Chapter 4
Rotation of the Polyatomic Molecule
Abstract The rotational spectroscopy of the polyatomic molecule is reviewed. The
determination of the rotational constants for the different types of rotors is discussed.
The rovibrational correction and the electronic correction to the rotational constants
are also described. Finally, the experimental methods are briefly presented.
4.1 Introduction
This chapter is not intended to be a comprehensive review of rotational spectroscopy
because there are several reference books: Bunker and Jensen (1998), Gordy and
Cook (1984), Kroto (1992), Papousek and Aliev (1982), Perrin et al. (2011), Quack
and Merkt (2011). Only the notions essential to understand how experimental data
and structural information will be given.
We will initially consider a molecule of N atoms assumed to be point masses before
examining the quantum mechanics of molecular rotation in Sects. 4.4–4.8. We will
furthermore first assume that this molecule is rigid: The distances between the atoms
remain constants, in other words, there is no vibration. The experimental observables
of moment of inertia and of rotational constant will be introduced. These parameters
play an essential part in a structure determination. From the study of the diatomic
molecule, it is known that the non-rigidity effects are not negligible. Centrifugal
distortion will be discussed succinctly as well as the vibrational dependence of the
rotational constants. The rovibrational correction to the rotational constants will be
discussed in more detail in Sects. 5.5, 5.6, and 6.2. In particular, the Coriolis interaction, which is sometimes important for the analysis of the spectra and for the determination of rotational constants in vibrationally excited states, will be introduced in
Sect. 5.5.
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_4
79
Rotation of the Polyatomic Molecule
Abstract The rotational spectroscopy of the polyatomic molecule is reviewed. The
determination of the rotational constants for the different types of rotors is discussed.
The rovibrational correction and the electronic correction to the rotational constants
are also described. Finally, the experimental methods are briefly presented.
4.1 Introduction
This chapter is not intended to be a comprehensive review of rotational spectroscopy
because there are several reference books: Bunker and Jensen (1998), Gordy and
Cook (1984), Kroto (1992), Papousek and Aliev (1982), Perrin et al. (2011), Quack
and Merkt (2011). Only the notions essential to understand how experimental data
and structural information will be given.
We will initially consider a molecule of N atoms assumed to be point masses before
examining the quantum mechanics of molecular rotation in Sects. 4.4–4.8. We will
furthermore first assume that this molecule is rigid: The distances between the atoms
remain constants, in other words, there is no vibration. The experimental observables
of moment of inertia and of rotational constant will be introduced. These parameters
play an essential part in a structure determination. From the study of the diatomic
molecule, it is known that the non-rigidity effects are not negligible. Centrifugal
distortion will be discussed succinctly as well as the vibrational dependence of the
rotational constants. The rovibrational correction to the rotational constants will be
discussed in more detail in Sects. 5.5, 5.6, and 6.2. In particular, the Coriolis interaction, which is sometimes important for the analysis of the spectra and for the determination of rotational constants in vibrationally excited states, will be introduced in
Sect. 5.5.
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_4
79