Appendix B
Nonzero Independent Electric Multipole
Moments and (Hyper)polarizabilities
for Molecules of Different Symmetry
Group
a
Group
Multipole moments
(Hyper)polarizabilities
l a
H ab
X abc
U abcd
N abcde
a ab
b abc
c abcd
A a;bc
E a;bcd
B a;b;cd
C ab;cd
C 1
3
5
7
9
11
6
10
15
15
21
30
15
C i
0
5
0
9
0
6
0
15
0
21
30
15
C s
2
3
4
5
6
4
6
9
8
1 1
1 6
9
C 2
1
3
3
5
5
4
4
9
7
1 1
1 6
9
C 2h
0
3
0
5
0
4
0
9
0
1 1
1 6
9
C 2v
1
2
2
3
3
3
3
6
4
6
9
6
D 2
0
2
1
3
2
3
1
6
3
6
9
6
D 2h
0
2
0
3
0
3
0
6
0
6
9
6
C 4
1
1
1
3
3
2
2
5
3
5
8
5
S 4
0
1
2
3
2
2
2
5
4
5
8
5
C 4h
0
1
0
3
0
2
0
5
0
5
8
5
C 4v
1
1
1
2
2
2
2
4
2
3
5
4
D 2d
0
1
1
2
1
2
1
4
2
3
5
4
D 4
0
1
0
2
1
2
0
4
1
3
5
4
D 4h
0
1
0
2
0
2
0
4
0
3
5
4
C 3
1
1
3
3
3
2
4
5
5
7
10
5
S 6
0
1
0
3
0
2
0
5
0
7
10
5
C 3v
1
1
2
2
2
2
3
4
3
4
6
4
D 3
0
1
1
2
1
2
1
4
2
4
6
4
D 3d
0
1
0
2
0
2
0
4
0
4
6
4
C 3h
0
1
2
1
2
2
2
3
2
3
6
3
C 6
1
1
1
1
1
2
2
3
3
3
6
3
C 6h
0
1
0
1
0
2
0
3
0
3
6
3
D 3h
0
1
1
1
1
2
1
3
1
2
4
3
C 6v
1
1
1
1
1
2
2
3
2
2
4
3
D 6
0
1
0
1
0
2
0
3
1
2
4
3
D 6h
0
1
0
1
0
2
0
3
0
2
4
3
T
0
0
1
1
0
1
1
2
1
2
3
2
T h
0
0
0
1
0
1
0
2
0
2
3
2
T d
0
0
1
1
0
1
1
2
1
1
2
2
O
0
0
0
1
0
1
0
2
0
1
2
2
O h
0
0
0
1
0
1
0
2
0
1
2
2
C ∞v
1
1
1
1
1
2
2
3
2
2
4
3
D ∞h
0
1
0
1
0
2
0
3
0
2
4
3
K h
0
0
0
0
0
1
0
1
0
0
1
1
a
A.D. Buckingham, in Intermolecular Interaction: From Diatomic to Biopolymers, edited by B. Pullman (Wiley, New
York, 1978), pp. 1–68
© The Author(s) 2017
V.N. Cherepanov et al., Interaction-induced Electric Properties of van der Waals Complexes,
SpringerBriefs in Electrical and Magnetic Properties of Atoms, Molecules, and Clusters,
DOI 10.1007/978-3-319-49032-8
107