A quantum‑mechanical function (orbital) that describes the allowed spatial distribution and energy of electrons delocalized over a molecule, constructed as combinations of atomic orbitals and categorized into bonding, antibonding, and nonbonding types.

Principle

Molecular orbitals form by linear combination of atomic orbitals (LCAO) or other basis functions; occupancy of MOs by electrons determines bond order, electronic excitations, and reactivity, while symmetry and energy ordering constrain feasible transitions.

Demonstration

In H2, the in‑phase combination of 1s orbitals produces a bonding σMO with increased electron density between nuclei, while the out‑of‑phase combination produces an antibonding σ*MO; occupation of σ* weakens or prevents bonding.

Misapplication

Treating MOs as permanently localized electron pairs identical to Lewis bonds, or assuming a single MO picture always captures correlated electron effects—this neglects electron correlation, resonance averaging, and environment-induced orbital mixing.

Consequence

Using MO theory correctly predicts spectroscopic transitions, frontier orbitals (HOMO/LUMO) that guide chemical reactivity, and delocalization effects that explain conjugation and aromaticity.

Reversal

The inverted viewpoint emphasizes localized orbitals or valence‑bond structures that represent electrons as pairwise localized bonds and lone pairs rather than delocalized MOs; both pictures can be complementary.

Boundary

Applies to electronic states describable by one‑electron-like orbitals in a given basis; excludes phenomena requiring explicit multiconfigurational treatment without reference to a single‑determinant MO picture and excludes strictly classical charge‑separation models.

Semantic Tension

Tension lies between MO and valence‑bond descriptions: MO emphasizes delocalized energy eigenfunctions and is powerful for spectroscopy and delocalization, while valence‑bond emphasizes localized bonding patterns and resonance structures.

Synthesis

A molecular orbital is a quantum function built from atomic orbitals whose occupancy and symmetry determine bonding character, electronic excitations, and reactivity patterns across a molecule.