Solution (source code)

= Solution

Here $\Delta_o/B=20$, so the ground term is ${}^6A_{1g}$. \b[There are no spin-allowed d–d bands in the displayed manifold under the <spin selection rule>:] the excited terms shown have doublet or quartet rather than sextet <multiplicity>. Very weak spin-forbidden <absorptions> can still gain intensity through spin–orbit coupling, and even spin-allowed d–d transitions would be forbidden by the <Laporte rule> in ideal centrosymmetric coordination. Thus a strong ordinary d–d spectrum should not be predicted simply by multiplying the splitting by a numerical factor. For scale, the lowest quartet branches read roughly $E/B\simeq17,23,33$ at this abscissa, corresponding to weak features around $1.4\times10^4$, $1.8\times10^4$ and $2.6\times10^4\ \mathrm{cm^{-1}}$ if such forbidden intensity is detectable. These are graphical estimates, not precision assignments of every weak line.