Chapter 3
Diatomic Molecules
Abstract The rovibrational spectroscopy of the diatomic molecule is reviewed.
The different structures are defined. The determination of the equilibrium structure
is discussed as well as the influence of higher-order effects, including the breakdown
of the Born–Oppenheimer approximation and the effect of the size of the nuclei.
3.1 Introduction
The case of the diatomic molecules is worth a separate treatment. As they are
much simpler, a more sophisticated theory may be used and the bond length is
determinable with a much higher accuracy, which permits to see the breakdown
of the Born-Oppenheimer (BO) approximation, among others. Furthermore, the
diatomic molecule is a good introduction to the more complicated case of polyatomic
molecules.
Using the center of mass as origin eliminates the translation. The vibration and the
rotation of the molecule remain. It is known from the experiment that the vibration of
the nuclei is much faster (about one hundred times) than the rotation of the molecule.
This large difference allows us to separate, to a first approximation, the vibration, and
the rotation of the molecule. In other words, the interaction between vibration and
rotation will be first neglected. We will see that this approximation is much worse
than the BO approximation (see Sect. 2.3) but it will allow us to treat in a second
step the rovibrational interaction as a perturbation.
We will also assume that the atoms are point masses. We already know that it is an
excellent approximation for the nuclei, see Appendix 2.19.2. For the atoms, it means
that the center of mass of the electrons coincides with the nucleus. We will see in
Sect. 3.7 that it is possible to check experimentally this approximation and that it is
a rather good one.
First, the behavior of the molecule will be treated according to classical mechanics.
Then, the classical Hamiltonian will be transformed into the quantum mechanical
one.
© 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_3
53
Diatomic Molecules
Abstract The rovibrational spectroscopy of the diatomic molecule is reviewed.
The different structures are defined. The determination of the equilibrium structure
is discussed as well as the influence of higher-order effects, including the breakdown
of the Born–Oppenheimer approximation and the effect of the size of the nuclei.
3.1 Introduction
The case of the diatomic molecules is worth a separate treatment. As they are
much simpler, a more sophisticated theory may be used and the bond length is
determinable with a much higher accuracy, which permits to see the breakdown
of the Born-Oppenheimer (BO) approximation, among others. Furthermore, the
diatomic molecule is a good introduction to the more complicated case of polyatomic
molecules.
Using the center of mass as origin eliminates the translation. The vibration and the
rotation of the molecule remain. It is known from the experiment that the vibration of
the nuclei is much faster (about one hundred times) than the rotation of the molecule.
This large difference allows us to separate, to a first approximation, the vibration, and
the rotation of the molecule. In other words, the interaction between vibration and
rotation will be first neglected. We will see that this approximation is much worse
than the BO approximation (see Sect. 2.3) but it will allow us to treat in a second
step the rovibrational interaction as a perturbation.
We will also assume that the atoms are point masses. We already know that it is an
excellent approximation for the nuclei, see Appendix 2.19.2. For the atoms, it means
that the center of mass of the electrons coincides with the nucleus. We will see in
Sect. 3.7 that it is possible to check experimentally this approximation and that it is
a rather good one.
First, the behavior of the molecule will be treated according to classical mechanics.
Then, the classical Hamiltonian will be transformed into the quantum mechanical
one.
© 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_3
53