6.2. Vibrational frequency analysis calculations

Within the BO approximation, the total energy of a molecule is the sum of the electronic, vibrational, and rotational energy:

Molecular vibrations can be modeled like the motion of particles connected by springs, representing atoms connected by chemical bonds of variable lengths. In the harmonic oscillator approximation, the force required to extend the spring is proportional to the extension (Hooke's law). When the vibrational energy is high, the harmonic oscillator approximation is no longer valid, and neither is the concept of normal mode. We now consider the simple case of a diatomic molecule.

Modeling the vibrational-rotational levels of a diatomic molecule

The rotational energies of a diatomic molecule are represented by a series of discrete values:

where:

• is the angular momentum quantum number.
• is the equilibrium distance.
• is the reduced Planck...