What should be this value when instead of pyridinium cation pyridinium derivative will be there(e.g. pyridinium ionic liquid)? How to assign the bond responsible for this?
Yes, We can observed a line at 3381.9 cm−1 for the NH-stretching mode in pyridinium cation
You're not likely to see anything in the 3100-3400 cm-1 range. The nitrogen is alkylated and there is no NH group.
If you do see a line around there, that would mean that the alkylation of the pyridine was not complete. You can have a mixture of mostly alkylated pyridine and some protonated pyridine, and it would still behave like an ionic liquid. The NH line may also be shifted due to hydrogen bonding with the anion (depends a lot on the anion).
Anything closer to 3500 cm-1 probably means water contamination. You can find out how much water you have by a Karl Fischer potentiometric titration.
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