Results for Point Group S8



Symmetric powers of degenerate representation E3
Vibrational overtones


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


Decomposition to irreducible representations
Power
To
A B E1* E2* E3*
1 0 0 0 0 1 E3
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 2 0 1 2E1⊕E3
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 2 0 3 2E1⊕3E3
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 4 0 3 4E1⊕3E3
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 4 0 5 4E1⊕5E3
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