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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.

Ev≈hν(v+1/2),EJ=BhcJ(J+1)E_v\approx h\nu(v+1/2),\qquad E_J=BhcJ(J+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.

Vibrational and rotational levels
QuantityModel / rule
Key relationVibrational–rotational spectra probe quantized vibrational and rotational levels, selection rules and molecular line structure.
Meaning / useFor 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

  1. Gerhard Herzberg (1945). Molecular Spectra and Molecular Structure