Then, for the hyper-Rayleigh scattering directed at 90° to the propagation of
incident light the intensity (I) of the scattered light and its degree of depolarization
(ρ) take the form [62]
I $ 7A
2
þ 5B
2
;
ð5:2:5Þ
q ¼
2B
2
7A 2 þ 3B 2 :
ð5:2:6Þ
Calculated values of I and ρ are also given in Table 5.3. These values show that
under complex formation both the intensity and degree of depolarization are
decreased by *11 % and *13 %, respectively.
5.2.3 First Hyperpolarizability of Free Oriented Interacting
CH 4 and N 2 Molecules
To get the hyperpolarizability of free oriented interacting molecules CH 4 and N 2
(the case of large intermolecular distances) the hyperpolarizability b abc should be
averaged over Euler angles using Eqs. (5.1.15) and (5.2.1). In this way, taking into
account the Kleinman symmetry rules [64] the following nonzero components are
kept [49]:
b xxx ¼
9
R 4
B
A
a
B
À
B
B
a
A
À
Á
;
ð5:2:7Þ
b xyy ¼
b xzz ¼ À
9
2R 4
B
A
a
B
À
B
B
a
A
À
Á :
ð5:2:8Þ
Table 5.1 The number of nonzero and independent components of b abc for general configurations
(Fig. 3.6) of the CH 4 -N 2 complex
Configurations:
symmetry
Number of
nonzero
components
Number of
independent
components
b abc [3]
1, 3: C 3v
11
3
b xxx ,
b yyy ¼ Àb yzz ¼ Àb zyz ¼ Àb zzy ,
b xzz ¼ b zxz ¼ b xxz ¼ b xyy ¼ b yxy ¼ b yyx
2, 6: C 2v
7
3
b xxx ,
b xzz ¼ b zxz ¼ b xxz ,
4, 5: C s
14
6
b xxx , b yyy ,
b xyy ¼ b yxy ¼ b yyx , b xxy ¼ b xyx ¼ b yxx ,
b xzz ¼ b zxz ¼ b zzx , b yzz ¼ b zyz ¼ b zzy
90
5 Interaction-induced Hyperpolarizability