= Solution
The <D4h molecular point group> contains an <inversion centre>, so <infrared and Raman mutual exclusion> applies. A <normal mode> of $u$ parity can have <vibrational infrared activity>, whereas the quadratic <polarizability tensor> components responsible for <Raman vibrational activity> have $g$ parity. No individual fundamental can be active in both spectra.
The <Td molecular point group> lacks an <inversion centre>. In particular, $T_2$ <normal modes> transform both as electric-dipole components and as off-diagonal <polarizability tensor> components, so they occur in both spectra. \b[Coincident IR and Raman fundamentals therefore favour the tetrahedral structure; symmetry requires no such coincidences for the square.] Weak or unresolved features can conceal coincidences experimentally, while accidental equality of different frequencies is not a violation of mutual exclusion.
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