Results for Point Group C12h



Symmetric powers of degenerate representation E2g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C12 2C6 2C4 2C3 2(C12)5 C2 i 2(S12)5 2S3 2S4 2S6 2S12 σh
1 2 1.000 -1 -2 -1 1.000 2 2 1.000 -1 -2 -1 1.000 2
2 3 0.000 0 3 0 0.000 3 3 0.000 0 3 0 0.000 3
3 4 -1.000 1 -4 1 -1.000 4 4 -1.000 1 -4 1 -1.000 4
4 5 -1.000 -1 5 -1 -1.000 5 5 -1.000 -1 5 -1 -1.000 5
5 6 0.000 0 -6 0 0.000 6 6 0.000 0 -6 0 0.000 6
6 7 1.000 1 7 1 1.000 7 7 1.000 1 7 1 1.000 7
7 8 1.000 -1 -8 -1 1.000 8 8 1.000 -1 -8 -1 1.000 8
8 9 0.000 0 9 0 0.000 9 9 0.000 0 9 0 0.000 9
9 10 -1.000 1 -10 1 -1.000 10 10 -1.000 1 -10 1 -1.000 10
10 11 -1.000 -1 11 -1 -1.000 11 11 -1.000 -1 11 -1 -1.000 11
11 12 0.000 0 -12 0 0.000 12 12 0.000 0 -12 0 0.000 12
12 13 1.000 1 13 1 1.000 13 13 1.000 1 13 1 1.000 13
13 14 1.000 -1 -14 -1 1.000 14 14 1.000 -1 -14 -1 1.000 14
14 15 0.000 0 15 0 0.000 15 15 0.000 0 15 0 0.000 15
15 16 -1.000 1 -16 1 -1.000 16 16 -1.000 1 -16 1 -1.000 16
16 17 -1.000 -1 17 -1 -1.000 17 17 -1.000 -1 17 -1 -1.000 17
17 18 0.000 0 -18 0 0.000 18 18 0.000 0 -18 0 0.000 18
18 19 1.000 1 19 1 1.000 19 19 1.000 1 19 1 1.000 19
19 20 1.000 -1 -20 -1 1.000 20 20 1.000 -1 -20 -1 1.000 20
20 21 0.000 0 21 0 0.000 21 21 0.000 0 21 0 0.000 21


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


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