We have assigned spectral species of a LIF spectrum with $^1\Pi$ -- $^1\Sigma$ rotational structure to SiOSi with the aid of $ab$ $initio$ quantum chemical calculations\footnote{M.~Fukushima and T.~Ishiwata, 73rd ISMS, paper MJ09 (2018).}.
Due to the spectrum's red-shaded structure, the $R$-branch forms a band head, and an analysis adopting the $P$- and $Q$-branches had not been satisfactory.
As the $ab$ $initio$ calculations suggest the ground electronic state is 1$^1\Sigma_g^+$, we attempted a more precise analysis via combination differences and noted heavy irregularities exclusive to the upper levels of the $Q$-branch.
Considering parities of the rotational levels of the upper $\Pi$ electronic state, we are investigating this irregularity with the aid of computation.
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