What occurs if a molecule possesses a center of inversion in relation to IR and Raman activity?

For a molecule with a center of inversion, the symmetry properties significantly influence its vibrational modes and their activity in infrared (IR) and Raman spectroscopy. When a molecule has a center of inversion, any vibrational mode that is symmetric with respect to this center cannot change the dipole moment of the molecule since inversion does not produce a net dipole change.

As a result, all vibrational modes that are IR active must result in a change in dipole moment. However, because a molecule with a center of inversion has certain symmetric vibrations that do not lead to such changes, it limits the IR activity to those modes that might not be calculated solely based on symmetry.

On the other hand, Raman activity is often correlated with changes in polarizability. In the case of a molecule with a center of inversion, it can also lead to some vibrational modes being prohibited from being Raman active due to their symmetric nature. Thus, for molecules with this type of symmetry, none of the modes will be both IR and Raman active simultaneously.

This means that while some modes may be IR active (if they happen to involve an asymmetric movement relative to the center of inversion), the requirement that the molecule lacks modes capable of being both IR and Raman active holds true.