Results for Point Group C18



Symmetric powers of degenerate representation E7
Vibrational overtones


Characters of symmetric powers
Power
To		 E C18 C9 C6 (C9)2 (C18)5 C3 (C18)7 (C9)4 C2 (C9)5 (C18)11 (C3)2 (C18)13 (C9)7 (C6)5 (C9)8 (C18)17
1 2 -1.532 0.347 1 -1.879 1.879 -1 -0.347 1.532 -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 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 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 -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 -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 -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 -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 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 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 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 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 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 -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 -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 -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 -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 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 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 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 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347


Decomposition to irreducible representations
Power
To		 A B E1* E2* E3* E4* E5* E6* E7* E8*
1 0 0 0 0 0 0 0 0 1 0 E7
2 1 0 0 0 0 1 0 0 0 0 A⊕E4
3 0 0 0 0 1 0 0 0 1 0 E3⊕E7
4 1 0 0 0 0 1 0 0 0 1 A⊕E4⊕E8
5 0 0 1 0 1 0 0 0 1 0 E1⊕E3⊕E7
6 1 0 0 0 0 1 0 1 0 1 A⊕E4⊕E6⊕E8
7 0 0 1 0 1 0 1 0 1 0 E1⊕E3⊕E5⊕E7
8 1 0 0 1 0 1 0 1 0 1 A⊕E2⊕E4⊕E6⊕E8
9 0 2 1 0 1 0 1 0 1 0 2B⊕E1⊕E3⊕E5⊕E7
10 1 0 0 2 0 1 0 1 0 1 A⊕2E2⊕E4⊕E6⊕E8
11 0 2 1 0 1 0 2 0 1 0 2B⊕E1⊕E3⊕2E5⊕E7
12 1 0 0 2 0 1 0 2 0 1 A⊕2E2⊕E4⊕2E6⊕E8
13 0 2 2 0 1 0 2 0 1 0 2B⊕2E1⊕E3⊕2E5⊕E7
14 1 0 0 2 0 1 0 2 0 2 A⊕2E2⊕E4⊕2E6⊕2E8
15 0 2 2 0 2 0 2 0 1 0 2B⊕2E1⊕2E3⊕2E5⊕E7
16 1 0 0 2 0 2 0 2 0 2 A⊕2E2⊕2E4⊕2E6⊕2E8
17 0 2 2 0 2 0 2 0 2 0 2B⊕2E1⊕2E3⊕2E5⊕2E7
18 3 0 0 2 0 2 0 2 0 2 3A⊕2E2⊕2E4⊕2E6⊕2E8
19 0 2 2 0 2 0 2 0 3 0 2B⊕2E1⊕2E3⊕2E5⊕3E7
20 3 0 0 2 0 3 0 2 0 2 3A⊕2E2⊕3E4⊕2E6⊕2E8


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