Results for Point Group D12h



Symmetric powers of degenerate representation E4g
Vibrational overtones


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


Decomposition to irreducible representations
Power
To		 A1g A2g B1g B2g E1g E2g E3g E4g E5g A1u A2u B1u B2u E1u E2u E3u E4u E5u
1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E4g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g
3 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E4g
4 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕2E4g
5 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E4g
6 2 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E4g
7 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕3E4g
8 2 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E4g
9 2 2 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕3E4g
10 2 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E4g
11 2 2 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕4E4g
12 3 2 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4E4g
13 2 2 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕5E4g
14 3 2 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕5E4g
15 3 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 3A1g⊕3A2g⊕5E4g
16 3 2 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕6E4g
17 3 3 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 3A1g⊕3A2g⊕6E4g
18 4 3 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕6E4g
19 3 3 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 3A1g⊕3A2g⊕7E4g
20 4 3 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 4A1g⊕3A2g⊕7E4g


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