130
6 Equilibrium Structures from Spectroscopy
The FTMW often permits measuring the rotational spectra of several isotopic
species in natural abundance such as
13 C,
15 N,
34 S. It is much more difficult to
measure the spectra of rare isotopic species such as
18 O or deuterium. In such a
case, the synthesis of an enriched sample is required, which can be tedious and
expensive. Another drawback is that only low J lines can be recorded (because of the
low temperature of the jet). For this reason, conventional Stark spectroscopy is still
used, but, now millimeterwave spectroscopy is frequently preferred because it has
access to many high J lines in a large frequency range although it is less sensitive.
See Sect. 4.12.
High-resolution infrared and Raman spectroscopies also allow us to determine
rotational constants with a precision almost as good as microwave spectroscopy.
They are particularly useful when the molecule has no dipole moment. When the
infrared spectrum is measured in the gas phase at low pressure and when the resolution
of the spectrometer is high enough, a fine structure may appear. This structure occurs
because rotational transitions are occurring at the same time as vibrational transitions.
The rovibrational energy of the molecule may be written
E υr = E υ (v) + E r (J, . . .)
(6.3)
where v is the vector of the vibrational quantum numbers (υ 1 , υ 2 , …) and J the
rotational quantum number. If a transition occurs between two levels of which the
upper is denoted by a single prime and the lower by a double prime, the frequency
ν of the rovibrational transition is given by
hν = [E υ
v
−E υ (v
)] + [E r
J
−E r (J
)]
(6.4)
where the selection rule for υ i is the same as in low-resolution vibrational spectroscopy and for J is the same as in pure rotational spectroscopy, i.e., J = 0, ±1.
From the analysis of a high-resolution rovibrational spectrum, it is possible to obtain
the ground-state rotational constants by the method of ground-state combination
differences (GSCD) (Blass and Edwards 1967). The principle of this method is quite
simple: when two transitions arrive at the same upper level, their frequency difference
only depends on the ground-state rotational constants.
A minor complication is that the values of the experimental rotational constants
of an asymmetric top depend on the reduced Hamiltonian used. For this reason, as
suggested by Watson (1977), the determinable combinations, which do not depend
on the reduction, should be used. However, these determinable combinations B
det
ξ
contain a small contribution of the distortion constants; see Sect. 4.8.2
B
rigid
ξ
= B
det
ξ − 2T ξ ξ
(6.5)
with ξ, ξ ‘, ξ “ = a, b, c and where T ξ ξ is a quartic centrifugal distortion constant as
defined by Watson, see (4.38) and (4.39). These distortion constants are small, and
they are easily calculated from the harmonic force field. It is therefore possible to take
them into account. Several computational chemistry programs provide the different
6 Equilibrium Structures from Spectroscopy
The FTMW often permits measuring the rotational spectra of several isotopic
species in natural abundance such as
13 C,
15 N,
34 S. It is much more difficult to
measure the spectra of rare isotopic species such as
18 O or deuterium. In such a
case, the synthesis of an enriched sample is required, which can be tedious and
expensive. Another drawback is that only low J lines can be recorded (because of the
low temperature of the jet). For this reason, conventional Stark spectroscopy is still
used, but, now millimeterwave spectroscopy is frequently preferred because it has
access to many high J lines in a large frequency range although it is less sensitive.
See Sect. 4.12.
High-resolution infrared and Raman spectroscopies also allow us to determine
rotational constants with a precision almost as good as microwave spectroscopy.
They are particularly useful when the molecule has no dipole moment. When the
infrared spectrum is measured in the gas phase at low pressure and when the resolution
of the spectrometer is high enough, a fine structure may appear. This structure occurs
because rotational transitions are occurring at the same time as vibrational transitions.
The rovibrational energy of the molecule may be written
E υr = E υ (v) + E r (J, . . .)
(6.3)
where v is the vector of the vibrational quantum numbers (υ 1 , υ 2 , …) and J the
rotational quantum number. If a transition occurs between two levels of which the
upper is denoted by a single prime and the lower by a double prime, the frequency
ν of the rovibrational transition is given by
hν = [E υ
v
−E υ (v
)] + [E r
J
−E r (J
)]
(6.4)
where the selection rule for υ i is the same as in low-resolution vibrational spectroscopy and for J is the same as in pure rotational spectroscopy, i.e., J = 0, ±1.
From the analysis of a high-resolution rovibrational spectrum, it is possible to obtain
the ground-state rotational constants by the method of ground-state combination
differences (GSCD) (Blass and Edwards 1967). The principle of this method is quite
simple: when two transitions arrive at the same upper level, their frequency difference
only depends on the ground-state rotational constants.
A minor complication is that the values of the experimental rotational constants
of an asymmetric top depend on the reduced Hamiltonian used. For this reason, as
suggested by Watson (1977), the determinable combinations, which do not depend
on the reduction, should be used. However, these determinable combinations B
det
ξ
contain a small contribution of the distortion constants; see Sect. 4.8.2
B
rigid
ξ
= B
det
ξ − 2T ξ ξ
(6.5)
with ξ, ξ ‘, ξ “ = a, b, c and where T ξ ξ is a quartic centrifugal distortion constant as
defined by Watson, see (4.38) and (4.39). These distortion constants are small, and
they are easily calculated from the harmonic force field. It is therefore possible to take
them into account. Several computational chemistry programs provide the different