Physical chemistry
Vibrational and rotational spectroscopy
Vibrational–rotational spectra probe quantized vibrational and rotational levels, selection rules and molecular line structure.
For a harmonic oscillator, fundamental transitions have Δv=±1; molecular rotation creates line branches with allowed changes in J.
Vibrational and rotational levels
Vibrational–rotational spectra probe quantized vibrational and rotational levels, selection rules and molecular line structure.
Definition: Core definition
A selection rule identifies transitions with nonzero probability; for a heteronuclear diatomic, electric-dipole rotation typically has ΔJ=±1.
Example: Worked example
Apply the model to a simple case: For a rigid rotor, adjacent rotational lines are spaced by about 2B in wavenumber. Coupled vibration-rotation gives P and R branches; homonuclear diatomics can be IR-inactive.
Solution
For a rigid rotor, adjacent rotational lines are spaced by about 2B in wavenumber. Coupled vibration-rotation gives P and R branches; homonuclear diatomics can be IR-inactive.
A selection rule identifies transitions with nonzero probability; for a heteronuclear diatomic, electric-dipole rotation typically has ΔJ=±1.
| Quantity | Model / rule |
|---|---|
| Key relation | Vibrational–rotational spectra probe quantized vibrational and rotational levels, selection rules and molecular line structure. |
| Meaning / use | For a rigid rotor, adjacent rotational lines are spaced by about 2B in wavenumber. Coupled vibration-rotation gives P and R branches; homonuclear diatomics can be IR-inactive. |
What is the fundamental selection rule for a harmonic vibrational transition?
Which statement best matches the model described?
References
- Gerhard Herzberg (1945). Molecular Spectra and Molecular Structure