Results for Point Group C18h



Symmetric powers of degenerate representation E1g
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 1.879 1.532 1 0.347 -0.347 -1 -1.532 -1.879 -2 2 1.879 1.532 1 0.347 -0.347 -1 -1.532 -1.879 -2
2 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3
3 4 2.879 0.532 -1 -0.653 0.653 1 -0.532 -2.879 -4 4 2.879 0.532 -1 -0.653 0.653 1 -0.532 -2.879 -4
4 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5
5 6 2.532 -1.347 0 0.879 -0.879 0 1.347 -2.532 -6 6 2.532 -1.347 0 0.879 -0.879 0 1.347 -2.532 -6
6 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 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 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11
11 12 -2.532 1.347 0 -0.879 0.879 0 -1.347 2.532 -12 12 -2.532 1.347 0 -0.879 0.879 0 -1.347 2.532 -12
12 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13
13 14 -2.879 -0.532 1 0.653 -0.653 -1 0.532 2.879 -14 14 -2.879 -0.532 1 0.653 -0.653 -1 0.532 2.879 -14
14 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15
15 16 -1.879 -1.532 -1 -0.347 0.347 1 1.532 1.879 -16 16 -1.879 -1.532 -1 -0.347 0.347 1 1.532 1.879 -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 1.879 1.532 1 0.347 -0.347 -1 -1.532 -1.879 -20 20 1.879 1.532 1 0.347 -0.347 -1 -1.532 -1.879 -20
20 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 21 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g
6 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g
7 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g
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 0 2 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E1g⊕E3g⊕E5g⊕E7g
10 1 0 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g⊕2E8g
11 0 2 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E1g⊕E3g⊕E5g⊕2E7g
12 1 0 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕2E6g⊕2E8g
13 0 2 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E1g⊕E3g⊕2E5g⊕2E7g
14 1 0 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕2E4g⊕2E6g⊕2E8g
15 0 2 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E1g⊕2E3g⊕2E5g⊕2E7g
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 0 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕2E1g⊕2E3g⊕2E5g⊕2E7g
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 0 2 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕3E1g⊕2E3g⊕2E5g⊕2E7g
20 3 0 0 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕3E2g⊕2E4g⊕2E6g⊕2E8g


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