In terms of active vibrational modes, when can a mode be classified as IR active?

A vibrational mode is classified as infrared (IR) active when it leads to a change in the dipole moment of a molecule during the vibration. For a mode to be IR active, it must match the symmetry of the electric dipole moment.

This is due to the principle that IR spectroscopy detects vibrations that cause fluctuations in the dipole moment, allowing for the molecule to interact with infrared radiation. Specifically, if a normal mode of vibration can create an electric dipole moment or alter the existing dipole moment in the molecule, it will be IR active.

In contrast, vibrational modes may not necessarily have symmetry characteristics related to quadratic functions or centers of inversion, as these factors primarily pertain to selection rules in other spectroscopic techniques such as Raman spectroscopy. Additionally, whether modes are Raman active or not is independent of their classification as IR active. Thus, the defining factor for IR activity is the relationship to the electric dipole moment.