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This question is in relation to the [FeCl4]- molecule, which is tetrahedral. I previously deduced, using symmetry analysis, that the vectors corresponding to the bonds of the molecule will be A1+T2, which, according to the table below and my scarce knowledge of spectroscopy, should mean that we will observe 1 IR band and 2 Raman bands. More specifically, we should see 3 IR stretching modes and 4 Raman stretching modes where 3 of the Raman ones will coincide with 3 IR ones and 1 will be Raman-unique (see character table at the bottom of the question).

This is a question from an assignment, which confirms my prediction with the data below and asks to sketch the stretching modes associated with each band. This is where I am stuck - I am yet to find a proper procedure to do this as most textbooks simply give the shapes of the modes with no explanation. I know that an IR stretch should involve a change in dipole moment, which rules out the 'breathing' mode, but this still leaves me guessing as to which ones will be correct as there are only 3 IR modes, but there are surely more ways than that to change the dipole moment?

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    $\begingroup$ you are on the right track. You can see that the sym stretch ($A_1$) is only seen in Raman, but its hard to see what $T_2$ will look like. You need to use projection operators. There is an example in this online book applying-maths-book.com/intro.html. see the section in chapter-7, matrices part 6 normal-mode-vibrations for a worked example. $\endgroup$
    – porphyrin
    Commented Mar 31, 2023 at 12:12

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