Question

Through reducible and irreducible representations, determine the number of peaks in the IR and Raman spectra due to Re-Cl stretching for PhReCl4, include the correct symmetry labels (e.g. A1, B2, etc.)

Through reducible and irreducible representations, determine the number of peaks in the IR and Raman spectra due to Re-Cl stretching for PhReCl, include the correct symmetry labels (e.g. A1, CI.... B2, etc.). (8 pts) ci-Reci

Answer 1

Group theory allows us to predict number of active stretch in both IR and Raman spectra.

The character table tells us whether the vibrational modes are IR active and/or Raman active. Vibrational Spectroscopy. IR active : the vibration must change the dipole moment of the molecule : Only irreducible representations with x,y,z symmetry can do this

Raman active : the vibration must change the polarizability of the molecule ;  Only irreducible representations that transform like the binary products of x,y, and z (i.e., xy, xz, yz, x², y², z ² or their linear combinations) can do this.

We are interested in the vibrations of specific groups (Rh-Cl stretching ) in a molecule rather than all possible motions in this metal complexe. In this case, we can create reducible representations of the bond vectors of planar (Rh(Cl)₄) :  and determine their irreducible components, and find the active modes.

for this molecule we will consider C_4v character table :

Reducible represntation:

Stretching	E	2C4 (z)	C2	2v	2d
Γ4-bonds	4	0	0	2	0

Irreducible representations (using character table of C_4v ) :

Γ_str = A₁ + B₁ + E

From character table :

We can see two irreducible representation A₁ and E (linear functions) is related to IR active vibrations. (2 IR peak)

And all irreducible representation A₁ ;  B₁ ; E (quadratic functions ) are related to Raman active vibrations. (3 peaks in Raman spectra ).