Results for Point Group C12h



Symmetric powers of degenerate representation E1g
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 1.732 1 0 -1 -1.732 -2 2 1.732 1 0 -1 -1.732 -2
2 3 2.000 0 -1 0 2.000 3 3 2.000 0 -1 0 2.000 3
3 4 1.732 -1 0 1 -1.732 -4 4 1.732 -1 0 1 -1.732 -4
4 5 1.000 -1 1 -1 1.000 5 5 1.000 -1 1 -1 1.000 5
5 6 0.000 0 0 0 0.000 -6 6 -0.000 0 0 0 -0.000 -6
6 7 -1.000 1 -1 1 -1.000 7 7 -1.000 1 -1 1 -1.000 7
7 8 -1.732 1 0 -1 1.732 -8 8 -1.732 1 0 -1 1.732 -8
8 9 -2.000 0 1 0 -2.000 9 9 -2.000 0 1 0 -2.000 9
9 10 -1.732 -1 0 1 1.732 -10 10 -1.732 -1 0 1 1.732 -10
10 11 -1.000 -1 -1 -1 -1.000 11 11 -1.000 -1 -1 -1 -1.000 11
11 12 -0.000 0 0 0 -0.000 -12 12 -0.000 0 0 0 0.000 -12
12 13 1.000 1 1 1 1.000 13 13 1.000 1 1 1 1.000 13
13 14 1.732 1 0 -1 -1.732 -14 14 1.732 1 0 -1 -1.732 -14
14 15 2.000 0 -1 0 2.000 15 15 2.000 0 -1 0 2.000 15
15 16 1.732 -1 0 1 -1.732 -16 16 1.732 -1 0 1 -1.732 -16
16 17 1.000 -1 1 -1 1.000 17 17 1.000 -1 1 -1 1.000 17
17 18 0.000 0 0 0 0.000 -18 18 0.000 0 0 0 -0.000 -18
18 19 -1.000 1 -1 1 -1.000 19 19 -1.000 1 -1 1 -1.000 19
19 20 -1.732 1 0 -1 1.732 -20 20 -1.732 1 0 -1 1.732 -20
20 21 -2.000 0 1 0 -2.000 21 21 -2.000 0 1 0 -2.000 21


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


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