Selection Rules for Pure Rotational Raman Transitions
Important for: CSIR-NET, GATE, SET, JAM, and other competitive exams in Physical Chemistry (Molecular Spectroscopy)
Pure rotational Raman spectroscopy involves scattering where the change is due to rotational energy levels. Unlike microwave (pure rotational absorption/emission), which requires a permanent dipole moment (ΔJ = ±1), Raman requires anisotropic polarizability (polarizability changes with orientation).
Gross Selection Rule
- The molecule must have anisotropic polarizability (polarizability tensor not spherical).
- Spherical tops (e.g., CH4, SF6) have isotropic polarizability → no pure rotational Raman spectrum.
- All other molecules (linear, symmetric tops, asymmetric tops) show rotational Raman spectra, even if non-polar (e.g., N2, CO2, H2).
Specific Selection Rules by Rotor Type
| Rotor Type | Selection Rules | Branches Observed | Examples | Notes |
|---|---|---|---|---|
| Linear Molecules | ΔJ = 0, ±2 (ΔJ = 0 is Rayleigh scattering) |
O (ΔJ = -2), Q (ΔJ = 0), S (ΔJ = +2) | HCl, CO, N2, CO2, HC≡CH | Stokes lines: S-branch (ΔJ = +2); Anti-Stokes: O-branch (ΔJ = -2). Lines spaced by ~4B (first Stokes at 6B). |
| Symmetric Tops (Prolate/Oblate) | ΔJ = 0, ±1, ±2 ΔK = 0 |
O, P, Q, R, S branches (But effectively similar to linear due to ΔK=0) |
NH3, CH3Cl, BF3, C6H6 | K-independent transitions dominate; spectrum resembles linear molecules with spacing ~4B. ΔJ=±1 allowed unlike linear. |
| Spherical Tops | No transitions | No spectrum | CH4, SF6, CCl4 | Isotropic polarizability → inactive. |
| Asymmetric Tops | ΔJ = 0, ±1, ±2 (No simple ΔK; complex rules based on symmetry) |
Complex (O, P, Q, R, S possible) | H2O, SO2, CH3OH | Spectrum is complicated; no closed-form expression; often resembles symmetric top if near-symmetric. |
Differences from Microwave Rotational Spectroscopy
- Microwave: Requires permanent dipole → ΔJ = ±1 (no Q branch).
- Raman: Requires anisotropic polarizability → ΔJ = 0, ±2 (primarily) for linear; allows study of non-polar molecules.
- Reason for ΔJ = ±2: Raman involves two photons (virtual absorption + emission), allowing change in angular momentum up to 2 units.
Important Points for Exams
- Linear molecules (even homonuclear like H2, N2) show rotational Raman but not microwave spectra.
- Spherical tops show neither (except weak due to distortion).
- Stokes lines (lower frequency): ΔJ = +2 (S-branch dominant).
- Anti-Stokes: ΔJ = -2 (O-branch).
- Intensity alternation in homonuclear diatomics (e.g., H2: 3:1 for ortho:para).
Exam Tip: Questions often compare IR/microwave vs Raman activity. Remember: Raman complements microwave for non-polar molecules; spherical tops inactive in both pure rotational techniques.