8.3 Multiple Bonds

Covalent bonds form when atoms share electrons, and the way their orbitals overlap determines whether you get single, double, or triple bonds. This section focuses on how multiple bonds form through sigma and pi bonding, how resonance stabilizes molecules through electron delocalization, and how Molecular Orbital Theory offers a deeper picture of bonding.

Covalent Bonding and Molecular Structure

Atomic orbital overlap in bonding

Covalent bonds form when atomic orbitals from two atoms overlap and share electrons. The type and number of overlaps determine whether you get a single, double, or triple bond.

Sigma ($\sigma$) bonds form by direct, end-to-end overlap of orbitals along the line connecting the two nuclei (the internuclear axis). Every single bond is a sigma bond, and every double or triple bond contains exactly one sigma bond as its foundation.

Pi ($\pi$) bonds form by the sideways, parallel overlap of unhybridized p orbitals. The electron density sits above and below the internuclear axis rather than directly between the nuclei. Pi bonds only appear in multiple bonds:

• A double bond = one $\sigma$ bond + one $\pi$ bond (as in $C_2H_4$, ethylene)
• A triple bond = one $\sigma$ bond + two $\pi$ bonds (as in $C_2H_2$, acetylene)

Hybridization is the mixing of atomic orbitals to form new hybrid orbitals with specific geometries. The type of hybridization tells you how many bonds and lone pairs surround an atom:

• sp$^3$ → four hybrid orbitals → tetrahedral geometry → only single bonds (e.g., $CH_4$)
• sp$^2$ → three hybrid orbitals → trigonal planar geometry → can form one double bond (e.g., $C_2H_4$). The leftover unhybridized p orbital forms the $\pi$ bond.
• sp → two hybrid orbitals → linear geometry → can form a triple bond (e.g., $C_2H_2$). Two leftover unhybridized p orbitals form two $\pi$ bonds.

A useful pattern: the more pi bonds a carbon forms, the fewer hybrid orbitals it needs, and the less "spread out" its geometry becomes (tetrahedral → trigonal planar → linear).

Resonance and electron delocalization

Sometimes a single Lewis structure can't accurately represent a molecule's bonding. When you can draw two or more valid Lewis structures by moving electrons (not atoms), those structures are called resonance structures.

No individual resonance structure is "real." The actual molecule is a resonance hybrid, a blend of all the contributing structures. Think of it like this: if you could average the electron arrangements from all the resonance structures, that average is closer to reality than any one drawing.

Benzene ($C_6H_6$) is the classic example. You can draw it with alternating single and double bonds in two different arrangements, but experiments show all six C–C bonds are identical, with a bond length between a single and double bond. The electrons in the pi bonds are delocalized, meaning they're spread across all six carbon atoms rather than locked between any two.

Electron delocalization lowers a molecule's energy and makes it more stable. The resonance energy (also called delocalization energy) is the difference in energy between the actual molecule and the most stable single resonance structure you could draw. The carboxylate ion ($COO^-$) is another good example: its two C–O bonds are equivalent because the negative charge is delocalized equally over both oxygen atoms.

Sigma vs. pi bonds

Sigma and pi bonds differ in strength, geometry, and how they affect molecular behavior:

The restricted rotation around pi bonds is a big deal. In $C_2H_4$, the molecule is locked in a planar shape because rotating around the double bond would break the pi bond. This restriction is what gives rise to cis-trans isomers in organic chemistry.

Bond length and strength trends:

Multiple bonds pull atoms closer together and hold them more tightly than single bonds. As bond order increases:

• Bond length decreases: triple < double < single. For carbon-carbon bonds: $C_2H_2$ (120 pm) < $C_2H_4$ (134 pm) < $C_2H_6$ (154 pm).
• Bond strength increases: triple > double > single. The bond dissociation energy rises with bond order because more shared electrons means a stronger attraction holding the nuclei together.

Molecular Orbital Theory

Molecular Orbital (MO) Theory provides an alternative to Lewis structures and hybridization for understanding bonding. Instead of electrons belonging to individual atoms, MO Theory says atomic orbitals combine to form molecular orbitals that belong to the molecule as a whole.

When two atomic orbitals combine, they produce two molecular orbitals:

• A bonding orbital, which is lower in energy than the original atomic orbitals. Electron density increases between the nuclei, stabilizing the molecule.
• An antibonding orbital (marked with an asterisk, like $\sigma^*$ or $\pi^*$), which is higher in energy. Electron density decreases between the nuclei, destabilizing the molecule.

Bond order tells you the net number of bonds and is calculated as:

$\text{Bond order} = \frac{\text{bonding electrons} - \text{antibonding electrons}}{2}$

A bond order of 1 corresponds to a single bond, 2 to a double bond, and 3 to a triple bond. A bond order of 0 means the molecule won't form (no net bonding). Higher bond order means a shorter, stronger bond.