(b) Interactions between crossing curves belonging the states of the same symmetry, N 2 (C
3 P u * C
0 3 P u ) [31], p. 514, as well as Rydberg and valence state
if their configurations differ by two orbitals [31], p. 310), for example.
Spin–orbit predissociation. The spin-orbit interaction is the strongest among the
fine-interaction components caused by the fine-structure operator b
H FS ¼
b
H SO þ b
H SS þ b
H SR þ b
H OR (see Table 4.2). Accordingly, the predissociation rate is
determined by the matrix elements of the S–O interaction b
H SO (see 4.6.16). Three
example of strong S–O predissociation are given in [31], Table 7.4, namely, OH
(A
2 R
+
*
4 P), electronic matrix element, H el = 57 cm
−1 , O 2 (B
3 R
À
u *
5 P u ),
H el = 65 cm
−1 , Se 2 ðB0
þ
u * 0
þ
u Þ, H el = 373 cm
−1 .
Gyroscopic (Coriolis) predissociation. It is caused mainly by the interaction of
the orbital and, to a lesser extent, the electron spin moment a with the momentum of
the rotational motion of the molecule ð b
L-uncoupling operator (4.6.20), and leads to
heterogeneous predissociation (DK = ± 1, DX = ± 1). The rate of gyroscopic
predissociation (before the discovery of hyperfine predissociation, see below, it was
called simply heterogeneous)
1=s gyr ¼ k v Á J Á J þ 1
ð
Þ
ð4:7:2Þ
where k v is the gyroscopic predissociation rate constant, J is the rotational quantum
number. For large values of J, k v can vary
k v ¼ C
2
v 1 þ p v Á JðJ þ 1Þ þ . . .
½
ð 4:7:3Þ
p v Á << C
2
v . Gyroscopic predissociation is manifested in iodine molecule B0
þ
u state.
The B state high rovibrational levels are populated in the B ← X transitions, and the
rate of gyroscopic predissociation, 1/s gyr could be large due to low rotational
constants of the X state ðB
X
e = 0.037 cm
−1 see Table A1 in [7]). The k v
250 s
−1 ,
(Fig. 4.24), and 1/s gyr < 1.3 Á 10
5 s
−1 is much less than the radiative decay rate.
It was proved that I 2 (B) state gyroscopic predissociationis due to the B * C1 u
coupling [68] since the predissociation rate follows v-dependences of B/C
Franck-Condon density (FCD) (Fig. 4.25).
Hyperfine predissociation. A coupling of the nuclear and electronic angular
momenta (the hyperfine magnetic-dipole (MD) and electric-quadrupole (MQ)
interaction, selection rules are DX = ± 1 and ± 2, respectively) is the only
non-Born–Oppenheimer term of molecular Hamiltonian that breaks g/u symmetry
of electronic states of a homonuclear diatomic molecule and mixes near-degenerate
rovibrational levels of the states of opposite electronic parity [50], see Sect. 4.6.1.4,
also. Hyperfine predissociation (HFP) was discovered in 1976 [67] and has been
fairly well studied using the example of the predissociation I 2 ðB0
þ
u Þ.
In principle, the I 2 (B) state HFP could be due to its perturbation by the all (aa)
states except the 3 u (see Sect. 4.2.3). However, it was proved that it is due to the
B * C coupling since the predissociation rate follows v-dependences of B/C
Franck-Condon density (FCD) (Fig. 4.25) just as those of B state gyroscopic
4.7 Electronic Predissociation of Di- and Polyatomic Molecules …
137
3 P u * C
0 3 P u ) [31], p. 514, as well as Rydberg and valence state
if their configurations differ by two orbitals [31], p. 310), for example.
Spin–orbit predissociation. The spin-orbit interaction is the strongest among the
fine-interaction components caused by the fine-structure operator b
H FS ¼
b
H SO þ b
H SS þ b
H SR þ b
H OR (see Table 4.2). Accordingly, the predissociation rate is
determined by the matrix elements of the S–O interaction b
H SO (see 4.6.16). Three
example of strong S–O predissociation are given in [31], Table 7.4, namely, OH
(A
2 R
+
*
4 P), electronic matrix element, H el = 57 cm
−1 , O 2 (B
3 R
À
u *
5 P u ),
H el = 65 cm
−1 , Se 2 ðB0
þ
u * 0
þ
u Þ, H el = 373 cm
−1 .
Gyroscopic (Coriolis) predissociation. It is caused mainly by the interaction of
the orbital and, to a lesser extent, the electron spin moment a with the momentum of
the rotational motion of the molecule ð b
L-uncoupling operator (4.6.20), and leads to
heterogeneous predissociation (DK = ± 1, DX = ± 1). The rate of gyroscopic
predissociation (before the discovery of hyperfine predissociation, see below, it was
called simply heterogeneous)
1=s gyr ¼ k v Á J Á J þ 1
ð
Þ
ð4:7:2Þ
where k v is the gyroscopic predissociation rate constant, J is the rotational quantum
number. For large values of J, k v can vary
k v ¼ C
2
v 1 þ p v Á JðJ þ 1Þ þ . . .
½
ð 4:7:3Þ
p v Á << C
2
v . Gyroscopic predissociation is manifested in iodine molecule B0
þ
u state.
The B state high rovibrational levels are populated in the B ← X transitions, and the
rate of gyroscopic predissociation, 1/s gyr could be large due to low rotational
constants of the X state ðB
X
e = 0.037 cm
−1 see Table A1 in [7]). The k v
250 s
−1 ,
(Fig. 4.24), and 1/s gyr < 1.3 Á 10
5 s
−1 is much less than the radiative decay rate.
It was proved that I 2 (B) state gyroscopic predissociationis due to the B * C1 u
coupling [68] since the predissociation rate follows v-dependences of B/C
Franck-Condon density (FCD) (Fig. 4.25).
Hyperfine predissociation. A coupling of the nuclear and electronic angular
momenta (the hyperfine magnetic-dipole (MD) and electric-quadrupole (MQ)
interaction, selection rules are DX = ± 1 and ± 2, respectively) is the only
non-Born–Oppenheimer term of molecular Hamiltonian that breaks g/u symmetry
of electronic states of a homonuclear diatomic molecule and mixes near-degenerate
rovibrational levels of the states of opposite electronic parity [50], see Sect. 4.6.1.4,
also. Hyperfine predissociation (HFP) was discovered in 1976 [67] and has been
fairly well studied using the example of the predissociation I 2 ðB0
þ
u Þ.
In principle, the I 2 (B) state HFP could be due to its perturbation by the all (aa)
states except the 3 u (see Sect. 4.2.3). However, it was proved that it is due to the
B * C coupling since the predissociation rate follows v-dependences of B/C
Franck-Condon density (FCD) (Fig. 4.25) just as those of B state gyroscopic
4.7 Electronic Predissociation of Di- and Polyatomic Molecules …
137