Raman spectroscopy is a powerful, non-destructive analytical technique used to study vibrational, rotational, and other low-frequency modes in a system. When analyzing Raman spectra, researchers report peak positions in terms of Raman shift (wavenumbers, cm⁻¹) rather than wavelength (nm). In this guide, we will explore why wavenumbers are preferred, the equations to convert between scattered wavelength and Raman shift, and how these relate to energy and frequency units.

1. The Raman Effect: Elastic vs. Inelastic Scattering

When monochromatic laser light illuminates a sample, the photons interact with molecular vibrations. Most of these photons scatter elastically, meaning they emerge with the exact same energy and wavelength as the incoming laser source. This is called Rayleigh scattering.

However, a tiny fraction (approximately 1 in 10 million photons) undergoes inelastic scattering. In this interaction, the scattered photon either loses energy to the molecule (Stokes scattering) or gains energy from the molecule (Anti-Stokes scattering). This change in energy provides direct information about the vibrational states of the chemical bonds inside the sample.

2. Why Do We Use Raman Shift (cm⁻¹)?

In spectroscopy, wavelength (λ) is measured in nanometers (nm). If you change the excitation laser (for example, from a 532 nm green laser to a 785 nm near-infrared laser), the absolute wavelength of the scattered light will change. This means that a particular chemical bond (such as the C-H stretch) would show peaks at different wavelengths depending on the laser used.

To make spectra comparable across different instruments, we calculate the Raman shift. The Raman shift is a measure of the energy difference between the incident photon and the scattered photon. Because it represents a relative difference in energy, the Raman shift of a given chemical bond remains identical regardless of the laser wavelength used. Wavenumbers (cm⁻¹) are directly proportional to energy, making them the standard unit.

3. The Conversion Formulas

To convert between the scattered wavelength (λ in nm) and the Raman shift (Δν in cm-1), we use the following equations, where λ0 is the excitation laser wavelength in nm:

Wavelength to Raman Shift:

Δν (cm⁻¹) = [ (1 / λ0) - (1 / λ) ] × 107

The factor of 107 is a conversion constant between nanometers and centimeters (1 cm = 107 nm).

Raman Shift to Wavelength:

λ (nm) = 1 / [ (1 / λ0) - (Δν / 107) ]
Example 1: Silicon Calibration Peak

Silicon has a very well-known Raman peak at 520 cm⁻¹ due to its crystal lattice vibration. If you use a 532 nm excitation laser, what scattered wavelength should your detector look for?
1. Apply the formula: λ = 1 / [ (1 / 532) - (520 / 107) ]
2. Calculate: 1/532 ≈ 0.0018797 cm⁻¹; 520 / 107 = 0.0000520 cm⁻¹.
3. Subtract: 0.0018797 - 0.0000520 = 0.0018277 cm⁻¹.
4. Invert: 1 / 0.0018277 ≈ 547.1 nm.
The scattered light for the Silicon peak will appear at 547.1 nm.

4. Relational Units: Frequency & Energy

A Raman shift of 1 cm-1 can also be expressed in other physical units representing frequency and phonon energy:

  • Frequency (GHz): Since the speed of light c ≈ 2.9979 × 1010 cm/s, a wavenumber of 1 cm-1 corresponds to a frequency of approximately 29.9792 GHz.
  • Phonon Energy (meV): Using Planck's relation (E = hν), a wavenumber shift of 1 cm-1 corresponds to an energy of approximately 0.12398 meV (millielectronvolts).

These conversions are critical when comparing optical Raman spectra with low-frequency acoustic studies, neutron scattering measurements, or theoretical DFT solid-state calculations.

For an instant way to perform these calculations and swap between laser wavelengths, check out our interactive Raman Shift Calculator.