Raman Scattering Simulator: Vibrational Spectroscopy & Molecular Fingerprints

simulator intermediate ~10 min
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Δν = 1070 cm⁻¹ — Raman shift for k=500 N/m, μ=7 amu

A bond with force constant 500 N/m and reduced mass 7 amu vibrates at ~1070 cm⁻¹. With a 532 nm laser, the Stokes line appears at 565 nm and the anti-Stokes at 503 nm.

Formula

ν = (1/2π)√(k/μ) (harmonic oscillator frequency)
Δν = ν / c (Raman shift in cm⁻¹)
I_aS/I_S = ((ν₀ + ν_m)/(ν₀ - ν_m))⁴ × exp(-hcν_m/kT)

Light Meets Vibration

When a photon encounters a molecule, the electric field distorts the electron cloud, creating a transient induced dipole. If the molecule is vibrating and this vibration changes the polarizability, the scattered photon emerges with a slightly different frequency — shifted by exactly one vibrational quantum. This inelastic scattering, predicted by Smekal in 1923 and observed by C.V. Raman in 1928, won Raman the Nobel Prize in 1930.

Stokes, Anti-Stokes, and Rayleigh

Three outcomes are possible when a photon interacts with a molecule. Rayleigh scattering (elastic) dominates — the photon rebounds with unchanged frequency. Stokes scattering (the photon loses energy to vibration) produces red-shifted lines. Anti-Stokes scattering (the photon gains energy from an already-vibrating molecule) produces blue-shifted lines. The simulation visualizes all three as spectral peaks, with anti-Stokes intensity controlled by Boltzmann statistics.

Molecular Fingerprinting

Every molecule has a unique set of vibrational frequencies determined by its bonds and masses. The Raman spectrum — a plot of intensity versus shift — serves as a spectral fingerprint. Carbon tetrachloride, diamond, and aspirin each produce instantly recognizable patterns. In forensics, Raman microscopy identifies unknown powders without destroying the sample. In pharmaceuticals, it verifies pill composition through sealed blister packs.

Advanced Raman Techniques

Surface-enhanced Raman spectroscopy (SERS) amplifies signals by factors of a million using nanostructured metal surfaces, enabling single-molecule detection. Coherent anti-Stokes Raman (CARS) provides fast, background-free imaging for biological tissue. Tip-enhanced Raman (TERS) achieves nanometer spatial resolution. These advances have transformed Raman from a niche technique into a versatile tool spanning materials science, biology, and art conservation.

FAQ

What is Raman scattering?

Raman scattering is the inelastic scattering of photons by molecular vibrations. When laser light interacts with a molecule, most photons scatter elastically (Rayleigh). A tiny fraction (~1 in 10 million) gain or lose energy equal to a vibrational quantum, producing shifted frequencies. The shift pattern is a molecular fingerprint.

What are Stokes and anti-Stokes lines?

Stokes lines appear at lower frequency (longer wavelength) than the laser — the photon lost energy to a vibrational excitation. Anti-Stokes lines appear at higher frequency — the photon gained energy from a molecule already in an excited vibrational state. Anti-Stokes lines are weaker because fewer molecules are vibrationally excited at room temperature (Boltzmann statistics).

How does Raman differ from infrared spectroscopy?

IR spectroscopy requires a change in dipole moment during vibration; Raman requires a change in polarizability. Symmetric vibrations inactive in IR are often strong in Raman, and vice versa. Together they provide complete vibrational information. Raman also works through glass, in water, and requires no sample preparation.

What is the Raman shift measured in?

Raman shift is measured in wavenumbers (cm⁻¹), calculated as 1/λ_laser - 1/λ_scattered. This convention makes the shift independent of laser wavelength, allowing spectra from different lasers to be directly compared. Typical molecular vibrations range from 200 to 4000 cm⁻¹.

Sources

Embed

<iframe src="https://homo-deus.com/lab/spectroscopy/raman-scattering/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub