2. Both states must have the same multiplicity if the spin-orbit interaction and
splitting are negligible (see Sect. 4.2.1), that is DS = 0. If it is not the case,
DS = ± 1 (see Sect. 4.2.3).
3. Both K values of the states may differ only 0 or ± 1 for Hund’s case (a, b),
DK = 0, ± 1. For Hund’s case (c), DX = 0, ± 1.
4. Rovibronic levels of both states must have the same parity: + $ + , − $ -
(see [23], p. 128)
5. For molecules with identical nuclei, u, g parity for the permutation of nuclei has
to be the same: g $ g, u $ u. The gerade and ungerade electronic state may
interact (mix) due to hyperfine or Stark perturbations, only. Besides, symmetric
(s) rotational level may interact with symmetric one, and antisymmetric (a) rotational level may interact with antisymmetric one, that is s&a (see [23], p.130
and 285).
One has to note that there are two r v -related symmetry classifications relating to
the topic under discussion, namely [31], p. 138 (r v is the operator of a reflection in
the molecule-fixed coordinate system through a plane containing the internuclear
axis; it specifies the ± parities [31], p. 70):
Total parity (the effect of the r v operator on the complete rovibronic wave
function (±);
Total parity of the complete rovibronic wave function exclusive of a (–1)
J or (–
1)
J−1/2 rotational factor for molecules with even or odd number of electrons,
respectively (e/f symmetry) (see below).
Selection rules for perturbation become more straightforward if one uses the e/f
labeling [40].
For molecules with even number of electrons (integer total angular momentum
J, omitting nuclear spin)
levels with parity þ À1
ð Þ
J is called e levels; and
levels with parity À À1
ð Þ
J is called f levels:
ð4:6:1Þ
For molecules with an odd number of electrons (half-integer total angular
momentum J, omitting nuclear spin)
Table 4.2 Parity selection
rules. The + (−) sign
indicates that the operator is
even (odd) [39] (reproduced
by permission of EDP
Science)
Operator
Total
parity
ug parity
Krönig parity for
X = 0
b
T N
+
+
+
b
H FS
a
+
+
+
b
H G
+
+
+
b
H HFS
+
No rule
No rule
b
H Z
+
+
−
b
H S
−
−
+
a b
H FS ¼ b
H SO þ b
H SS þ b
H SR þ b
H OR is fine-structure operator
108
4 Photolysis of Free Molecules
splitting are negligible (see Sect. 4.2.1), that is DS = 0. If it is not the case,
DS = ± 1 (see Sect. 4.2.3).
3. Both K values of the states may differ only 0 or ± 1 for Hund’s case (a, b),
DK = 0, ± 1. For Hund’s case (c), DX = 0, ± 1.
4. Rovibronic levels of both states must have the same parity: + $ + , − $ -
(see [23], p. 128)
5. For molecules with identical nuclei, u, g parity for the permutation of nuclei has
to be the same: g $ g, u $ u. The gerade and ungerade electronic state may
interact (mix) due to hyperfine or Stark perturbations, only. Besides, symmetric
(s) rotational level may interact with symmetric one, and antisymmetric (a) rotational level may interact with antisymmetric one, that is s&a (see [23], p.130
and 285).
One has to note that there are two r v -related symmetry classifications relating to
the topic under discussion, namely [31], p. 138 (r v is the operator of a reflection in
the molecule-fixed coordinate system through a plane containing the internuclear
axis; it specifies the ± parities [31], p. 70):
Total parity (the effect of the r v operator on the complete rovibronic wave
function (±);
Total parity of the complete rovibronic wave function exclusive of a (–1)
J or (–
1)
J−1/2 rotational factor for molecules with even or odd number of electrons,
respectively (e/f symmetry) (see below).
Selection rules for perturbation become more straightforward if one uses the e/f
labeling [40].
For molecules with even number of electrons (integer total angular momentum
J, omitting nuclear spin)
levels with parity þ À1
ð Þ
J is called e levels; and
levels with parity À À1
ð Þ
J is called f levels:
ð4:6:1Þ
For molecules with an odd number of electrons (half-integer total angular
momentum J, omitting nuclear spin)
Table 4.2 Parity selection
rules. The + (−) sign
indicates that the operator is
even (odd) [39] (reproduced
by permission of EDP
Science)
Operator
Total
parity
ug parity
Krönig parity for
X = 0
b
T N
+
+
+
b
H FS
a
+
+
+
b
H G
+
+
+
b
H HFS
+
No rule
No rule
b
H Z
+
+
−
b
H S
−
−
+
a b
H FS ¼ b
H SO þ b
H SS þ b
H SR þ b
H OR is fine-structure operator
108
4 Photolysis of Free Molecules