Molecular Orbital Theory

• In MO theory, valence electrons are delocalized over the entire molecule, not confined to individual atoms or bonds

• Molecular orbitals arise from adding together (superimposing) atomic orbitals

• A linear combination of atomic orbitals (LCAO) creates molecular orbitals (bonding and antibonding orbitals)

  • An electron in a bonding MO will be attracted to both nuclei, and will be lower in energy (more stable) compared to an atomic orbital for a single nuclei

  • An electron in an antibonding MO will be excluded from the internuclear region, and thus have a higher energy than if in an atomic orbital

• N molecular orbitals can be created from N atomic orbitals

  • 2 atomic orbitals generate 2 MOs (one is bonding (lower in energy) and one is antibonding (higher in energy))

• Bond order = ½ (# of bonding electrons - # of antibonding electrons)

Homonuclear Diatomic Molecules with MOs Originating From s Orbitals

• 1s + 1s = σ₁ₛ (bonding MO)

  • σ orbital: cylindrically symmetric about the bond axis; no nodal plane along the bond axis

  • 1s - 1s = σ₁ₛ* (antibonding MO)

Homonuclear Diatomic Molecules with MOs Originating From s and p Orbitals

• Bonding orbitals formed by LCAO of 2pₓ and 2pᵧ

  • 2pₓ + 2pₓ = 𝜋₂ₚₓ

  • 2pᵧ + 2pᵧ = 𝜋₂ₚᵧ

  • 𝜋 orbital (bonding orbital): molecular orbital with a nodal plane along the bond axis

• Antibonding orbitals formed by LCAO of 2pₓ and 2pᵧ

  • 2pₓ - 2pₓ = 𝜋₂ₚₓ*

  • 2pᵧ - 2pᵧ = 𝜋₂ₚᵧ*

  • 𝜋 orbital (antibonding orbital): MO with 2 nodal planes along the bond axis

• The stability of the resulting molecule depends on the number of electrons that occupy lower energy orbitals compared to the number that occupy higher energy orbitals

  • If the net molecule formation is that more electrons have a lower energy, then the molecule is stable

  • If the energy differential is small, then the molecule is not as stable

• Bonding orbitals formed by LCAO of 2pz

  • 2pz +  2pz = σ2pz

  • Nodes pass through the nuclei but no nodes along the bond axis

• Antibonding orbitals formed by LCAO of 2pz

  • 2pz   -  2pz = σ2pz *

  • Nodes pass through and between the nuclei, but not along the bond axis

• The relative energies of the σ2pz compared to the  𝜋₂ₚₓ or y orbitals depend on the z value of the atoms

  • The relative energy ordering is 𝜋₂ₚₓ and 𝜋₂ₚy < σ2pz if Z < 8

  • The relative energy ordering is σ2pz < 𝜋₂ₚₓ and 𝜋₂ₚ if Z = or > 8

  • This only applies to the bonding orbitals because the relative energy ordering of the antibonding orbitals is the same regardless of Z (𝜋₂ₚₓ* and 𝜋₂ₚy*< σ2pz*)