334
6 Molecular Systems
Fig. 6.20 Microdensitometer trace from a photographic plate recording the pure rotational Raman
spectrum of 12 C 16 O 2 . This spectrum shows both anti-Stokes and Stokes components of the
O-branch and a strong Q-branch. From Edwards [39], with permission by Springer
Although the 12 C 17 O 2 isotopologue of CO 2 is also a centrosymmetric linear
molecule, the equivalent 17 O nuclei, with nuclear spin I a =
5
2 , are fermions, so
that z rot−nuc (T ) is given by
z rot−nuc (T ) = 15
j =even
(2j + 1)e
−j (j+1)) rot /T
+ 21
j =odd
(2j + 1)e
−j (j+1)) rot /T
according to Eq. (6.2.108). The rotational fine-structure P - and R-branches for this
isotopologue of CO 2 will thus have alternating intensities in the ratio 5:7 for j e :j o
and adjacent lines in each branch will be separated by 2B 0 , rather than by 4B 0 .
Finally, the 18 O 12 C 16 O isotopologue of CO 2 is a noncentrosymmetric linear
molecule, so that the combined rotational-nuclear spin partition function is given
by z rot (T )z nuc , with z nuc = 1 and z rot (T ) given by Eq. (6.2.59), as
z rot−nuc (T ) =
∞
j =0
(2j + 1)e
−j (j+1)) rot /T .
There will thus be no intensity alternations in the rotational fine-structure infrared
spectra of this CO 2 isotopologue, and the separation between adjacent lines in each
fine-structure branch will be 2B 0 .
6 Molecular Systems
Fig. 6.20 Microdensitometer trace from a photographic plate recording the pure rotational Raman
spectrum of 12 C 16 O 2 . This spectrum shows both anti-Stokes and Stokes components of the
O-branch and a strong Q-branch. From Edwards [39], with permission by Springer
Although the 12 C 17 O 2 isotopologue of CO 2 is also a centrosymmetric linear
molecule, the equivalent 17 O nuclei, with nuclear spin I a =
5
2 , are fermions, so
that z rot−nuc (T ) is given by
z rot−nuc (T ) = 15
j =even
(2j + 1)e
−j (j+1)) rot /T
+ 21
j =odd
(2j + 1)e
−j (j+1)) rot /T
according to Eq. (6.2.108). The rotational fine-structure P - and R-branches for this
isotopologue of CO 2 will thus have alternating intensities in the ratio 5:7 for j e :j o
and adjacent lines in each branch will be separated by 2B 0 , rather than by 4B 0 .
Finally, the 18 O 12 C 16 O isotopologue of CO 2 is a noncentrosymmetric linear
molecule, so that the combined rotational-nuclear spin partition function is given
by z rot (T )z nuc , with z nuc = 1 and z rot (T ) given by Eq. (6.2.59), as
z rot−nuc (T ) =
∞
j =0
(2j + 1)e
−j (j+1)) rot /T .
There will thus be no intensity alternations in the rotational fine-structure infrared
spectra of this CO 2 isotopologue, and the separation between adjacent lines in each
fine-structure branch will be 2B 0 .