Molecular Orbital Theory
Molecular orbital (MO) theory provides a more complete description of chemical bonding than Lewis structures or valence bond theory can offer. By treating electrons as belonging to the entire molecule rather than to individual atoms, MO theory naturally explains phenomena such as the paramagnetism of oxygen, the stability of the hydrogen molecule, and the electronic transitions responsible for the colors of transition metal complexes.
From Atomic Orbitals to Molecular Orbitals
When two atoms approach each other, their atomic orbitals (AOs) overlap and combine to form molecular orbitals that extend over both nuclei. This combination follows the same quantum mechanical principles that govern atomic structure, but the resulting orbitals belong to the molecule as a whole.
The number of molecular orbitals formed always equals the number of atomic orbitals that combine. Two 1s atomic orbitals, for example, produce two molecular orbitals: one bonding and one antibonding.
Bonding and Antibonding Orbitals
Bonding orbitals (σ, π) result from the constructive interference of atomic orbital wave functions. Electron density accumulates between the two nuclei, stabilizing the molecule. A bonding orbital has lower energy than the original atomic orbitals.
Antibonding orbitals (σ, π) result from destructive interference. A node appears between the nuclei where electron density is zero, and the electrons in these orbitals actually destabilize the molecule. An antibonding orbital has higher energy than the original atomic orbitals.
The energy gap between bonding and antibonding orbitals depends on how effectively the atomic orbitals overlap. Greater overlap produces a larger splitting and stronger bonds.
Bond Order
Bond order quantifies the net bonding in a molecule:
Bond Order = (electrons in bonding MOs − electrons in antibonding MOs) / 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 zero means no stable bond forms — the molecule will not exist. Fractional bond orders are possible and represent bonds intermediate in strength between standard single and double bonds.
MO Diagrams
MO diagrams arrange molecular orbitals by energy and show how electrons fill them according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle — the same rules that govern atomic electron configurations.
For homonuclear diatomic molecules of the second period, two ordering schemes exist:
- O₂, F₂, Ne₂: The standard ordering places σ₂p below π₂p in energy.
- B₂, C₂, N₂: A modified ordering places π₂p below σ₂p because of significant s-p mixing (orbital interaction between the 2s and 2p σ orbitals).
The crossover occurs between N₂ and O₂, and getting the order right is essential for predicting magnetic properties.
Oxygen's Paramagnetism
Lewis structures for O₂ suggest all electrons are paired, predicting a diamagnetic molecule. Experimentally, however, liquid oxygen is attracted to a magnetic field — it is paramagnetic.
MO theory resolves this puzzle. The MO diagram for O₂ shows that after filling the lower-energy orbitals, two electrons remain to be placed in two degenerate (equal-energy) π* antibonding orbitals. By Hund's rule, one electron enters each orbital with parallel spins. These two unpaired electrons make O₂ paramagnetic, with a bond order of 2.
This successful prediction was one of the early triumphs of MO theory and remains a classic demonstration of its power over Lewis structures.
Comparison with Valence Bond Theory
Valence bond (VB) theory describes bonds as overlapping atomic orbitals localized between two atoms. It works well for simple molecules and provides an intuitive picture of sigma and pi bonds. However, VB theory struggles with delocalized electrons (as in benzene), paramagnetic species (O₂), and electronically excited states.
MO theory handles delocalization naturally because molecular orbitals extend over the entire molecule. The downside is that MO theory can be mathematically more demanding and may obscure the localized bonding picture that chemists find intuitive for simple molecules.
In practice, chemists use both approaches depending on the problem. Organic chemistry relies heavily on localized VB-like descriptions with resonance structures, while inorganic chemistry and spectroscopy lean on MO theory.
HOMO and LUMO
The Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) are the frontier orbitals that dominate chemical reactivity.
- The HOMO represents the electrons most available for donation — a nucleophile acts through its HOMO.
- The LUMO represents the orbital most accessible for accepting electrons — an electrophile acts through its LUMO.
The HOMO-LUMO gap (energy difference between these two orbitals) determines many molecular properties: a small gap leads to easier electronic excitation, lower-energy absorption (longer wavelength light, often making the compound colored), and higher chemical reactivity. A large gap corresponds to greater kinetic stability and transparency to visible light.
Applications
MO theory underpins modern computational chemistry. Density functional theory (DFT) and Hartree-Fock methods compute molecular orbitals for complex molecules, predicting geometries, reaction energies, and spectra. In materials science, MO theory evolves into band theory to describe solids. In organic electronics, HOMO-LUMO engineering guides the design of organic LEDs, solar cells, and semiconducting polymers.