Results for Point Group D9d



Symmetric powers of degenerate representation E4g
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C9 2(C9)2 2C3 2(C9)4 9C'2 i 2(S18)7 2(S18)5 2S6 2S18 d
1 2 -1.879 1.532 -1 0.347 0 2 -1.879 1.532 -1 0.347 0
2 3 2.532 1.347 0 -0.879 1 3 2.532 1.347 0 -0.879 1
3 4 -2.879 0.532 1 -0.653 0 4 -2.879 0.532 1 -0.653 0
4 5 2.879 -0.532 -1 0.653 1 5 2.879 -0.532 -1 0.653 1
5 6 -2.532 -1.347 0 0.879 0 6 -2.532 -1.347 0 0.879 0
6 7 1.879 -1.532 1 -0.347 1 7 1.879 -1.532 1 -0.347 1
7 8 -1.000 -1.000 -1 -1.000 0 8 -1.000 -1.000 -1 -1.000 0
8 9 -0.000 0.000 0 0.000 1 9 -0.000 0.000 0 0.000 1
9 10 1.000 1.000 1 1.000 0 10 1.000 1.000 1 1.000 0
10 11 -1.879 1.532 -1 0.347 1 11 -1.879 1.532 -1 0.347 1
11 12 2.532 1.347 0 -0.879 0 12 2.532 1.347 0 -0.879 0
12 13 -2.879 0.532 1 -0.653 1 13 -2.879 0.532 1 -0.653 1
13 14 2.879 -0.532 -1 0.653 0 14 2.879 -0.532 -1 0.653 0
14 15 -2.532 -1.347 0 0.879 1 15 -2.532 -1.347 0 0.879 1
15 16 1.879 -1.532 1 -0.347 0 16 1.879 -1.532 1 -0.347 0
16 17 -1.000 -1.000 -1 -1.000 1 17 -1.000 -1.000 -1 -1.000 1
17 18 -0.000 0.000 0 0.000 0 18 -0.000 0.000 0 0.000 0
18 19 1.000 1.000 1 1.000 1 19 1.000 1.000 1 1.000 1
19 20 -1.879 1.532 -1 0.347 0 20 -1.879 1.532 -1 0.347 0
20 21 2.532 1.347 0 -0.879 1 21 2.532 1.347 0 -0.879 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g A1u A2u E1u E2u E3u E4u
1 0 0 0 0 0 1 0 0 0 0 0 0 E4g
2 1 0 1 0 0 0 0 0 0 0 0 0 A1g⊕E1g
3 0 0 0 0 1 1 0 0 0 0 0 0 E3g⊕E4g
4 1 0 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g
5 0 0 0 1 1 1 0 0 0 0 0 0 E2g⊕E3g⊕E4g
6 1 0 1 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
7 0 0 1 1 1 1 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g
8 1 0 1 1 1 1 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g
9 1 1 1 1 1 1 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g
10 1 0 1 1 1 2 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕2E4g
11 1 1 2 1 1 1 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g
12 1 0 1 1 2 2 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕2E4g
13 1 1 2 2 1 1 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕E3g⊕E4g
14 1 0 1 2 2 2 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕2E4g
15 1 1 2 2 2 1 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g⊕E4g
16 1 0 2 2 2 2 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g⊕2E4g
17 1 1 2 2 2 2 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g⊕2E4g
18 2 1 2 2 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g⊕2E4g
19 1 1 2 2 2 3 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g⊕3E4g
20 2 1 3 2 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕2E2g⊕2E3g⊕2E4g



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