Inactive Vibrations

Not all vibrational modes are IR-active. For a vibration to be IR-active, it must result in a change in the dipole moment of the molecule. Vibrations that do not change the dipole moment are IR-inactive and will not appear in the IR spectrum. For example:

In a symmetric molecule like CO₂, the symmetric stretch (where both C=O bonds stretch simultaneously in the same direction) is IR-inactive because it does not change the dipole moment. However, the asymmetric stretch (where one bond stretches while the other compresses) is IR-active and appears in the spectrum.

The fundamental principle behind infrared (IR) spectroscopy is the interaction of infrared radiation with the vibrational modes of molecules. However, not all molecular vibrations lead to absorption of IR radiation. For a vibration to be detected in an IR spectrum, it must result in a change in the molecule's dipole moment. This requirement leads to the concept of IR-active and IR-inactive vibrations.

1. Dipole Moment and Vibrational Activity:

  • Dipole Moment: A dipole moment arises from the separation of positive and negative charges within a molecule. It is a vector quantity, meaning it has both magnitude and direction.
  • Change in Dipole Moment (dμ/dQ): During a vibration, the positions of the atoms change, which can alter the molecule's dipole moment.
    • If the vibration causes a change in the dipole moment (dμ/dQ ≠ 0), the vibration is IR-active, and it will result in an absorption band in the IR spectrum.
    • If the vibration does not cause a change in the dipole moment (dμ/dQ = 0), the vibration is IR-inactive, and it will not be observed in the IR spectrum.

2. Symmetry and IR Activity:

  • Symmetry plays a crucial role in determining whether a vibration is IR-active or IR-inactive.
  • Symmetrical Molecules: Molecules with high symmetry often exhibit IR-inactive vibrations.
    • For example, homonuclear diatomic molecules (e.g., O₂, N₂, Cl₂) have no permanent dipole moment, and their stretching vibrations do not create a dipole moment. Therefore, they are IR-inactive.
    • In polyatomic molecules, symmetrical stretching vibrations may not change the overall dipole moment, making them IR-inactive.
  • Asymmetrical Molecules: Asymmetrical molecules generally have more IR-active vibrations because most of their vibrations result in a change in dipole moment.

3. Examples:

  • Carbon Dioxide (CO₂):
    • CO₂ is a linear, symmetrical molecule.
    • Symmetric Stretch: In the symmetric stretch, both C=O bonds stretch and contract simultaneously. This vibration does not change the overall dipole moment of the molecule, so it is IR-inactive.
    • Asymmetric Stretch: In the asymmetric stretch, one C=O bond stretches while the other contracts. This vibration creates a change in the dipole moment, making it IR-active.
    • Bending Vibration: The bending vibration of CO₂ also results in a change in dipole moment and is therefore IR-active.
  • Methane (CH₄):
    • Methane is a tetrahedral molecule.
    • Some of its stretching and bending vibrations are IR-active, while others are IR-inactive, depending on the symmetry of the vibration. (see animation below)
  • Ethene (C₂H₄):
    • The symmetric stretch of the C=C bond is IR inactive, while the asymmetric stretch is IR active.

IR Inactive Methane Vibration

 

4. Importance of IR Inactive Vibrations:

  • While IR-inactive vibrations do not appear in IR spectra, they can be observed using other spectroscopic techniques, such as Raman spectroscopy.
  • Understanding IR-inactive vibrations is essential for a complete analysis of molecular vibrations and for interpreting vibrational spectra.
  • By understanding which vibrations are active and inactive, a scientist can gain a greater understanding of the structure of the molecule.

In essence, the rule is simple: if a vibration changes the dipole moment of the molecule, it will be seen in an IR spectrum; if it does not, it will not.