Electron configuration

An electron configuration records the occupation of electron shells and electron subshells by electrons. For neutral sodium in its ground state, $1s^{2}2s^{2}2p^{6}3s^1$ gives $2+2+6+1=11$ electrons; adding the occupations within each electron shell gives $(2,8,1)$. A superscript counts electrons, rather than multiplying the preceding labels. Removing the outer electron gives the sodium ion ${\mathrm{Na}}^{+}$ with $1s^{2}2s^{2}2p^6$, or $(2,8)$. See Flowers et al., Chemistry 2e, electron configurations of atoms and ions.

A filled electronic shell has all its orbital and spin states occupied. Its total orbital and spin angular momenta cancel, so a closed core does not supply the valence angular momentum in an elementary alkali-atom term assignment.

An approximate scheme for constructing an atomic electron configuration by filling lower-energy atomic orbitals before higher-energy ones, subject to the Pauli exclusion principle. Orbital ordering can change on ionization and has exceptions in interacting chemical atoms. Selecting the free-ion ground term within a specified open-shell configuration additionally requires Hund's rules or a more detailed interaction calculation.

Atoms, molecules or ions with the same electron count, often compared because their orbital occupations or bonding patterns are related. Equal electron counts do not guarantee identical energies or geometry.

An orbital- and model-dependent parameter representing nuclear attraction after electronic screening. A screening construction writes $Z_{\mathrm{eff}}=Z-S$; a binding-energy construction requires an additional orbital-energy model.

Probability density within the inner electron shells. Greater penetration can reduce screening and lower an orbital energy; this helps distinguish many-electron s and p levels with the same principal quantum number.

The screening parameter $S$ in $Z_{\mathrm{eff}}=Z-S$. Different atomic orbitals can have different shielding parameters.

An empirical orbital-screening prescription. Other electrons in an $ns,np$ group count $0.35$ each; electrons in shell $n-1$ count $0.85$, deeper electrons $1.00$, and outer electrons zero. For $1s$, the partner contributes $0.30$. d and f groups use separate rules.^[ref]

Friedrich Hund's rules describe the usual ground-term ordering within an atomic electron configuration in the LS coupling regime. First maximize the total spin $S$ subject to the Pauli exclusion principle. Among the terms with that spin, maximize total orbital angular momentum $L$. Within the resulting term, the lowest level has $J=|L-S|$ for a less-than-half-filled open subshell and $J=L+S$ for a more-than-half-filled one. These are ordering rules, not universal replacements for diagonalizing an arbitrary atomic Hamiltonian operator.

For two equivalent $p$ electrons, parallel spins give $S=1$. Their spatial wavefunction must be antisymmetric; the highest allowed orbital projection with parallel spins is $1+0=1$, giving $L=1$. A $p^2$ subshell is less than half filled, so its lowest term symbol is ${}^3{P}_0$, followed within that term by ${}^3{P}_1$ and ${}^3{P}_2$. Closed subshells contribute zero total $L$ and $S$.

An effective local exchange coupling can favor parallel electron spins in different orbitals on the same atom. The displayed sign convention represents that preference. It underlies the high-spin tendency in Hund's rules and the alignment of itinerant and core spins used in double exchange. The coupling is an effective description of intra-atomic Coulomb and exchange energies, rather than a separate classical magnetic force.

An electron shell collects the allowed electronic quantum states sharing a principal quantum number $n$. Its occupancy is the number of electrons assigned to those states in an electron configuration. An electron shell is not a material surface or a prescribed orbit.

The innermost atomic electron shell, with principal quantum number $n=1$. Its $s$ orbital has nonzero nuclear overlap, making its electrons important in electron capture.

An electron occupying the K shell, with orbital angular momentum zero and total angular momentum $1/2$.

An electron in an inner electron shell, contrasted with a valence electron.

An electron subshell groups the allowed electronic quantum states within an electron shell by their orbital angular momentum quantum number $\ell$. Labels $s$ and $p$ mean $\ell =0$ and $\ell =1$, respectively; their capacities are two and six electrons. The leading number in $2p$ identifies the electron shell, while $p$ identifies the electron subshell.

An electron occupying an atomic orbital without a partner of opposite spin in that atomic orbital.