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For IR Spectroscopy, I noticed that there are aromatic overtones or "benzene fingers" a bit below the $\mathrm{2200~cm^{-1}}$ region. Why do these occur in IR spectroscopy? And is there any way to prevent them?

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In general there are 'fundamental' lines at frequency $v_1, v_2$ etc. Weak overtone transitions can occur for any fundamental vibration at frequency $nv_1$, $nv_2$ etc. where $n=2, 3,..$ and so on for each vibration $v_i$. Combination bands can also be present and involve exciting two (or more) vibrations and have frequency $nv_1+mv_2$, where n and m are integers and $v_1,v_2$ represent any two different vibrations. Relative to the fundamental frequencies the overtone and combination transitions are inherently weak. There is no way to prevent them unless you are able to align molecules in your sample and do polarisation spectroscopy and even then many lines will still be present depending on dipole direction and selection rules.

Transitions from the ground vibrational state are the most intense as these have the greatest population, but 'hot' bands starting from $v=1$ can also occur if the temperature is high enough. Greatly lowering the temperature will remove these.

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