‘Far nuclei’ case (c), types I and II. If the interatomic distance in a molecule is
fairly large, and the dissociation energy is low (iodine molecule, for example), the
spin–orbit couplings in the atoms may be conserved despite of axial interatomic
field. As a result, the total momentum of an atom J a does not become meaningless.
In this case, the molecule electronic state is characterized by the quantum number
X, only (X is the sum of the J a 1 ; J a 2 projections onto the Z axis). The K, S, R
quantum numbers become meaningless. The symmetry properties (g/u; ± ) are
conserved. Mulliken subdivides case (c) into (c), type I and (c), type II cases. In the
first case, states having the same species belonging to different molecular configurations but formed from the same atomic configurations or having the same
species in terms of K-s coupling, interact and mix. In the second case, states formed
from different atomic configurations and having different species in terms of Ks coupling may interact. In the case (c), types I and II couplings, the
3 P 0 state splits
to the
3 P
þ
0 and
3 P
À
0 (0
+ and 0
− ). The relative positions of the
3 P 2 ,
3 P 1 ,
3 P
þ
0 ,
3 P
À
0
and
1 P states (2, 1, 0
+
, 0
− and 1) change compared to the X-x coupling as a result
of interactions of these and higher states. It is also essential that possibilities for the
interaction of states are increased since X is the only meaningful quantum number.
The iodine molecule is the most studied molecule described in the terms ‘far
nuclei’ case (c), types I and II. Electronic configuration of the I 2 ground state is (5p
r g )
2 (5p p u )
4 (5p p g )
4 (5p r
Ã
u Þ
0 X
1 R
þ
g ð0
þ
g Þ, common designation is 2440 X0
þ
g . The
iodine molecule has 23 valence states, that are grouped by correlation with three
dissociation limits: I(
2
P 3/2 ) + I(
2
P 3/2 ) (aa), I(
2
P 3/2 ) + I(
2
P 1/2 ) (ab) and I(
2
P 1/2 ) + I
(
2
P 1/2 ) (bb) (Fig. 4.4).
Ten states, X0
þ
g , A
0 2 u , A1 u , B′0
À
u , a1 g , C(B′′)1 u , a′0
þ
g , 2 g , as well as 3 u , (2)0
À
u ,
which unstudied at present, correlate with the (aa) limit. Ten states B0
þ
u ,0
þ
g , c1 g ,
c’1 g , 0
À
g , 2 u , (3,4)1 u , correlate with the (ab) limit and three, 0
þ
g ,1 u and 0
À
u , with the
(bb) limit (see Figs. 4.4, 4.5). The lower excited states are populated when one or
two r g , p u , p g electrons transfer to the antibonding r
Ã
u orbital.
The parallel I 2 ðB0
þ
u ← X0
þ
g Þ as well perpendicular I 2 (A1 u , C1 u ← X0
þ
g Þ
transitions occur (Fig. 4.6), and transitions to the ‘triplet’ 2431 B0
þ
u state correlating with the ab dissociation limit is the strongest.
Thus, the difference between X-x coupling and ‘far nuclei’ case (c), types I and
II implies a different classification of the electronic states and different forbiddances
for mixing. One should note that different types of coupling can occur not only in
other molecules but also in various states of the same molecule or the same state but
at different interatomic distances (see [22] and references).
Mulliken has carried out an analysis assuming that case (c), types I and II
coupling is feasible [18, 19]. He has shown that transitions to the 2431 state of I 2
molecule are the strongest mainly due to mixing of the ‘singlet’ ground 2440 state
with the 4.1 eV higher 2441 ‘triplet’ state (c), types I mixing since both states
correlate with the same p
5
Á p
5 configuration of iodine atoms. To a certain extent,
94
4 Photolysis of Free Molecules
fairly large, and the dissociation energy is low (iodine molecule, for example), the
spin–orbit couplings in the atoms may be conserved despite of axial interatomic
field. As a result, the total momentum of an atom J a does not become meaningless.
In this case, the molecule electronic state is characterized by the quantum number
X, only (X is the sum of the J a 1 ; J a 2 projections onto the Z axis). The K, S, R
quantum numbers become meaningless. The symmetry properties (g/u; ± ) are
conserved. Mulliken subdivides case (c) into (c), type I and (c), type II cases. In the
first case, states having the same species belonging to different molecular configurations but formed from the same atomic configurations or having the same
species in terms of K-s coupling, interact and mix. In the second case, states formed
from different atomic configurations and having different species in terms of Ks coupling may interact. In the case (c), types I and II couplings, the
3 P 0 state splits
to the
3 P
þ
0 and
3 P
À
0 (0
+ and 0
− ). The relative positions of the
3 P 2 ,
3 P 1 ,
3 P
þ
0 ,
3 P
À
0
and
1 P states (2, 1, 0
+
, 0
− and 1) change compared to the X-x coupling as a result
of interactions of these and higher states. It is also essential that possibilities for the
interaction of states are increased since X is the only meaningful quantum number.
The iodine molecule is the most studied molecule described in the terms ‘far
nuclei’ case (c), types I and II. Electronic configuration of the I 2 ground state is (5p
r g )
2 (5p p u )
4 (5p p g )
4 (5p r
Ã
u Þ
0 X
1 R
þ
g ð0
þ
g Þ, common designation is 2440 X0
þ
g . The
iodine molecule has 23 valence states, that are grouped by correlation with three
dissociation limits: I(
2
P 3/2 ) + I(
2
P 3/2 ) (aa), I(
2
P 3/2 ) + I(
2
P 1/2 ) (ab) and I(
2
P 1/2 ) + I
(
2
P 1/2 ) (bb) (Fig. 4.4).
Ten states, X0
þ
g , A
0 2 u , A1 u , B′0
À
u , a1 g , C(B′′)1 u , a′0
þ
g , 2 g , as well as 3 u , (2)0
À
u ,
which unstudied at present, correlate with the (aa) limit. Ten states B0
þ
u ,0
þ
g , c1 g ,
c’1 g , 0
À
g , 2 u , (3,4)1 u , correlate with the (ab) limit and three, 0
þ
g ,1 u and 0
À
u , with the
(bb) limit (see Figs. 4.4, 4.5). The lower excited states are populated when one or
two r g , p u , p g electrons transfer to the antibonding r
Ã
u orbital.
The parallel I 2 ðB0
þ
u ← X0
þ
g Þ as well perpendicular I 2 (A1 u , C1 u ← X0
þ
g Þ
transitions occur (Fig. 4.6), and transitions to the ‘triplet’ 2431 B0
þ
u state correlating with the ab dissociation limit is the strongest.
Thus, the difference between X-x coupling and ‘far nuclei’ case (c), types I and
II implies a different classification of the electronic states and different forbiddances
for mixing. One should note that different types of coupling can occur not only in
other molecules but also in various states of the same molecule or the same state but
at different interatomic distances (see [22] and references).
Mulliken has carried out an analysis assuming that case (c), types I and II
coupling is feasible [18, 19]. He has shown that transitions to the 2431 state of I 2
molecule are the strongest mainly due to mixing of the ‘singlet’ ground 2440 state
with the 4.1 eV higher 2441 ‘triplet’ state (c), types I mixing since both states
correlate with the same p
5
Á p
5 configuration of iodine atoms. To a certain extent,
94
4 Photolysis of Free Molecules