Solution (source code)

= Solution

\b[Only $^1\Delta_g\to{}^1\Delta_u$ is electric-dipole allowed within the listed terms.] For a <diatomic molecule>, the <electric-dipole selection rule> requires $\Delta S=0$, $g\leftrightarrow u$, and $\Delta\Lambda=0,\pm1$. The lower singlet of part (a) is $^1\Delta_g$. Every candidate from the same configuration fails the inversion rule, while the $^1\Sigma_u^{\pm}$ terms of part (b) require $|\Delta\Lambda|=2$. Triplet destinations fail the spin rule. The surviving $\Delta\to\Delta$ transition uses the axial dipole component, so it is a parallel electronic transition. Weak spin-orbit or other intensity-borrowing transitions are outside this leading electric-dipole classification.