6.3 Determination of the Rotational Constants
131
kinds of rotational constants, see Sect. 6.11.1. A recent determination of the structure
of sulfine, CH 2 =SO, confirms that taking into account this small correction improves
the fit (Demaison et al. 2020). Neglecting the centrifugal distortion correction in the
case of SO 2 decreases the bond length by 0.00003 Å (0.003 pm) and increases the
bond angle by 0.005°.
There is another correction that is small but often larger than the centrifugal
correction: the electronic correction. This effect is discussed in Sect. 4.10.
6.3.2 Rotational Constants in a Vibrationally Excited State
Rotational constants in a vibrationally excited state are determined in the same way
as the ground-state constants. However, doing so is much more difficult. The very
efficient pulsed-jet supersonic expansion Fourier transform spectroscopy cannot be
used because the very low temperature of the jet depopulates the excited vibrational
states. The less-sensitive Stark or millimeterwave spectroscopies can only access
the low-lying vibrational states because the intensity of a rotational transition is
proportional to the population of its lower state, which is given by the Boltzmann
law exp(–E’’/kT ). If the energy of the excited vibrational state is high, above about
1000 cm
−1 , the population of its rotational levels will be small and the rotational
transitions between them will be too weak to observe. In this rather common case,
only infrared spectroscopy may be used to determine the α-constants. Of course, it
is still much more difficult for the isotopologues measured in natural abundance.
Furthermore, the rotational spectra in excited states are often complicated by
Coriolis interactions or/and Fermi resonances; see Sects. 5.5, 5.6, and 6.6.
6.4 Empirical Structures
6.4.1 Introduction
Although much progress has recently been made in the field of equilibrium structure
determinations, it is still a time-consuming task and is furthermore limited to rather
small molecules. For this reason, empirical methods are still currently used. Most
of them only use the ground-state rotational constants. They are much simpler, but
their accuracy may be rather poor.
131
kinds of rotational constants, see Sect. 6.11.1. A recent determination of the structure
of sulfine, CH 2 =SO, confirms that taking into account this small correction improves
the fit (Demaison et al. 2020). Neglecting the centrifugal distortion correction in the
case of SO 2 decreases the bond length by 0.00003 Å (0.003 pm) and increases the
bond angle by 0.005°.
There is another correction that is small but often larger than the centrifugal
correction: the electronic correction. This effect is discussed in Sect. 4.10.
6.3.2 Rotational Constants in a Vibrationally Excited State
Rotational constants in a vibrationally excited state are determined in the same way
as the ground-state constants. However, doing so is much more difficult. The very
efficient pulsed-jet supersonic expansion Fourier transform spectroscopy cannot be
used because the very low temperature of the jet depopulates the excited vibrational
states. The less-sensitive Stark or millimeterwave spectroscopies can only access
the low-lying vibrational states because the intensity of a rotational transition is
proportional to the population of its lower state, which is given by the Boltzmann
law exp(–E’’/kT ). If the energy of the excited vibrational state is high, above about
1000 cm
−1 , the population of its rotational levels will be small and the rotational
transitions between them will be too weak to observe. In this rather common case,
only infrared spectroscopy may be used to determine the α-constants. Of course, it
is still much more difficult for the isotopologues measured in natural abundance.
Furthermore, the rotational spectra in excited states are often complicated by
Coriolis interactions or/and Fermi resonances; see Sects. 5.5, 5.6, and 6.6.
6.4 Empirical Structures
6.4.1 Introduction
Although much progress has recently been made in the field of equilibrium structure
determinations, it is still a time-consuming task and is furthermore limited to rather
small molecules. For this reason, empirical methods are still currently used. Most
of them only use the ground-state rotational constants. They are much simpler, but
their accuracy may be rather poor.