For a mode of vibration to be IR active, which condition must be met?

For a mode of vibration to be infrared (IR) active, it is essential that there is a change in the dipole moment during the vibration. Option A states that the symmetry of the vibration must match that of the x, y, or z axes, which directly relates to how the molecule interacts with the electric field of infrared light. If a vibration leads to a displacement that changes the molecule's dipole moment, the vibration will be IR active. This is because IR spectroscopy relies on the interaction between the dipole moment and the electric field associated with the infrared radiation.

When a vibration has symmetry that corresponds with the coordinates of the molecular dipole (x, y, z), it indicates that there will be a change in the distribution of charge as the atoms move during the vibration, allowing for the absorption of IR radiation. This requirement is fundamentally tied to the principles of group theory as applied to molecular vibrations.

In contrast, the other options misinterpret the necessary conditions for IR activity. They may involve symmetry considerations, but they do not correctly define the necessary relationship between vibrational modes and dipole moment changes. Recognizing the importance of dipole moment changes is crucial for understanding the factors that determine IR activity in vibrational modes of molecules.