Results for Point Group D8h



Symmetric powers of degenerate representation E1g
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 1.414 0 -1.414 -2 0 0 2 1.414 0 -1.414 -2 0 0
2 3 1.000 -1 1.000 3 1 1 3 1.000 -1 1.000 3 1 1
3 4 0.000 0 0.000 -4 0 0 4 0.000 0 0.000 -4 0 0
4 5 -1.000 1 -1.000 5 1 1 5 -1.000 1 -1.000 5 1 1
5 6 -1.414 0 1.414 -6 0 0 6 -1.414 0 1.414 -6 0 0
6 7 -1.000 -1 -1.000 7 1 1 7 -1.000 -1 -1.000 7 1 1
7 8 -0.000 0 -0.000 -8 0 0 8 -0.000 0 -0.000 -8 0 0
8 9 1.000 1 1.000 9 1 1 9 1.000 1 1.000 9 1 1
9 10 1.414 0 -1.414 -10 0 0 10 1.414 0 -1.414 -10 0 0
10 11 1.000 -1 1.000 11 1 1 11 1.000 -1 1.000 11 1 1
11 12 0.000 0 0.000 -12 0 0 12 0.000 0 0.000 -12 0 0
12 13 -1.000 1 -1.000 13 1 1 13 -1.000 1 -1.000 13 1 1
13 14 -1.414 0 1.414 -14 0 0 14 -1.414 0 1.414 -14 0 0
14 15 -1.000 -1 -1.000 15 1 1 15 -1.000 -1 -1.000 15 1 1
15 16 -0.000 0 -0.000 -16 0 0 16 -0.000 0 -0.000 -16 0 0
16 17 1.000 1 1.000 17 1 1 17 1.000 1 1.000 17 1 1
17 18 1.414 0 -1.414 -18 0 0 18 1.414 0 -1.414 -18 0 0
18 19 1.000 -1 1.000 19 1 1 19 1.000 -1 1.000 19 1 1
19 20 0.000 0 0.000 -20 0 0 20 0.000 0 0.000 -20 0 0
20 21 -1.000 1 -1.000 21 1 1 21 -1.000 1 -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 1 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 1 0 1 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 1 1 0 1 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g
5 0 0 0 0 1 0 2 0 0 0 0 0 0 0 E1g⊕2E3g
6 1 0 1 1 0 2 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕2E2g
7 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2E1g⊕2E3g
8 2 1 1 1 0 2 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕2E2g
9 0 0 0 0 3 0 2 0 0 0 0 0 0 0 3E1g⊕2E3g
10 2 1 1 1 0 3 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕3E2g
11 0 0 0 0 3 0 3 0 0 0 0 0 0 0 3E1g⊕3E3g
12 2 1 2 2 0 3 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g⊕3E2g
13 0 0 0 0 3 0 4 0 0 0 0 0 0 0 3E1g⊕4E3g
14 2 1 2 2 0 4 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g⊕4E2g
15 0 0 0 0 4 0 4 0 0 0 0 0 0 0 4E1g⊕4E3g
16 3 2 2 2 0 4 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g⊕4E2g
17 0 0 0 0 5 0 4 0 0 0 0 0 0 0 5E1g⊕4E3g
18 3 2 2 2 0 5 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g⊕5E2g
19 0 0 0 0 5 0 5 0 0 0 0 0 0 0 5E1g⊕5E3g
20 3 2 3 3 0 5 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕3B1g⊕3B2g⊕5E2g



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