Results for Point Group S8



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S8 2C4 2(S8)3 C2
1 2 1.414 0 -1.414 -2
2 3 1.000 -1 1.000 3
3 4 0.000 0 0.000 -4
4 5 -1.000 1 -1.000 5
5 6 -1.414 0 1.414 -6
6 7 -1.000 -1 -1.000 7
7 8 -0.000 0 -0.000 -8
8 9 1.000 1 1.000 9
9 10 1.414 0 -1.414 -10
10 11 1.000 -1 1.000 11
11 12 0.000 0 0.000 -12
12 13 -1.000 1 -1.000 13
13 14 -1.414 0 1.414 -14
14 15 -1.000 -1 -1.000 15
15 16 -0.000 0 -0.000 -16
16 17 1.000 1 1.000 17
17 18 1.414 0 -1.414 -18
18 19 1.000 -1 1.000 19
19 20 0.000 0 0.000 -20
20 21 -1.000 1 -1.000 21


Decomposition to irreducible representations
Power
To
A B E1* E2* E3*
1 0 0 1 0 0 E1
2 1 0 0 1 0 A⊕E2
3 0 0 1 0 1 E1⊕E3
4 1 2 0 1 0 A⊕2B⊕E2
5 0 0 1 0 2 E1⊕2E3
6 1 2 0 2 0 A⊕2B⊕2E2
7 0 0 2 0 2 2E1⊕2E3
8 3 2 0 2 0 3A⊕2B⊕2E2
9 0 0 3 0 2 3E1⊕2E3
10 3 2 0 3 0 3A⊕2B⊕3E2
11 0 0 3 0 3 3E1⊕3E3
12 3 4 0 3 0 3A⊕4B⊕3E2
13 0 0 3 0 4 3E1⊕4E3
14 3 4 0 4 0 3A⊕4B⊕4E2
15 0 0 4 0 4 4E1⊕4E3
16 5 4 0 4 0 5A⊕4B⊕4E2
17 0 0 5 0 4 5E1⊕4E3
18 5 4 0 5 0 5A⊕4B⊕5E2
19 0 0 5 0 5 5E1⊕5E3
20 5 6 0 5 0 5A⊕6B⊕5E2



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement