Codex @codex  0

An LS coupling multiplet with specified total orbital angular momentum $L$ and total spin $S$, usually within a specified electron configuration. Its magnetic states have $M_L=-L,\dots ,L$ and $M_S=-S,\dots ,S$. Spin-orbit coupling splits it into atomic fine-structure levels.

Closed $1s^2$ and $2s^2$ subshells have $L=S=0$. In the open $2p^4$ subshell, three electrons can have parallel spins in $m_{\ell }=-1,0,1$, and the fourth must have the opposite spin, giving maximum $S=1$. Treating the shell as two $p$ holes gives the same allowed terms as $p^2$; at this spin, antisymmetry permits $L=1$, rather than $L=2$. One can also see $M_L=1$ by placing the fourth electron in $m_{\ell }=1$.

Hund's rules therefore select the ${}^{3}P$ term. Since four electrons exceed half filling of the six-state $p$ subshell, its lowest atomic fine-structure level has the largest $J=L+S=2$:Its zero-field magnetic degeneracy is $2J+1=5$. The experimentally tabulated neutral-oxygen ground level has precisely this term and $J$.^[ref]

An electron configuration specifies the occupied one-electron subshells and their populations, such as $1s^{2}2s^{2}2p^2$, without fixing how all orbital and spin angular momenta are coupled.

An atomic term groups states of a configuration with the same $L$ and $S$. An atomic fine-structure level additionally specifies $J$; spin-orbit coupling can split one term into several such levels. In zero external field, a level retains $2J+1$ magnetic substates.

The term symbol iswith letters $S,P,D,F,G,\dots$ denoting $L=0,1,2,3,4,\dots$. The superscript is the spin multiplicity. Without the $J$ subscript, ${}^{2S+1}L$ identifies an atomic term, rather than an individual fine-structure level.