When I'm Learning - 20250921

This post is mainly about the Raman Scattering and some thought about it.

Basic Principle

When a Light Wave meets a Molecule, it will change the polarization state of the molecule periodically.
The frequency of the modulation is the same as the frequency of the light wave.
But as the molecule vibrates or rotates, the Polarizability of the molecule changes as well.

The total electric dipole moment is

$\vec{P}(t) = \alpha(t) \cdot \vec{E}(t)$

where

$\alpha(t)$ is the polarizability of the molecule.
$E(t)$ is the electric field (of light wave).

The Vibration and Rotation of the molecule will apparently affect the final dipole moment.

Particularly, when the molecule uniformly rotates or oscillates, the change of the polarizability is sinusoidal, which make the total dipole moment an oscillation consists of three frequencies $\nu_{0},\ \nu_{0} + \nu_{vib},\ \nu_{0}-\nu_{vib}$ .

Intrinsic Property

The energy of the molecular vibrations that are responsible for the Raman scattering is an intrinsic property of the molecule itself, which means it’s independent of the wavelength of incident light.

Oscillation of Polarizability

The oscillation of polarizability is not always sinusoidal.
Our sinusoidal description is just a simplified model, namely Harmonic Oscillator Model, which assumes that the Potential Energy of a molecule’s vibration is a perfect Parabola.

But the oscillation in reality is not harmonic, namely Anharmonicity.
There’s more detailed information when it comes to Morse Potential and Fermi Resonance.