% 140–167 nm) is due to this feature. The CO 2 ground state is linear (
1 R
þ
g , D ∞h )
and first excited are bent, C 2v (
1
A 2 ,
1
B 2 (
1 R
À
u and
1 D u in the linear configuration).
Molecule CO 2 ‘remember’ that it is linear in the Franck–Condon zone, and vibronic
transitions
1 R
À
u ,
1 D u ←
1 R
þ
g are forbidden. Therefore, the absorption is weak,
though the
1
B 2 ←
1
A 1 transition is allowed.
Often, electronic and vibrational wave functions are totally symmetric for
ground electronic states, and vibronic transitions (transitions allowed due to
vibronic interactions) [13] can occur from higher vibrational antisymmetric vibrational states, which are not populated at low temperature.
4.2.2.2 Transitions in Polyatomic Molecules Allowed Due
to Electronic-Rotational Interactions
In general, electronic-rotational (Coriolis) perturbation is very weak. However, if no
other stronger perturbations exist, the Coriolis interaction can lead to weak transitions. It occurs if a neighboring state has species of rotational wave functions
different from those of the states that cannot combine in an allowed transition. This
interaction increases with quantum numbers of angular momenta J, K strongly [10],
p. 141.
4.2.2.3 Magnetic-Dipole and Electric-Quadrupole Transitions
Transition probabilities and selection rules for magnetic-dipole and
electric-quadrupole transitions are obtained if magnetic dipole moment b l(R x , R y ,
R z ) and electric-quadrupole b
Q(x
2 , y
2 , z
2 ; xy, xz, yz) operators are substituted in place
of the electric dipole transition operator in (4.2.3). One can find the selection rules
of magnetic-dipole and electric-quadrupole transitions for some most important
point groups in Table 10 of [10]. Intensities of magnetic-dipole and
electric-quadrupole transitions are *10
5 and *10
8 than those of strong electric
dipole transitions in the visible range [10], p. 134.
4.2.3 Spin–Orbit Coupling and Spin-Forbidden Transitions
If the spin-orbit interaction and splitting are not negligible, (4.2.6, 4.2.7) are invalid,
and the total electronic wave function is more complicated:
W es ¼ U Á r þ n es ;
ð4:2:13Þ
4.2 Radiative Electronic Transitions …
89
1 R
þ
g , D ∞h )
and first excited are bent, C 2v (
1
A 2 ,
1
B 2 (
1 R
À
u and
1 D u in the linear configuration).
Molecule CO 2 ‘remember’ that it is linear in the Franck–Condon zone, and vibronic
transitions
1 R
À
u ,
1 D u ←
1 R
þ
g are forbidden. Therefore, the absorption is weak,
though the
1
B 2 ←
1
A 1 transition is allowed.
Often, electronic and vibrational wave functions are totally symmetric for
ground electronic states, and vibronic transitions (transitions allowed due to
vibronic interactions) [13] can occur from higher vibrational antisymmetric vibrational states, which are not populated at low temperature.
4.2.2.2 Transitions in Polyatomic Molecules Allowed Due
to Electronic-Rotational Interactions
In general, electronic-rotational (Coriolis) perturbation is very weak. However, if no
other stronger perturbations exist, the Coriolis interaction can lead to weak transitions. It occurs if a neighboring state has species of rotational wave functions
different from those of the states that cannot combine in an allowed transition. This
interaction increases with quantum numbers of angular momenta J, K strongly [10],
p. 141.
4.2.2.3 Magnetic-Dipole and Electric-Quadrupole Transitions
Transition probabilities and selection rules for magnetic-dipole and
electric-quadrupole transitions are obtained if magnetic dipole moment b l(R x , R y ,
R z ) and electric-quadrupole b
Q(x
2 , y
2 , z
2 ; xy, xz, yz) operators are substituted in place
of the electric dipole transition operator in (4.2.3). One can find the selection rules
of magnetic-dipole and electric-quadrupole transitions for some most important
point groups in Table 10 of [10]. Intensities of magnetic-dipole and
electric-quadrupole transitions are *10
5 and *10
8 than those of strong electric
dipole transitions in the visible range [10], p. 134.
4.2.3 Spin–Orbit Coupling and Spin-Forbidden Transitions
If the spin-orbit interaction and splitting are not negligible, (4.2.6, 4.2.7) are invalid,
and the total electronic wave function is more complicated:
W es ¼ U Á r þ n es ;
ð4:2:13Þ
4.2 Radiative Electronic Transitions …
89