Hund's rules

Hund's rules predict the lowest-energy atomic term for an electron configuration by ranking terms according to spin, orbital angular momentum, and total angular momentum.

Atomic term symbol: A notation encoding an atom's total spin, orbital, and angular momentum quantum numbers. The rules select among the terms this notation identifies.
Electron configuration: A specification of how electrons occupy atomic or molecular orbitals. The rules take an electron configuration as their starting point.
Ground state: The lowest-energy state available to a physical system. Hund's rules identify the ground term within a configuration, not the ground state across all configurations.
Madelung rule: An empirical rule for ordering atomic orbitals by the sum of principal and azimuthal quantum numbers. It predicts orbital filling, whereas Hund's rules rank terms within a specified configuration.
Spin multiplicity: The number of possible spin projections for a state, equal to twice its total spin quantum number plus one. The first rule favors the term with the greatest spin multiplicity.
Pauli exclusion principle: The quantum principle that identical fermions cannot occupy the same quantum state. It restricts which combinations of electron spins and orbitals are allowed.
Atomic spectroscopy: The study of atoms through their absorption, emission, or scattering of electromagnetic radiation. Predicted terms help interpret the fine structure and transitions in atomic spectra.
J–J coupling: An atomic angular-momentum coupling scheme in which each electron's spin and orbital angular momentum combine first. It contrasts with the Russell–Saunders scheme underlying the usual statement of Hund's rules.
Orbital angular momentum: Angular momentum associated with the spatial motion of particles, including atomic electrons. The second rule ranks terms with equal spin by their total orbital angular momentum.
Slater determinant: An antisymmetric wavefunction used to represent a system of identical fermions. It enforces electron indistinguishability and exclusion when constructing atomic states.

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