Results for Point Group C8h



Symmetric powers of degenerate representation E1u
Vibrational overtones


Characters of symmetric powers
Power
To
E C8 C4 (C8)3 C2 (C8)5 (C4)3 (C8)7 i (S8)5 (S4)3 (S8)7 σh S8 S4 (S8)3
1 2 1.414 0 -1.414 -2 -1.414 0 1.414 -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 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 -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 -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 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 -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 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 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 -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 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 -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 -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 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 -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 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 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 -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 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 -0.000 0 -0.000 20 0.000 0 0.000
20 21 -1.000 1 -1.000 21 -1.000 1 -1.000 21 -1.000 1 -1.000 21 -1.000 1 -1.000


Decomposition to irreducible representations
Power
To
Ag Bg E1g* E2g* E3g* Au Bu E1u* E2u* E3u*
1 0 0 0 0 0 0 0 1 0 0 E1u
2 1 0 0 1 0 0 0 0 0 0 Ag⊕E2g
3 0 0 0 0 0 0 0 1 0 1 E1u⊕E3u
4 1 2 0 1 0 0 0 0 0 0 Ag⊕2Bg⊕E2g
5 0 0 0 0 0 0 0 1 0 2 E1u⊕2E3u
6 1 2 0 2 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g
7 0 0 0 0 0 0 0 2 0 2 2E1u⊕2E3u
8 3 2 0 2 0 0 0 0 0 0 3Ag⊕2Bg⊕2E2g
9 0 0 0 0 0 0 0 3 0 2 3E1u⊕2E3u
10 3 2 0 3 0 0 0 0 0 0 3Ag⊕2Bg⊕3E2g
11 0 0 0 0 0 0 0 3 0 3 3E1u⊕3E3u
12 3 4 0 3 0 0 0 0 0 0 3Ag⊕4Bg⊕3E2g
13 0 0 0 0 0 0 0 3 0 4 3E1u⊕4E3u
14 3 4 0 4 0 0 0 0 0 0 3Ag⊕4Bg⊕4E2g
15 0 0 0 0 0 0 0 4 0 4 4E1u⊕4E3u
16 5 4 0 4 0 0 0 0 0 0 5Ag⊕4Bg⊕4E2g
17 0 0 0 0 0 0 0 5 0 4 5E1u⊕4E3u
18 5 4 0 5 0 0 0 0 0 0 5Ag⊕4Bg⊕5E2g
19 0 0 0 0 0 0 0 5 0 5 5E1u⊕5E3u
20 5 6 0 5 0 0 0 0 0 0 5Ag⊕6Bg⊕5E2g



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