= Hund's rules
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<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 $^3P_0$, followed within that term by $^3P_1$ and $^3P_2$. Closed subshells contribute zero total $L$ and $S$.
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