Results for Point Group C18h



Symmetric powers of degenerate representation E2g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C18 2C9 2C6 2(C9)2 2(C18)5 2C3 2(C18)7 2(C9)4 C2 i 2(S9)13 2(S18)7 2S3 2(S18)5 2(S9)11 2S6 2S9 2S18 σh
1 2 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 2 2 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 2
2 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3
3 4 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 4 4 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 4
4 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5
5 6 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 6 6 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 6
6 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8
8 9 -0.000 -0.000 0 -0.000 0.000 0 0.000 0.000 9 9 -0.000 -0.000 0 -0.000 0.000 0 -0.000 0.000 9
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10
10 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11
11 12 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 12 12 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 12
12 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13
13 14 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 14 14 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 14
14 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15
15 16 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 16 16 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 16
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17
17 18 -0.000 -0.000 0 -0.000 0.000 0 0.000 0.000 18 18 -0.000 -0.000 0 -0.000 0.000 0 -0.000 0.000 18
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19
19 20 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 20 20 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 20
20 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 21 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 21


Decomposition to irreducible representations
Power
To		 Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u*
1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g
3 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E6g
4 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g⊕E8g
5 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E6g⊕E8g
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g⊕E6g⊕E8g
7 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E4g⊕E6g⊕E8g
8 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g⊕E8g
9 2 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 2Ag⊕E2g⊕E4g⊕E6g⊕E8g
10 1 0 0 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕E4g⊕E6g⊕E8g
11 2 0 0 1 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 2Ag⊕E2g⊕2E4g⊕E6g⊕E8g
12 1 0 0 2 0 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕E4g⊕2E6g⊕E8g
13 2 0 0 1 0 2 0 1 0 2 0 0 0 0 0 0 0 0 0 0 2Ag⊕E2g⊕2E4g⊕E6g⊕2E8g
14 1 0 0 2 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕E4g⊕2E6g⊕2E8g
15 2 0 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2Ag⊕E2g⊕2E4g⊕2E6g⊕2E8g
16 1 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕2E4g⊕2E6g⊕2E8g
17 2 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2Ag⊕2E2g⊕2E4g⊕2E6g⊕2E8g
18 3 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 2 0 0 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2Ag⊕3E2g⊕2E4g⊕2E6g⊕2E8g
20 3 0 0 2 0 3 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E2g⊕3E4g⊕2E6g⊕2E8g


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