Irreducible Representation and IR stretching bands

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SUMMARY

The discussion focuses on determining the number of infrared (IR) active bands in molecules after identifying their irreducible representations. In the case of methane (CH4), which belongs to the Td point group, the irreducible representation is A1 + T2. This representation indicates that there are 2 IR active bands, as the T2 representation is triple degenerate, contributing to the vibrational modes. Given that methane has 9 vibrational modes (calculated as 3N-6 for N=5 atoms), the remaining modes are accounted for by the A1 representation.

PREREQUISITES
  • Understanding of molecular symmetry and point groups
  • Familiarity with irreducible representations in group theory
  • Knowledge of vibrational modes in molecular spectroscopy
  • Basic concepts of infrared (IR) and Raman spectroscopy
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  • Study the application of group theory in molecular vibrations
  • Learn about the relationship between irreducible representations and vibrational modes
  • Explore the calculation of IR and Raman active bands in other molecules
  • Investigate the implications of degeneracy in molecular symmetry
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Chemists, molecular physicists, and students studying molecular spectroscopy who seek to understand the relationship between molecular symmetry and vibrational activity in IR and Raman spectroscopy.

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After you find the irreducible representation of a molecule, how do you determine the number of IR active bands?

For example, in methane, the pointgroup is Td , then you found that the irreducible representation is A1 + T2.

How do you find the number of IR active and Raman active bands?

Thanks

Btw, a friend of mine said there are 2 IR active bands but I am not sure how to figure that out. Also, I know that T is triple degenerate and A is nondegenerate. But not sure how that relates to the number of IR active bands.
 
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Methane is composed of N=5 atoms so there are 3N-6=9 different vibrations. A1+T2 makes up for only 4 of them.
 

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