In polyatomic molecules, the atoms can move in various ways that correspond to different vibrational modes. These vibrations can be classified into distinct types based on the ways the atoms oscillate relative to each other. The modes of vibration are influenced by the molecular structure, and they are typically described in terms of normal modes, which are independent vibrational motions. Each normal mode involves a specific pattern of atomic displacements that occur simultaneously across the molecule.

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1. Stretching Vibrations

Stretching refers to the vibrations that change the bond lengths between atoms. There are two types of stretching:

  • Symmetric Stretching: In symmetric stretching, bonds between atoms lengthen or shorten in unison. For instance, in a molecule like CO₂, the two C=O bonds can stretch in and out simultaneously.

  • Asymmetric Stretching: In asymmetric stretching, one bond lengthens while the other shortens. In the case of CO₂, one C=O bond can stretch while the other contracts.

2. Bending Vibrations

Bending vibrations occur when the angle between two bonds changes. There are several types of bending vibrations, which depend on the direction and nature of the motion:

  • In-plane Bending:

    • Scissoring: Two atoms move towards or away from each other within the plane.
    • Rocking: Atoms move in the same direction, maintaining a constant angle relative to each other, but with an overall tilting motion.

  • Out-of-plane Bending:

    • Wagging: Two atoms move up and down together, like a wagging motion, but out of the molecular plane.
    • Twisting: Two atoms move in opposite directions perpendicular to the molecular plane, creating a twisting motion around the bond axis.

3. Torsional Vibrations

Torsional vibrations involve the twisting of parts of the molecule relative to each other around a bond. These vibrations are common in larger molecules with free rotation around single bonds (e.g., in organic molecules like ethane).

Number of Vibrational Modes

For a non-linear polyatomic molecule, the number of possible normal modes of vibration is given by the formula: 3N−6 where N is the number of atoms in the molecule. For a linear molecule, the formula becomes: 3N−5 These equations account for the fact that some degrees of freedom are associated with translation and rotation, leaving the remaining degrees for vibrations.

Example: Water (H₂O) Molecule

Water is a non-linear triatomic molecule (N = 3), so it has:

3(3)−6=3 vibrational modes

The vibrational modes of water include:

  1. Symmetric stretching
  2. Asymmetric stretching
  3. Bending (scissoring)

Example: Carbon Dioxide (CO₂) Molecule

CO₂ is a linear triatomic molecule (N = 3), so it has:

3(3)−5=4 vibrational modes

The modes include:

  1. Symmetric stretching
  2. Asymmetric stretching
  3. Two bending modes (degenerate in-plane bending and out-of-plane bending)

Summary of Vibrational Types:

  • Stretching: Symmetric and Asymmetric
  • Bending: Scissoring, Rocking, Wagging, Twisting
  • Torsional: Twisting around a bond axis

Each of these vibrations corresponds to specific energy levels and can be observed in infrared (IR) spectroscopy, which detects changes in the dipole moment of the molecule during vibration.