Results for Point Group C12h



Symmetric powers of degenerate representation E2u
Vibrational overtones


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


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