Which of the following describes a vibrational mode that is Raman active?

To understand why the choice regarding the symmetry species matching xy or x² describes a Raman-active vibrational mode, it's essential to consider the selection rules governing Raman spectroscopy.

Raman activity is linked to the polarizability of the molecule during vibration. A vibrational mode is Raman active if the change in polarizability during that mode is non-zero. Generally, this means that the vibration must involve a change in the electron cloud distribution that can affect how the molecule interacts with light.

In the context of symmetry, vibrational modes that belong to symmetric species in the point group of the molecule often meet this requirement. Vibrational modes associated with molecular symmetry species like xy or x² suggest that there are directional components to the polarizability change, as these terms represent combinations of coordinates that indicate how electron density is distributed in space during the vibration. Such terms reflect angular dependence, which typically leads to significant changes in polarizability during vibrational motion, making these modes Raman active.

In contrast, other options either focus on features that do not directly correlate with polarizability changes or restrict the conditions to specific characteristics that do not necessarily enable Raman activity. Understanding this relationship is crucial in identifying which vibrational modes will be detected in Raman spectroscopy, and the