Results for Point Group D9d



Symmetric powers of degenerate representation E1g
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 9σd
1 2 1.532 0.347 -1 -1.879 0 2 1.532 0.347 -1 -1.879 0
2 3 1.347 -0.879 0 2.532 1 3 1.347 -0.879 0 2.532 1
3 4 0.532 -0.653 1 -2.879 0 4 0.532 -0.653 1 -2.879 0
4 5 -0.532 0.653 -1 2.879 1 5 -0.532 0.653 -1 2.879 1
5 6 -1.347 0.879 0 -2.532 0 6 -1.347 0.879 0 -2.532 0
6 7 -1.532 -0.347 1 1.879 1 7 -1.532 -0.347 1 1.879 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 1.532 0.347 -1 -1.879 1 11 1.532 0.347 -1 -1.879 1
11 12 1.347 -0.879 0 2.532 0 12 1.347 -0.879 0 2.532 0
12 13 0.532 -0.653 1 -2.879 1 13 0.532 -0.653 1 -2.879 1
13 14 -0.532 0.653 -1 2.879 0 14 -0.532 0.653 -1 2.879 0
14 15 -1.347 0.879 0 -2.532 1 15 -1.347 0.879 0 -2.532 1
15 16 -1.532 -0.347 1 1.879 0 16 -1.532 -0.347 1 1.879 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 1.532 0.347 -1 -1.879 0 20 1.532 0.347 -1 -1.879 0
20 21 1.347 -0.879 0 2.532 1 21 1.347 -0.879 0 2.532 1


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


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