Results for Point Group C8h



Symmetric powers of degenerate representation E1g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C8 2C4 2(C8)3 C2 i 2(S8)3 2S4 2S8 σh
1 2 1.414 0 -1.414 -2 2 1.414 0 -1.414 -2
2 3 1.000 -1 1.000 3 3 1.000 -1 1.000 3
3 4 0.000 0 0.000 -4 4 0.000 0 0.000 -4
4 5 -1.000 1 -1.000 5 5 -1.000 1 -1.000 5
5 6 -1.414 0 1.414 -6 6 -1.414 0 1.414 -6
6 7 -1.000 -1 -1.000 7 7 -1.000 -1 -1.000 7
7 8 -0.000 0 -0.000 -8 8 -0.000 0 -0.000 -8
8 9 1.000 1 1.000 9 9 1.000 1 1.000 9
9 10 1.414 0 -1.414 -10 10 1.414 0 -1.414 -10
10 11 1.000 -1 1.000 11 11 1.000 -1 1.000 11
11 12 0.000 0 0.000 -12 12 0.000 0 0.000 -12
12 13 -1.000 1 -1.000 13 13 -1.000 1 -1.000 13
13 14 -1.414 0 1.414 -14 14 -1.414 0 1.414 -14
14 15 -1.000 -1 -1.000 15 15 -1.000 -1 -1.000 15
15 16 -0.000 0 -0.000 -16 16 -0.000 0 -0.000 -16
16 17 1.000 1 1.000 17 17 1.000 1 1.000 17
17 18 1.414 0 -1.414 -18 18 1.414 0 -1.414 -18
18 19 1.000 -1 1.000 19 19 1.000 -1 1.000 19
19 20 0.000 0 0.000 -20 20 0.000 0 0.000 -20
20 21 -1.000 1 -1.000 21 21 -1.000 1 -1.000 21


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement