Molecular Orbital Theory

• Molecular orbital (MO) theory describes the electronic structure of molecules using molecular orbitals which span the molecule
• It contrasts with valence bond theory, which localizes electrons to individual bonds between atoms
• MO theory is a delocalized approach
• MO theory suggests that electrons in a molecule are not assigned to individual chemical bonds between atoms, but instead are treated as moving under the influence of the nuclei in the whole molecule
• Atomic orbitals combine to form molecular orbitals
• The number of molecular orbitals (MOs) formed is equal to the number of atomic orbitals (AOs) combined
• MOs are associated with the entire molecule
• Each MO has a definite energy level
• MOs can be bonding, antibonding, or non-bonding
• Electrons fill MOs in accordance with the Pauli exclusion principle and Hund's rule

Formation of Molecular Orbitals

• MOs are formed by linear combinations of atomic orbitals (LCAO)
• When atomic orbitals combine, they can form bonding MOs (lower energy) and antibonding MOs (higher energy)
• Bonding MOs result from constructive interference
• Electron density is concentrated between the nuclei
• Antibonding MOs result from destructive interference
• There is a node between the nuclei
• Sigma (σ) MOs are formed by end-on overlap of atomic orbitals
• Pi (π) MOs are formed by sideways overlap of atomic orbitals

Bond Order

• Bond order is defined as one-half the difference between the number of electrons in bonding MOs and the number of electrons in antibonding MOs
• Bond order = 1/2 (Number of electrons in bonding MOs - Number of electrons in antibonding MOs)
• A higher bond order indicates greater stability
• A bond order of zero indicates that the molecule is unstable

MO Diagrams for Diatomic Molecules

• MO diagrams show the relative energy levels of the atomic and molecular orbitals
• For diatomic molecules, atomic orbitals from each atom combine to form sigma (σ) and pi (π) molecular orbitals
• The filling of MOs follows the same rules as for atomic orbitals (Aufbau principle, Hund's rule, Pauli exclusion principle)
• For example, in H2, two 1s atomic orbitals combine to form a σ1s bonding MO and a σ*1s antibonding MO
• The two electrons fill the σ1s bonding MO, resulting in a bond order of 1

MO Diagrams for Diatomic Molecules of Second-Row Elements

• For diatomic molecules of second-row elements (Li2 to Ne2), the 2s and 2p atomic orbitals combine to form MOs
• The order of energy levels of the MOs can vary depending on the specific molecule
• Sigma (σ) MOs are formed from the end-on overlap of 2s and 2p atomic orbitals
• Pi (π) MOs are formed from the sideways overlap of 2p atomic orbitals
• The σ2p MO can be higher or lower in energy than the π2p MOs depending on the molecule
• This is due to s-p mixing
• Oxygen (O2) is paramagnetic due to the presence of unpaired electrons in the π*2p antibonding MOs

s-p mixing

• s-p mixing occurs when the 2s and 2p atomic orbitals are close in energy
• It affects the energy levels of the σ molecular orbitals
• In molecules like Li2, Be2, B2, C2, and N2, the σ2p MO is higher in energy than the π2p MOs due to s-p mixing
• In molecules like O2, F2, and Ne2, the σ2p MO is lower in energy than the π2p MOs, and s-p mixing is less significant

Application of MO Theory

• MO theory can be used to predict the magnetic properties of molecules
• Molecules with unpaired electrons are paramagnetic and are attracted to a magnetic field
• Molecules with all paired electrons are diamagnetic and are repelled by a magnetic field
• MO theory can also be used to explain the bonding in complex molecules and ions
• It provides a more accurate description of bonding than valence bond theory, especially for molecules with delocalized electrons