Results for Point Group D9d



Symmetric powers of degenerate representation E4u
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 -1.879 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 0 0 0 0 0 0 1 E4u
2 1 0 1 0 0 0 0 0 0 0 0 0 A1g⊕E1g
3 0 0 0 0 0 0 0 0 0 0 1 1 E3u⊕E4u
4 1 0 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g
5 0 0 0 0 0 0 0 0 0 1 1 1 E2u⊕E3u⊕E4u
6 1 0 1 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
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 1 1 1 2 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕2E4g
11 0 0 0 0 0 0 1 1 2 1 1 1 A1u⊕A2u⊕2E1u⊕E2u⊕E3u⊕E4u
12 1 0 1 1 2 2 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕2E4g
13 0 0 0 0 0 0 1 1 2 2 1 1 A1u⊕A2u⊕2E1u⊕2E2u⊕E3u⊕E4u
14 1 0 1 2 2 2 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕2E4g
15 0 0 0 0 0 0 1 1 2 2 2 1 A1u⊕A2u⊕2E1u⊕2E2u⊕2E3u⊕E4u
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 2 2 2 3 A1u⊕A2u⊕2E1u⊕2E2u⊕2E3u⊕3E4u
20 2 1 3 2 2 2 0 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕2E2g⊕2E3g⊕2E4g


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