Rotational and Vibrational Spectra
Rotational spectra in the microwave and vibration–rotation spectra in the infrared arise from transitions among a molecule's nuclear-motion levels and reveal its bond lengths and force constants.
Definition
Rotational and vibrational spectra are the absorption or emission spectra produced by transitions between a molecule's rotational levels (microwave region) or between vibration–rotation levels (infrared region), allowed when the transition changes the molecule's electric dipole moment.
Scope
This topic covers pure rotational spectroscopy in the microwave region and rotation–vibration spectroscopy in the infrared: the selection rules requiring a changing dipole moment, the equally spaced rotational lines, the P, Q, and R branches of a vibration–rotation band, and the extraction of rotational constants, bond lengths, and vibrational frequencies from line positions. It treats both diatomic and simple polyatomic molecules.
Core questions
- What selection rules govern pure rotational and vibration–rotation transitions?
- Why do rotational lines appear nearly equally spaced in the microwave region?
- What are the P, Q, and R branches of an infrared band?
- How are bond lengths and force constants obtained from these spectra?
Key concepts
- Permanent dipole and infrared activity
- Rotational selection rule ΔJ = ±1
- Rotational constant and moment of inertia
- P, Q, and R branches
- Vibrational fundamental and overtones
- Bond length and force constant determination
Key theories
- Pure rotational spectra
- A molecule with a permanent dipole moment absorbs microwaves in transitions with ΔJ = ±1, producing a series of nearly equally spaced lines whose spacing gives the rotational constant and hence the moment of inertia and bond length.
- Vibration–rotation bands
- An infrared-active vibration combined with simultaneous rotational changes produces a band with P (ΔJ = −1) and R (ΔJ = +1) branches, and sometimes a Q branch (ΔJ = 0), from which the vibrational frequency and rotational constants are determined.
Clinical relevance
Infrared spectroscopy is a standard tool for identifying functional groups and monitoring reactions in chemistry, microwave spectroscopy gives the most precise gas-phase molecular structures, and both are central to detecting and quantifying greenhouse and trace gases in atmospheric and astrochemical remote sensing.
History
Infrared band spectra were measured in the nineteenth century but understood only after quantum mechanics provided the rotational and vibrational level scheme in the late 1920s. The development of microwave techniques during and after the Second World War turned pure rotational spectroscopy into the most accurate method for determining molecular geometries.
Key figures
- Gerhard Herzberg
- Harald Bethe
- David Dennison
Related topics
Seminal works
- herzberg1950
- hollas2004
Frequently asked questions
- Why does a homonuclear diatomic like N₂ have no infrared or microwave spectrum?
- N₂ has no permanent dipole moment, and its symmetric stretch does not create one, so neither its rotation nor its vibration can interact with light through the dipole mechanism. It is, however, detectable by Raman scattering.
- What does the spacing of rotational lines tell you?
- The lines are spaced by twice the rotational constant, which is inversely proportional to the moment of inertia. Measuring the spacing therefore yields the moment of inertia and, for a diatomic molecule, the bond length directly.