Results for Point Group D8h



Symmetric powers of degenerate representation E2u
Vibrational overtones


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


Decomposition to irreducible representations
Power
To
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 E2u
2 1 0 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g
3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2E2u
4 2 1 1 1 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g
5 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3E2u
6 2 1 2 2 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g
7 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4E2u
8 3 2 2 2 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g
9 0 0 0 0 0 0 0 0 0 0 0 0 5 0 5E2u
10 3 2 3 3 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕3B1g⊕3B2g
11 0 0 0 0 0 0 0 0 0 0 0 0 6 0 6E2u
12 4 3 3 3 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕3B1g⊕3B2g
13 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7E2u
14 4 3 4 4 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕4B1g⊕4B2g
15 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8E2u
16 5 4 4 4 0 0 0 0 0 0 0 0 0 0 5A1g⊕4A2g⊕4B1g⊕4B2g
17 0 0 0 0 0 0 0 0 0 0 0 0 9 0 9E2u
18 5 4 5 5 0 0 0 0 0 0 0 0 0 0 5A1g⊕4A2g⊕5B1g⊕5B2g
19 0 0 0 0 0 0 0 0 0 0 0 0 10 0 10E2u
20 6 5 5 5 0 0 0 0 0 0 0 0 0 0 6A1g⊕5A2g⊕5B1g⊕5B2g



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