1 Introduction
3
• Rotational spectra: The electric field of the radiation enters in interaction with
the rotating permanent dipole moment of the molecule. The transitions are in the
microwave (or centimeter wave) and millimeter wave ranges.
To a good approximation, it is possible to assume that the energy of the molecule is
the sum of independent electronic (E e ), vibrational (E V ), and rotational (E R ) energies.
In other words, the Hamiltonian of the molecule may be written
H = H e + H V + H R
We will see that the separation of the electronic Hamiltonian, H e , is an extremely
good approximation which, furthermore, considerably simplifies the problem. On
the other hand, the separation of the vibrational and rotational motions is only
approximate, and it will be necessary to take into account their interaction.
After the Second World War appeared nuclear magnetic resonance
(NMR) (Abragam 1961) and microwave spectroscopy (Townes and Schawlow 1955).
NMR spectroscopy is widely used to identify molecules. Although it provides information about the structure, it generally does not deliver geometrical parameters.
Nevertheless, there are two exceptions worth to be noted: (i) the NMR spectrum of a
molecule dissolved in a nematic solvent gives relations between molecular parameters. However, solvent effects limit the accuracy of this method (Diehl 1992), and (ii)
in saturated X–C–C–Y units, the spin–spin coupling constant over three bonds
3 J XY
depends primarily on the dihedral angle τ( X–C–C–Y) which can thus be obtained
using the empirical Karplus equation (1959).
Microwave spectroscopy is generally considered to be the most precise technique for obtaining molecular geometries in gas phase. This spectroscopy (as well
as high-resolution infrared spectroscopy) now determines rotational constants with
a precision close to 1 in 10
8 . If there were a simple relation between experimental
rotational constants and equilibrium geometry, it would be possible to determine the
structure of molecules with a tremendous accuracy. However, we will see that many
factors limit this accuracy. In the early days, the resolution of infrared spectra did
not permit to observe the rotational fine structure but, starting from the sixties, the
advent of Fourier transform and laser spectroscopies allowed the determination of
accurate rotational constants. This is particularly useful for molecules with no dipole
moment or with a very small dipole moment. More recently, synchrotron radiation
was used to measure rotational spectra in the submillimeter wave range with a good
sensitivity.
In quantum chemistry, the first successful attempt to calculate the structure of a
molecule was by Burrau (1927) on H 2
+ . It was followed, the same year, by the calculation of the bond length in H 2 by Heitler and London (1927). The apparition of the
computer and its considerable increase in power are also extremely important because
it permitted the development of ab initio methods, which can now provide accurate
estimates of equilibrium structures. In many cases, high-level ab initio calculations
deliver structures faster than the experimental methods and, often, with a better accuracy. Ab initio methods permit also to calculate the anharmonic force field, which
3
• Rotational spectra: The electric field of the radiation enters in interaction with
the rotating permanent dipole moment of the molecule. The transitions are in the
microwave (or centimeter wave) and millimeter wave ranges.
To a good approximation, it is possible to assume that the energy of the molecule is
the sum of independent electronic (E e ), vibrational (E V ), and rotational (E R ) energies.
In other words, the Hamiltonian of the molecule may be written
H = H e + H V + H R
We will see that the separation of the electronic Hamiltonian, H e , is an extremely
good approximation which, furthermore, considerably simplifies the problem. On
the other hand, the separation of the vibrational and rotational motions is only
approximate, and it will be necessary to take into account their interaction.
After the Second World War appeared nuclear magnetic resonance
(NMR) (Abragam 1961) and microwave spectroscopy (Townes and Schawlow 1955).
NMR spectroscopy is widely used to identify molecules. Although it provides information about the structure, it generally does not deliver geometrical parameters.
Nevertheless, there are two exceptions worth to be noted: (i) the NMR spectrum of a
molecule dissolved in a nematic solvent gives relations between molecular parameters. However, solvent effects limit the accuracy of this method (Diehl 1992), and (ii)
in saturated X–C–C–Y units, the spin–spin coupling constant over three bonds
3 J XY
depends primarily on the dihedral angle τ( X–C–C–Y) which can thus be obtained
using the empirical Karplus equation (1959).
Microwave spectroscopy is generally considered to be the most precise technique for obtaining molecular geometries in gas phase. This spectroscopy (as well
as high-resolution infrared spectroscopy) now determines rotational constants with
a precision close to 1 in 10
8 . If there were a simple relation between experimental
rotational constants and equilibrium geometry, it would be possible to determine the
structure of molecules with a tremendous accuracy. However, we will see that many
factors limit this accuracy. In the early days, the resolution of infrared spectra did
not permit to observe the rotational fine structure but, starting from the sixties, the
advent of Fourier transform and laser spectroscopies allowed the determination of
accurate rotational constants. This is particularly useful for molecules with no dipole
moment or with a very small dipole moment. More recently, synchrotron radiation
was used to measure rotational spectra in the submillimeter wave range with a good
sensitivity.
In quantum chemistry, the first successful attempt to calculate the structure of a
molecule was by Burrau (1927) on H 2
+ . It was followed, the same year, by the calculation of the bond length in H 2 by Heitler and London (1927). The apparition of the
computer and its considerable increase in power are also extremely important because
it permitted the development of ab initio methods, which can now provide accurate
estimates of equilibrium structures. In many cases, high-level ab initio calculations
deliver structures faster than the experimental methods and, often, with a better accuracy. Ab initio methods permit also to calculate the anharmonic force field, which