Molecular orbital

A molecular orbital is a mathematical function describing an electron’s spatial distribution and energy in a molecule. It commonly extends across multiple atoms and can be occupied by one or two electrons.

Linear combination of atomic orbitals: A method for approximating molecular orbitals as weighted sums of atomic orbitals. This approximation constructs molecular orbitals by combining atomic orbital wavefunctions.
Atomic orbital: A wavefunction describing an electron’s spatial distribution and energy in an atom. Atomic orbitals are the functions combined to form molecular orbitals.
HOMO–LUMO gap: The energy difference between the highest occupied and lowest unoccupied molecular orbitals. This gap helps predict electronic excitation energies and chemical reactivity.
Valence bond theory: A bonding model that describes molecules using localized electron pairs and overlapping atomic orbitals. Unlike molecular orbital theory, it emphasizes localized bonds rather than orbitals spread across the molecule.
Hydrogen molecule: A diatomic molecule consisting of two hydrogen atoms joined by a covalent bond. Its two electrons occupy a bonding orbital formed from two hydrogen 1s orbitals.
Molecular orbital diagram: An energy-level diagram showing molecular orbitals and their electron occupancy. The diagram organizes orbitals by energy and shows how electrons fill them.
Schrödinger equation: A fundamental equation of quantum mechanics that determines how quantum states evolve or what energies they can have. Molecular orbitals approximate solutions to this equation for electrons in molecules.
Frontier molecular orbital theory: A theory explaining chemical reactivity through interactions of the highest occupied and lowest unoccupied orbitals. It uses orbital shapes and energies to predict which molecules react and where.
Localized molecular orbital: A molecular orbital concentrated in a limited region, such as a bond or lone pair. Localization contrasts with the delocalized orbitals often used to describe whole molecules.
Helium dimer: A weakly bound pair of helium atoms with an exceptionally diffuse ground-state wavefunction. Its orbital occupancy illustrates why filling bonding and antibonding orbitals can cancel net bonding.

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