Which vibrational modes of CO2 and CSO do not lead to IR absorption bands? [closed]








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I recently came across this question, I have no idea about IR:



> 
> Which of the following vibrational modes show no IR absorption bands?
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> A) Symmetric CO2 stretch
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> B) Antisymmetric CO2 stretch
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> C) Symmetric S=C=O stretch
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> D) Antisymmetric S=C=O stretch
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> 




A) Symmetric $\ce{CO2}$ stretch.


A particular vibrational mode is considered IR active, if there is a change of *transition dipole moment*. $\ce{CO2}$ is linear, and the symmetric stretching mode means both oxygens move in/outward concurrently.
You can see an illustration of the symmetric and antisymmetric stretching modes of $\ce{CO2}$ here: <https://www.youtube.com/watch?v=TMLnUmbLwUI&t=1m50s>


* For the symmetric mode, the overall center of charge stays the same, thus no change in dipole moment, thus the mode is not IR active.
* For the antisymmetric mode, the center of charge shifts, thus the dipole moment changes and the mode is IR active. This is also true of the $\ce{S=C=O}$ antisymmetric stretch.
* The $\ce{S=C=O}$ symmetric stretching mode is also IR active, since $\ce{S}$ and $\ce{O}$ are two different atoms, with different partial charges. As they vibrate, the total center of charge moves.


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