Results for Point Group D9d



Symmetric powers of degenerate representation E1u
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 1.532 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 0 0 0 0 0 0 1 0 0 0 E1u
2 1 0 0 1 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 0 0 0 0 1 0 1 0 E1u⊕E3u
4 1 0 0 1 0 1 0 0 0 0 0 0 A1g⊕E2g⊕E4g
5 0 0 0 0 0 0 0 0 1 0 1 1 E1u⊕E3u⊕E4u
6 1 0 0 1 1 1 0 0 0 0 0 0 A1g⊕E2g⊕E3g⊕E4g
7 0 0 0 0 0 0 0 0 1 1 1 1 E1u⊕E2u⊕E3u⊕E4u
8 1 0 1 1 1 1 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g
9 0 0 0 0 0 0 1 1 1 1 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕E4u
10 1 0 2 1 1 1 0 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕E3g⊕E4g
11 0 0 0 0 0 0 1 1 1 2 1 1 A1u⊕A2u⊕E1u⊕2E2u⊕E3u⊕E4u
12 1 0 2 1 2 1 0 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕2E3g⊕E4g
13 0 0 0 0 0 0 1 1 1 2 1 2 A1u⊕A2u⊕E1u⊕2E2u⊕E3u⊕2E4u
14 1 0 2 1 2 2 0 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕2E3g⊕2E4g
15 0 0 0 0 0 0 1 1 1 2 2 2 A1u⊕A2u⊕E1u⊕2E2u⊕2E3u⊕2E4u
16 1 0 2 2 2 2 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g⊕2E4g
17 0 0 0 0 0 0 1 1 2 2 2 2 A1u⊕A2u⊕2E1u⊕2E2u⊕2E3u⊕2E4u
18 2 1 2 2 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g⊕2E4g
19 0 0 0 0 0 0 1 1 3 2 2 2 A1u⊕A2u⊕3E1u⊕2E2u⊕2E3u⊕2E4u
20 2 1 2 3 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕3E2g⊕2E3g⊕2E4g



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