Understanding IR Spectra and CO Stretching Bands

Infrared (IR) spectroscopy is a powerful technique used to identify functional groups in molecules. For metal carbonyl complexes, the stretching vibrations of the carbon-oxygen (\(\nu_{CO}\)) bond are particularly useful. The number and positions of these bands in the IR spectrum depend strongly on the molecular structure and symmetry.

Symmetry plays a crucial role because only vibrations that cause a change in the dipole moment of the molecule are IR active. By analyzing the symmetry of a complex (using point groups) and applying group theory, we can predict the number of expected IR-active \(\nu_{CO}\) bands.

CO Bands in fac-[Mo(PPh₃)₃(CO)₃]

The complex fac-[Mo(PPh₃)₃(CO)₃] is a facial isomer of an octahedral complex. In this isomer, the three carbonyl ligands (CO) are located on one face of the octahedron, and the three triphenylphosphine ligands (PPh₃) are on the opposite face.

This arrangement gives the molecule a specific symmetry, which belongs to the C₃v point group. For three CO ligands in a facial arrangement within a C₃v point group, the three CO stretching vibrations transform according to group theory as a combination of irreducible representations:

\( \Gamma_{CO} = A_1 + E \)

In the C₃v point group, both the A₁ and the E irreducible representations correspond to modes that are IR active (A₁ transforms as z, and E transforms as x and y). The E mode is a degenerate mode, meaning it represents two vibrations with the same energy under ideal symmetry conditions, but it appears as a single band in the spectrum unless the symmetry is lowered. Therefore, we expect to see one IR band corresponding to the A₁ mode and one IR band corresponding to the E mode.

Thus, the expected number of \(\nu_{CO}\) bands in the IR spectrum of fac-[Mo(PPh₃)₃(CO)₃] is 2.

CO Bands in trans-[Mo(PPh₃)₂(CO)₄]

The complex trans-[Mo(PPh₃)₂(CO)₄] is a trans isomer of an octahedral complex. In this isomer, the two triphenylphosphine ligands (PPh₃) are positioned opposite each other (trans). This arrangement forces the four carbonyl ligands (CO) to lie in a plane around the metal center.

This structure possesses a higher symmetry than the facial isomer. With the Mo at the center, the two PPh₃ ligands on the z-axis, and the four CO ligands in the xy-plane, the complex belongs to the D₄h point group. For four CO ligands in a planar arrangement within a D₄h point group, the four CO stretching vibrations transform as:

\( \Gamma_{CO} = A_{1g} + B_{1g} + E_u \)

Now, we need to determine which of these modes are IR active. In the D₄h point group, IR active modes transform as x, y, or z. The irreducible representations corresponding to x, y, and z are Eᵤ (for x and y) and A₂ᵤ (for z).

Looking at the transformed modes (\(A_{1g}, B_{1g}, E_u\)), only the Eᵤ mode is IR active as it transforms as (x, y). The A₁g and B₁g modes are IR inactive.

The Eᵤ mode is degenerate, but again, it typically appears as a single band in the IR spectrum. Therefore, we expect to see only one IR band corresponding to the Eᵤ mode.

Thus, the expected number of \(\nu_{CO}\) bands in the IR spectrum of trans-[Mo(PPh₃)₂(CO)₄] is 1.

Summary

Based on the symmetry analysis:

• fac-[Mo(PPh₃)₃(CO)₃] (C₃v symmetry) is expected to show 2 IR-active \(\nu_{CO}\) bands (\(A_1 + E\)).
• trans-[Mo(PPh₃)₂(CO)₄] (D₄h symmetry) is expected to show 1 IR-active \(\nu_{CO}\) band (\(E_u\)).

Therefore, the expected number of \(\nu_{CO}\) bands for fac-[Mo(PPh₃)₃(CO)₃] and trans-[Mo(PPh₃)₂(CO)₄] are 2 and 1, respectively.