Results for Point Group C9



Symmetric powers of degenerate representation E1
Vibrational overtones


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


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



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