Results for Point Group D18d



Symmetric powers of degenerate representation E14
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S36 2C18 2S12 2C9 2(S36)5 2C6 2(S36)7 2(C9)2 2S4 2(C18)5 2(S36)11 2C3 2(S36)13 2(C18)7 2(S12)5 2(C9)4 2(S36)17 C2 18C'2 18σd
1 2 -1.532 0.347 1.000 -1.879 1.879 -1 -0.347 1.532 -2 1.532 -0.347 -1 1.879 -1.879 1.000 0.347 -1.532 2 0 0
2 3 1.347 -0.879 0.000 2.532 2.532 0 -0.879 1.347 3 1.347 -0.879 0 2.532 2.532 0.000 -0.879 1.347 3 1 1
3 4 -0.532 -0.653 -1.000 -2.879 2.879 1 0.653 0.532 -4 0.532 0.653 1 2.879 -2.879 -1.000 -0.653 -0.532 4 0 0
4 5 -0.532 0.653 -1.000 2.879 2.879 -1 0.653 -0.532 5 -0.532 0.653 -1 2.879 2.879 -1.000 0.653 -0.532 5 1 1
5 6 1.347 0.879 0.000 -2.532 2.532 0 -0.879 -1.347 -6 -1.347 -0.879 0 2.532 -2.532 0.000 0.879 1.347 6 0 0
6 7 -1.532 -0.347 1.000 1.879 1.879 1 -0.347 -1.532 7 -1.532 -0.347 1 1.879 1.879 1.000 -0.347 -1.532 7 1 1
7 8 1.000 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 -8 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 1.000 8 0 0
8 9 0.000 0.000 0.000 0.000 0.000 0 -0.000 -0.000 9 -0.000 -0.000 0 0.000 0.000 0.000 -0.000 -0.000 9 1 1
9 10 -1.000 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -10 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 -1.000 10 0 0
10 11 1.532 0.347 -1.000 -1.879 -1.879 -1 0.347 1.532 11 1.532 0.347 -1 -1.879 -1.879 -1.000 0.347 1.532 11 1 1
11 12 -1.347 -0.879 0.000 2.532 -2.532 0 0.879 1.347 -12 1.347 0.879 0 -2.532 2.532 0.000 -0.879 -1.347 12 0 0
12 13 0.532 -0.653 1.000 -2.879 -2.879 1 -0.653 0.532 13 0.532 -0.653 1 -2.879 -2.879 1.000 -0.653 0.532 13 1 1
13 14 0.532 0.653 1.000 2.879 -2.879 -1 -0.653 -0.532 -14 -0.532 -0.653 -1 -2.879 2.879 1.000 0.653 0.532 14 0 0
14 15 -1.347 0.879 0.000 -2.532 -2.532 0 0.879 -1.347 15 -1.347 0.879 0 -2.532 -2.532 0.000 0.879 -1.347 15 1 1
15 16 1.532 -0.347 -1.000 1.879 -1.879 1 0.347 -1.532 -16 -1.532 0.347 1 -1.879 1.879 -1.000 -0.347 1.532 16 0 0
16 17 -1.000 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 17 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 -1.000 17 1 1
17 18 -0.000 0.000 0.000 0.000 -0.000 0 0.000 -0.000 -18 -0.000 0.000 0 -0.000 0.000 0.000 -0.000 0.000 18 0 0
18 19 1.000 1.000 1.000 1.000 1.000 1 1.000 1.000 19 1.000 1.000 1 1.000 1.000 1.000 1.000 1.000 19 1 1
19 20 -1.532 0.347 1.000 -1.879 1.879 -1 -0.347 1.532 -20 1.532 -0.347 -1 1.879 -1.879 1.000 0.347 -1.532 20 0 0
20 21 1.347 -0.879 0.000 2.532 2.532 0 -0.879 1.347 21 1.347 -0.879 0 2.532 2.532 0.000 -0.879 1.347 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 E14
2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A1⊕E8
3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 E6⊕E14
4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 A1⊕E8⊕E16
5 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 E2⊕E6⊕E14
6 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 A1⊕E8⊕E12⊕E16
7 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 E2⊕E6⊕E10⊕E14
8 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 A1⊕E4⊕E8⊕E12⊕E16
9 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 B1⊕B2⊕E2⊕E6⊕E10⊕E14
10 1 0 0 0 0 0 0 2 0 0 0 1 0 0 0 1 0 0 0 1 0 A1⊕2E4⊕E8⊕E12⊕E16
11 0 0 1 1 0 1 0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 B1⊕B2⊕E2⊕E6⊕2E10⊕E14
12 1 0 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 1 0 A1⊕2E4⊕E8⊕2E12⊕E16
13 0 0 1 1 0 2 0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 B1⊕B2⊕2E2⊕E6⊕2E10⊕E14
14 1 0 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 2 0 A1⊕2E4⊕E8⊕2E12⊕2E16
15 0 0 1 1 0 2 0 0 0 2 0 0 0 2 0 0 0 1 0 0 0 B1⊕B2⊕2E2⊕2E6⊕2E10⊕E14
16 1 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 A1⊕2E4⊕2E8⊕2E12⊕2E16
17 0 0 1 1 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 B1⊕B2⊕2E2⊕2E6⊕2E10⊕2E14
18 2 1 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 2A1⊕A2⊕2E4⊕2E8⊕2E12⊕2E16
19 0 0 1 1 0 2 0 0 0 2 0 0 0 2 0 0 0 3 0 0 0 B1⊕B2⊕2E2⊕2E6⊕2E10⊕3E14
20 2 1 0 0 0 0 0 2 0 0 0 3 0 0 0 2 0 0 0 2 0 2A1⊕A2⊕2E4⊕3E8⊕2E12⊕2E16



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