Aufbau principle

The Aufbau principle is a rule of thumb for filling atomic orbitals: electrons occupy lower-energy orbitals before higher-energy ones, subject to quantum constraints.

Madelung rule: An empirical rule that orders orbitals by increasing principal quantum number plus azimuthal quantum number, with ties resolved by the lower principal quantum number. It supplies the familiar sequence used to apply Aufbau filling in many neutral atoms.
Principal quantum number: A quantum number that identifies an electron shell and strongly influences an atomic orbital's size and energy. It provides one of the two quantum numbers used in the Madelung ordering.
Ionization: The removal of one or more electrons from an atom or molecule, producing a positively charged ion. Transition-metal electrons are removed in an order that need not reverse their neutral-atom filling order.
Periodic table: A tabular arrangement of chemical elements ordered by atomic number and recurring chemical properties. Its blocks and recurring patterns reflect the order in which atomic subshells fill.
Pauli exclusion principle: No two identical fermions in a system can occupy the same quantum state; atomic orbitals therefore hold at most two electrons with opposite spins. It limits each orbital to two electrons as the filling sequence is followed.
Azimuthal quantum number: A quantum number that identifies an orbital's subshell and angular momentum, conventionally labeled s, p, d, or f. Its value helps determine orbital ordering in the common filling rule.
Hartree–Fock method: An approximation for many-electron quantum systems that represents each electron as moving in an average field from the others. Unlike the rule of thumb, it calculates approximate electronic structure from a many-electron model.
Valence electron: An electron in an atom's outer shell that can participate in chemical bonding and reactions. Predicted configurations identify the electrons most relevant to an element's chemistry.
Hund's rule: Electrons occupy degenerate orbitals singly with parallel spins before pairing, minimizing energy in many atomic configurations. It determines how electrons fill equal-energy orbitals within a subshell.
Electron spin: An intrinsic angular momentum of an electron, with two possible spin projections in a chosen direction. Opposite spin states allow two electrons to share one spatial orbital.

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