Molecular Spectra

Phase 3: Molecules and Spectroscopy

Syllabus Goal

Rotational, vibrational, and electronic spectra. Franck-Condon principle. Raman effect.

Spectra Types

1. Rotational (Microwave): $\Delta J = \pm 1$. Energy $E_J = B J(J+1)$.
2. Vibrational (IR): $\Delta v = \pm 1$. Energy $E_v = \hbar\omega(v + 1/2)$.
3. Electronic (UV/Visible): Transitions between electronic states.

Franck-Condon Principle

Electronic transitions are vertical on the potential energy diagram. Nuclear positions don’t change during the fast electronic transition. Intensity $\propto |\langle \psi_{v’} | \psi_{v} \rangle|^2$.

Raman Effect

Inelastic scattering of photons.

• Stokes: Emitted photon has lower energy (molecule gains energy).
• Anti-Stokes: Emitted photon has higher energy (molecule loses energy).