Rotational and Vibrational Spectroscopy

Rotational spectroscopy in the microwave region measures how molecules tumble, and vibrational spectroscopy in the infrared measures how their bonds stretch and bend, together yielding precise structural and bonding information.

Definition

Rotational and vibrational spectroscopy are the techniques that probe the quantized rotational and vibrational energy levels of molecules through absorption or scattering of microwave, infrared, and visible radiation, revealing bond lengths, force constants, and molecular geometry.

Scope

This topic covers the spectroscopy of nuclear motion: the rigid and non-rigid rotor models that give rotational energy levels and bond lengths from microwave spectra; the harmonic and anharmonic oscillator models that give vibrational frequencies and force constants from infrared spectra; and the combined rovibrational structure. It includes the gross and specific selection rules requiring a changing dipole moment for infrared and a changing polarizability for Raman scattering, normal modes of polyatomic molecules, and the use of group frequencies for identification. Electronic transitions and magnetic resonance are treated separately.

Core questions

• How do rotational energy levels yield bond lengths and moments of inertia?
• How does the harmonic oscillator model account for vibrational spectra, and why is anharmonicity needed?
• What selection rules distinguish infrared-active from Raman-active vibrations?
• How are normal modes of polyatomic molecules counted and characterized?

Key concepts

• Rigid rotor and rotational constants
• Harmonic and anharmonic oscillator
• Normal modes of vibration
• Infrared and Raman selection rules
• Group frequencies and fingerprint region

Key theories

Rigid rotor model

Treating a molecule as a rigid body gives evenly spaced rotational lines whose spacing fixes the moment of inertia and hence the bond length, with centrifugal distortion as a small correction at high rotational states.

Anharmonic oscillator and infrared selection rules

Real bonds vibrate anharmonically, giving overtones and convergence toward dissociation; absorption requires a change in dipole moment, while Raman scattering requires a change in polarizability, so the two techniques are complementary.

Clinical relevance

Infrared and Raman spectroscopy provide rapid, non-destructive identification of functional groups and compounds in chemical analysis, quality control, forensics, and materials characterization, while microwave spectroscopy yields the precise geometries used in structural chemistry and the detection of molecules in interstellar space.

History

Infrared studies of molecular vibration date to the early twentieth century and were given quantum interpretation in the 1920s; Raman's 1928 discovery of inelastic scattering opened a complementary route, and the development of microwave spectroscopy after the Second World War enabled highly precise determination of molecular geometries.

Key figures

• Gerhard Herzberg
• C. V. Raman
• Walter Gordy

Seminal works

• atkins2018
• banwell1994

Frequently asked questions

Why is carbon dioxide infrared active even though it has no permanent dipole moment?

Infrared activity requires that a vibration changes the dipole moment, not that a permanent dipole exists; the asymmetric stretch and bending modes of carbon dioxide create a transient dipole, which is also why it acts as a greenhouse gas.

How are infrared and Raman spectroscopy complementary?

A vibration is infrared active if it changes the dipole moment and Raman active if it changes the polarizability; in molecules with a centre of symmetry these are mutually exclusive, so the two methods together reveal modes that neither alone can detect.