Results for Point Group C12h



Symmetric powers of degenerate representation E3g
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 0.000 -2 0 2 0.000 -2 0.000 2 0 -2 0.000 2 0.000 -2 0 2 0.000 -2 0.000 2 0 -2 0.000
2 3 -1.000 3 -1 3 -1.000 3 -1.000 3 -1 3 -1.000 3 -1.000 3 -1 3 -1.000 3 -1.000 3 -1 3 -1.000
3 4 0.000 -4 0 4 0.000 -4 0.000 4 0 -4 0.000 4 0.000 -4 0 4 0.000 -4 0.000 4 0 -4 0.000
4 5 1.000 5 1 5 1.000 5 1.000 5 1 5 1.000 5 1.000 5 1 5 1.000 5 1.000 5 1 5 1.000
5 6 0.000 -6 0 6 0.000 -6 0.000 6 0 -6 0.000 6 0.000 -6 0 6 0.000 -6 0.000 6 0 -6 0.000
6 7 -1.000 7 -1 7 -1.000 7 -1.000 7 -1 7 -1.000 7 -1.000 7 -1 7 -1.000 7 -1.000 7 -1 7 -1.000
7 8 0.000 -8 0 8 0.000 -8 0.000 8 0 -8 0.000 8 0.000 -8 0 8 0.000 -8 0.000 8 0 -8 0.000
8 9 1.000 9 1 9 1.000 9 1.000 9 1 9 1.000 9 1.000 9 1 9 1.000 9 1.000 9 1 9 1.000
9 10 0.000 -10 0 10 0.000 -10 0.000 10 0 -10 0.000 10 0.000 -10 0 10 0.000 -10 0.000 10 0 -10 0.000
10 11 -1.000 11 -1 11 -1.000 11 -1.000 11 -1 11 -1.000 11 -1.000 11 -1 11 -1.000 11 -1.000 11 -1 11 -1.000
11 12 0.000 -12 0 12 0.000 -12 0.000 12 0 -12 0.000 12 0.000 -12 0 12 0.000 -12 0.000 12 0 -12 0.000
12 13 1.000 13 1 13 1.000 13 1.000 13 1 13 1.000 13 1.000 13 1 13 1.000 13 1.000 13 1 13 1.000
13 14 0.000 -14 0 14 0.000 -14 0.000 14 0 -14 0.000 14 0.000 -14 0 14 0.000 -14 0.000 14 0 -14 0.000
14 15 -1.000 15 -1 15 -1.000 15 -1.000 15 -1 15 -1.000 15 -1.000 15 -1 15 -1.000 15 -1.000 15 -1 15 -1.000
15 16 0.000 -16 0 16 0.000 -16 0.000 16 0 -16 0.000 16 0.000 -16 0 16 0.000 -16 0.000 16 0 -16 0.000
16 17 1.000 17 1 17 1.000 17 1.000 17 1 17 1.000 17 1.000 17 1 17 1.000 17 1.000 17 1 17 1.000
17 18 0.000 -18 0 18 0.000 -18 0.000 18 0 -18 0.000 18 0.000 -18 0 18 0.000 -18 0.000 18 0 -18 0.000
18 19 -1.000 19 -1 19 -1.000 19 -1.000 19 -1 19 -1.000 19 -1.000 19 -1 19 -1.000 19 -1.000 19 -1 19 -1.000
19 20 0.000 -20 0 20 0.000 -20 0.000 20 0 -20 0.000 20 0.000 -20 0 20 0.000 -20 0.000 20 0 -20 0.000
20 21 1.000 21 1 21 1.000 21 1.000 21 1 21 1.000 21 1.000 21 1 21 1.000 21 1.000 21 1 21 1.000


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 1 0 0 0 0 0 0 0 0 0 E3g
2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg
3 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2E3g
4 3 2 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg
5 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3E3g
6 3 4 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕4Bg
7 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4E3g
8 5 4 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕4Bg
9 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5E3g
10 5 6 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕6Bg
11 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6E3g
12 7 6 0 0 0 0 0 0 0 0 0 0 0 0 7Ag⊕6Bg
13 0 0 0 0 7 0 0 0 0 0 0 0 0 0 7E3g
14 7 8 0 0 0 0 0 0 0 0 0 0 0 0 7Ag⊕8Bg
15 0 0 0 0 8 0 0 0 0 0 0 0 0 0 8E3g
16 9 8 0 0 0 0 0 0 0 0 0 0 0 0 9Ag⊕8Bg
17 0 0 0 0 9 0 0 0 0 0 0 0 0 0 9E3g
18 9 10 0 0 0 0 0 0 0 0 0 0 0 0 9Ag⊕10Bg
19 0 0 0 0 10 0 0 0 0 0 0 0 0 0 10E3g
20 11 10 0 0 0 0 0 0 0 0 0 0 0 0 11Ag⊕10Bg


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