Results for Point Group D9



Symmetric powers of degenerate representation E1
Vibrational overtones


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


Decomposition to irreducible representations
Power
To		 A1 A2 E1 E2 E3 E4
1 0 0 1 0 0 0 E1
2 1 0 0 1 0 0 A1⊕E2
3 0 0 1 0 1 0 E1⊕E3
4 1 0 0 1 0 1 A1⊕E2⊕E4
5 0 0 1 0 1 1 E1⊕E3⊕E4
6 1 0 0 1 1 1 A1⊕E2⊕E3⊕E4
7 0 0 1 1 1 1 E1⊕E2⊕E3⊕E4
8 1 0 1 1 1 1 A1⊕E1⊕E2⊕E3⊕E4
9 1 1 1 1 1 1 A1⊕A2⊕E1⊕E2⊕E3⊕E4
10 1 0 2 1 1 1 A1⊕2E1⊕E2⊕E3⊕E4
11 1 1 1 2 1 1 A1⊕A2⊕E1⊕2E2⊕E3⊕E4
12 1 0 2 1 2 1 A1⊕2E1⊕E2⊕2E3⊕E4
13 1 1 1 2 1 2 A1⊕A2⊕E1⊕2E2⊕E3⊕2E4
14 1 0 2 1 2 2 A1⊕2E1⊕E2⊕2E3⊕2E4
15 1 1 1 2 2 2 A1⊕A2⊕E1⊕2E2⊕2E3⊕2E4
16 1 0 2 2 2 2 A1⊕2E1⊕2E2⊕2E3⊕2E4
17 1 1 2 2 2 2 A1⊕A2⊕2E1⊕2E2⊕2E3⊕2E4
18 2 1 2 2 2 2 2A1⊕A2⊕2E1⊕2E2⊕2E3⊕2E4
19 1 1 3 2 2 2 A1⊕A2⊕3E1⊕2E2⊕2E3⊕2E4
20 2 1 2 3 2 2 2A1⊕A2⊕2E1⊕3E2⊕2E3⊕2E4


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