A e B;v 0 ! e X ;v 00 $ l v 0 v 00
j
j
2 ¼ a
2
n l e B! e X
2 q v 0 v 00
ð4:6:61Þ
i.e., a
2
n =
P
n a
2
n less than that of from unperturbed e
B; v
0 level (see 4.4.2 and 4.6.59).
The e
B; v
0
! e
X ; v
00 transition oscillator strength is ‘spread’ over n—l e
A; v
0 state
levels. The authors of the [63, 64] have shown that anomalously long radiative
lifetimes of some electronically excited states of the CS 2 , SO 2 , and NO 2 molecules
are due to this factor, mainly (see a describing the similar effect in Sect. 4.8).
The radiative lifetime of the NO 2 molecule states populated at 4358 Å is *44 ls,
while that of calculated from the absorption coefficient in the 2600–7000 Å is 0.26 ls
[65], *170 times lower. The dissociation limit of the NO 2 ð e
X
2 A 1 ) state corresponds
to 3997 Å [10], Table 64), and 4358 Å corresponds to transitions to rovibronic levels
of the
2
B 1 and
2
B 2 states which lie lower than the dissociation limit. Therefore,
rovibronic levels of the
2
B 1 and
2
B 2 states interact with those of the e
X
2
A 1 state.
To describe the effect under discussion, one can apply a semi-classical
approximation. Following the e
B; v
0
e
X ; v
00 transition, a nonradiative transition
occurs from the e
B; v
0 state to the ensemble of the e
A; v levels, which cannot optically
combine with the state e
X ; v
00 and back. Let the number of levels in the e
A; v state be
large. Therefore, most of the time, the molecule is in this state. Consequently, the
radiative lifetime of the excited state ‘must’ increase.
One can note that the intermodal energy exchange in the e
A; v state can significantly increase the effect under discussion. Suppose that there are optical transitions
to the vibrational levels v
0
¼ 0 À k of the e
B state, e
B,0-k, and, as noted above, to the
vibrational levels of the e
A; v 1 state, mixing with which is allowed by energy and
symmetry considerations (active mode v 1 [66]) (see Fig. 4.21). Let mixing of the
e
B; v
0 levels with the e
A; v 2 ; v 3 levels be forbidden by the selection rules ðv 2 ; v 3 are
passive modes), and the number of active and passive levels is limited. If the k level
is high enough and, therefore, the anharmonism is great, an effective intermodal
energy exchange between the e
A; v 1 and e
A; v 2 ; v 3 levels can occur. This exchange
leads to the fact that the excited state is no longer described by the superposition of
the e
B,k and e
A; v 1 state wave functions. There is a ‘drain’ of excitation from these
levels to levels that are not mixed with the e
B; v
0 state. This ‘drain’ leads to a
decrease of the a n coefficients in (4.6.57) and a greater increase in the radiation
lifetime of the excited state. The described effect should be even stronger if the
bottom of the potential well of the e
A state is lower than the level. This is the case in
the NO 2 molecule.
In conclusion, the author notes the following. The above quantum–mechanical
explanation of the anomalously long radiative lifetime was based on a rough adiabatic approximation, i.e., assuming that the optical transition moment is independent of the nuclear coordinates. However, in many cases, this may not be the
case at all: the optical transition in absorption occurs in one nuclear configuration
4.6 Intramolecular Perturbations …
133
j
j
2 ¼ a
2
n l e B! e X
2 q v 0 v 00
ð4:6:61Þ
i.e., a
2
n =
P
n a
2
n less than that of from unperturbed e
B; v
0 level (see 4.4.2 and 4.6.59).
The e
B; v
0
! e
X ; v
00 transition oscillator strength is ‘spread’ over n—l e
A; v
0 state
levels. The authors of the [63, 64] have shown that anomalously long radiative
lifetimes of some electronically excited states of the CS 2 , SO 2 , and NO 2 molecules
are due to this factor, mainly (see a describing the similar effect in Sect. 4.8).
The radiative lifetime of the NO 2 molecule states populated at 4358 Å is *44 ls,
while that of calculated from the absorption coefficient in the 2600–7000 Å is 0.26 ls
[65], *170 times lower. The dissociation limit of the NO 2 ð e
X
2 A 1 ) state corresponds
to 3997 Å [10], Table 64), and 4358 Å corresponds to transitions to rovibronic levels
of the
2
B 1 and
2
B 2 states which lie lower than the dissociation limit. Therefore,
rovibronic levels of the
2
B 1 and
2
B 2 states interact with those of the e
X
2
A 1 state.
To describe the effect under discussion, one can apply a semi-classical
approximation. Following the e
B; v
0
e
X ; v
00 transition, a nonradiative transition
occurs from the e
B; v
0 state to the ensemble of the e
A; v levels, which cannot optically
combine with the state e
X ; v
00 and back. Let the number of levels in the e
A; v state be
large. Therefore, most of the time, the molecule is in this state. Consequently, the
radiative lifetime of the excited state ‘must’ increase.
One can note that the intermodal energy exchange in the e
A; v state can significantly increase the effect under discussion. Suppose that there are optical transitions
to the vibrational levels v
0
¼ 0 À k of the e
B state, e
B,0-k, and, as noted above, to the
vibrational levels of the e
A; v 1 state, mixing with which is allowed by energy and
symmetry considerations (active mode v 1 [66]) (see Fig. 4.21). Let mixing of the
e
B; v
0 levels with the e
A; v 2 ; v 3 levels be forbidden by the selection rules ðv 2 ; v 3 are
passive modes), and the number of active and passive levels is limited. If the k level
is high enough and, therefore, the anharmonism is great, an effective intermodal
energy exchange between the e
A; v 1 and e
A; v 2 ; v 3 levels can occur. This exchange
leads to the fact that the excited state is no longer described by the superposition of
the e
B,k and e
A; v 1 state wave functions. There is a ‘drain’ of excitation from these
levels to levels that are not mixed with the e
B; v
0 state. This ‘drain’ leads to a
decrease of the a n coefficients in (4.6.57) and a greater increase in the radiation
lifetime of the excited state. The described effect should be even stronger if the
bottom of the potential well of the e
A state is lower than the level. This is the case in
the NO 2 molecule.
In conclusion, the author notes the following. The above quantum–mechanical
explanation of the anomalously long radiative lifetime was based on a rough adiabatic approximation, i.e., assuming that the optical transition moment is independent of the nuclear coordinates. However, in many cases, this may not be the
case at all: the optical transition in absorption occurs in one nuclear configuration
4.6 Intramolecular Perturbations …
133