Such as the linear rotor HC5N (v11=1) or the symmetric top methyl cyanide, CH3CN (v8=1)?
l-type doubling is caused by Coriolis-interaction and thus J (rotational quantum number) dependent. Not the bending vibration itself is effected by l-type doubling but the rotational pattern. (see e.g. H.H. Nielsen, Rev.Mod.Phys. 23 (1951) 90)
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