ is the number of bonding electrons and $N_a$ the number of antibonding electrons. For example, bond order is 1 for $\mathrm{H_2}$, 2 for $\mathrm{O_2}$ and 3 for $\mathrm{N_2}$. A higher bond order means a shorter and stronger bond.

Coordinate covalent (dative) bond

In a coordinate bond, both electrons of the shared pair come from one atom (the donor), which has a lone pair. The other atom (the acceptor) has an empty orbital.

• $\mathrm{H_3N{\to}BF_3}$: N donates its lone pair to electron-deficient B.
• $\mathrm{NH_4^+}$ and $\mathrm{H_3O^+}$ each contain one coordinate bond.
• $\mathrm{Al_2Cl_6}$ dimer: Al in $\mathrm{AlCl_3}$ has only 6 electrons. A Cl atom of a neighbouring molecule donates a lone pair to it, forming Cl bridges, and Al completes its octet.
• NaCl and CaO are ionic. $\mathrm{H_2O}$ has only ordinary covalent bonds.

Common MDCAT traps

• The π bond is formed by parallel overlap and is weaker than a σ bond, not stronger.
• Remember to count every C–H bond as a σ bond when totalling bonds.
• VSEPR is the theory that does not explain σ/π bond formation.
• Bond order is half the difference, not the full difference.
• Al does not donate a lone pair in the dimer. Chlorine donates and aluminium accepts.

Quick revision

• σ bonds come from head-on overlap and π bonds from sideways p–p overlap.
• A double bond is 1σ + 1π and a triple bond is 1σ + 2π.
• Ethene has 1 π bond and benzene has 3.
• A bonding MO is lower in energy than an antibonding MO.
• $\mathrm{NH_3BF_3}$ contains a coordinate bond.