Raman spectroscopy: vibrational modes, Stokes and anti-Stokes lines
Aim: to record the Raman spectra of liquids, measure the Raman shifts of the Stokes and anti-Stokes lines, assign the vibrational modes, determine the sample temperature from the anti-Stokes/Stokes intensity ratio, find depolarisation ratios, and identify unknown samples.
Raman spectrometer
CCD spectrum
Positive shifts are Stokes (red-shifted) lines; negative shifts are anti-Stokes. Click a peak to fit it; drag to zoom; double-click to reset.
Observation table
Raman shift Δν̃ = 1/λ₀ − 1/λsAnalysis
Theory
Light at wavenumber \(\tilde\nu_0\) induces a dipole \(\mathbf p = \alpha\mathbf E\). If the polarisability α changes as the molecule vibrates at \(\tilde\nu_v\), the scattered light contains \(\tilde\nu_0\) (Rayleigh) and the sidebands \(\tilde\nu_0 \mp \tilde\nu_v\): the Stokes and anti-Stokes lines. The Raman shift \(\Delta\tilde\nu = \tilde\nu_0 - \tilde\nu_s\) is independent of the laser. Change the laser and check.
Anti-Stokes scattering starts from the thermally excited v = 1 level, so (counting photons with a CCD)
$$ \frac{I_{AS}}{I_S} = \left(\frac{\tilde\nu_0+\Delta\tilde\nu}{\tilde\nu_0-\Delta\tilde\nu}\right)^{3} e^{-hc\Delta\tilde\nu/kT} \;\Rightarrow\; T = \frac{hc\Delta\tilde\nu/k}{\ln\!\left[\dfrac{I_S}{I_{AS}}\left(\dfrac{\tilde\nu_0+\Delta\tilde\nu}{\tilde\nu_0-\Delta\tilde\nu}\right)^{3}\right]} .$$(The power ratio uses exponent 4. Photon counts carry one less factor of ν.)
Depolarisation ratio
\(\rho = I_\perp/I_\parallel\). Totally symmetric vibrations (A₁) give ρ < 3/4 ("polarised" bands, e.g. CCl₄ 459 cm⁻¹ with ρ ≈ 0.005). All other symmetries give ρ = 3/4.
Reference shifts (cm⁻¹)
- CCl₄: 218 (E), 314 (T₂), 459 (A₁), 762/791 (Fermi doublet)
- Benzene: 606, 849, 992 (ring breathing), 1178, 1586/1606, 3047, 3062
- Cyclohexane: 384, 426, 801, 1028, 1157, 1266, 1444, 2853, 2923, 2938
- Chloroform: 261, 366, 668, 760, 1216, 3019
- Ethanol: 433, 882, 1052, 1096, 1276, 1454, 2876, 2928, 2974
Procedure
- Insert the notch filter, focus the laser into the cuvette, and acquire.
- Click each Stokes peak and the corresponding anti-Stokes peak, and add both to the table.
- Compute the shifts and compare them with the reference values to assign the modes.
- For one strong mode, calculate T from IAS/IS. Repeat at a different set temperature.
- Record the strongest bands with the analyser ∥ and then ⊥ to obtain ρ.
- Identify the two unknown samples from their shifts.
Things to notice
- Anti-Stokes lines of high-frequency modes (C–H stretches near 3000 cm⁻¹) are invisible at room temperature, since e−hcΔν̃/kT ≈ 10⁻⁶.
- Remove the notch filter and the Rayleigh line (about 10⁶ times stronger) swamps everything.
- With the 785 nm laser the Stokes region moves into the near-IR, while the shifts stay the same.
Viva questions
Why is the Stokes line stronger than the anti-Stokes line?
Most molecules are in v = 0 at room temperature (Boltzmann). Only the small population in v = 1 can give anti-Stokes scattering.
What is the rule of mutual exclusion?
In molecules with a centre of symmetry (e.g. benzene, CO₂), no mode is both IR and Raman active. Raman needs a change in polarisability; IR needs a change in dipole moment.
Why does CCl₄ show a doublet near 776 cm⁻¹?
Fermi resonance: the ν₃ fundamental is nearly degenerate with the ν₁+ν₄ combination band (459+314 = 773 cm⁻¹) of the same symmetry, so they mix and repel.