and spontaneous emission in another. For example, in CO 2 molecule, the absorption
in the A-band is realized from the linear ground state to the linear one in the Franck–
Condon zone, whereas the upper state is bent in the equilibrium configuration.
Besides, radiation takes place from the bent excited state to the ground state bent
configuration, though its equilibrium configuration is linear. Moreover, if the
equilibrium configurations of the upper and lower states are different, then the
transition in absorption can be carried out on one part of the PES, and the spontaneous emission occurs from the other. Part of the PES, from which the spontaneous radiative transition occurs, can be mixed with the metastable non-emitting
state, and the part of the PES, to which the transition in absorption occurs, is not
mixed. All this may lead to the fact that the matrix elements of transitions in
absorption and radiation can be different.
4.7 Electronic Predissociation of Di- and Polyatomic
Molecules. Types of Predissociation Processes
Electronic predissociation (otherwise, the first case of Herzberg predissociation
[10], p. 458) is a nonadiabatic process (on the one hand) and a consequence of
mutual perturbation of various electronic states (on the other). Here one of the
interacting states belongs to the continuous spectrum in the considered energy
region (Fig. 4.22, see Fig. 4.23, also).
Mixing of the bound W 1,v, J and repulsive (continuum) W 2,v, J states are governed
by the interaction matrix element
H v;J;E;J ¼ W 1;v;J b
H
W 2;E;J
D
E
¼ U 1 r; R
ð Þv v;J b
H
U 2 r; R
ð Þv E;J R
ð Þ
D
E
ð4:7:1Þ
The coupling operator for predissociation b
H in (4.7.1) has the same origin as for
perturbations (see [31], p. 505, Sect. 4.6.1 and Table 4.1).
Vibrational and rotational predissociation (the second and third cases of predissociation, according to Herzberg) are adiabatic processes in the sense that they
can be considered as proceeding along one PES.
We have examined the general laws for the mutual perturbation of electronic
states in Sects. 3.6 and 4.6.1.1 and seen that two adiabatic states are mixed if:
1. The species of their electronic, vibronic, electron-rotational, or rovibronic wave
functions are the same (see 3.6.5, 3.6.6a–3.6.6e);
2. In a particular region of the internal coordinates, the energy difference between
their adiabatic PECs (PESs) is relatively small, i.e., adiabatic PECs (PESs) are
close enough to each other (Fig. 4.22a), intersected (Fig. 4.22b, c)or
quasi-intersected (Fig. 4.22 d);
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4 Photolysis of Free Molecules
in the A-band is realized from the linear ground state to the linear one in the Franck–
Condon zone, whereas the upper state is bent in the equilibrium configuration.
Besides, radiation takes place from the bent excited state to the ground state bent
configuration, though its equilibrium configuration is linear. Moreover, if the
equilibrium configurations of the upper and lower states are different, then the
transition in absorption can be carried out on one part of the PES, and the spontaneous emission occurs from the other. Part of the PES, from which the spontaneous radiative transition occurs, can be mixed with the metastable non-emitting
state, and the part of the PES, to which the transition in absorption occurs, is not
mixed. All this may lead to the fact that the matrix elements of transitions in
absorption and radiation can be different.
4.7 Electronic Predissociation of Di- and Polyatomic
Molecules. Types of Predissociation Processes
Electronic predissociation (otherwise, the first case of Herzberg predissociation
[10], p. 458) is a nonadiabatic process (on the one hand) and a consequence of
mutual perturbation of various electronic states (on the other). Here one of the
interacting states belongs to the continuous spectrum in the considered energy
region (Fig. 4.22, see Fig. 4.23, also).
Mixing of the bound W 1,v, J and repulsive (continuum) W 2,v, J states are governed
by the interaction matrix element
H v;J;E;J ¼ W 1;v;J b
H
W 2;E;J
D
E
¼ U 1 r; R
ð Þv v;J b
H
U 2 r; R
ð Þv E;J R
ð Þ
D
E
ð4:7:1Þ
The coupling operator for predissociation b
H in (4.7.1) has the same origin as for
perturbations (see [31], p. 505, Sect. 4.6.1 and Table 4.1).
Vibrational and rotational predissociation (the second and third cases of predissociation, according to Herzberg) are adiabatic processes in the sense that they
can be considered as proceeding along one PES.
We have examined the general laws for the mutual perturbation of electronic
states in Sects. 3.6 and 4.6.1.1 and seen that two adiabatic states are mixed if:
1. The species of their electronic, vibronic, electron-rotational, or rovibronic wave
functions are the same (see 3.6.5, 3.6.6a–3.6.6e);
2. In a particular region of the internal coordinates, the energy difference between
their adiabatic PECs (PESs) is relatively small, i.e., adiabatic PECs (PESs) are
close enough to each other (Fig. 4.22a), intersected (Fig. 4.22b, c)or
quasi-intersected (Fig. 4.22 d);
134
4 Photolysis of Free Molecules