= Solution
\b[The terms are $^3\Sigma_g^-$, $^1\Delta_g$ and $^1\Sigma_g^+$.] Closed <molecular orbital> shells contribute no net <spin angular momentum> or axial orbital projection, so only the two equivalent $\pi_g$ electrons need be coupled. Their individual projections are $\lambda=\pm1$.
Putting both electrons in the same projection gives $|\Lambda|=2$ and forces opposite spins by the <Pauli exclusion principle>, yielding $^1\Delta_g$. With one electron in each projection, the spin-adapted symmetric and antisymmetric spatial combinations give a singlet $\Sigma$ and a triplet $\Sigma$. Their reflection parities are $+$ and $-$, respectively. Both open-shell electrons are gerade, so their product is gerade. The dimensions $3+2+1=6$ exhaust the $\binom42=6$ microstates. By <Hund's rules>, the triplet is the lowest term, and $^1\Delta_g$ is the lower singlet.
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