Results for Point Group Oh



Symmetric powers of degenerate representation Eg
Vibrational overtones


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


Decomposition to irreducible representations
Power
To		 A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
1 0 0 1 0 0 0 0 0 0 0 Eg
2 1 0 1 0 0 0 0 0 0 0 A1g⊕Eg
3 1 1 1 0 0 0 0 0 0 0 A1g⊕A2g⊕Eg
4 1 0 2 0 0 0 0 0 0 0 A1g⊕2Eg
5 1 1 2 0 0 0 0 0 0 0 A1g⊕A2g⊕2Eg
6 2 1 2 0 0 0 0 0 0 0 2A1g⊕A2g⊕2Eg
7 1 1 3 0 0 0 0 0 0 0 A1g⊕A2g⊕3Eg
8 2 1 3 0 0 0 0 0 0 0 2A1g⊕A2g⊕3Eg
9 2 2 3 0 0 0 0 0 0 0 2A1g⊕2A2g⊕3Eg
10 2 1 4 0 0 0 0 0 0 0 2A1g⊕A2g⊕4Eg
11 2 2 4 0 0 0 0 0 0 0 2A1g⊕2A2g⊕4Eg
12 3 2 4 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4Eg
13 2 2 5 0 0 0 0 0 0 0 2A1g⊕2A2g⊕5Eg
14 3 2 5 0 0 0 0 0 0 0 3A1g⊕2A2g⊕5Eg
15 3 3 5 0 0 0 0 0 0 0 3A1g⊕3A2g⊕5Eg
16 3 2 6 0 0 0 0 0 0 0 3A1g⊕2A2g⊕6Eg
17 3 3 6 0 0 0 0 0 0 0 3A1g⊕3A2g⊕6Eg
18 4 3 6 0 0 0 0 0 0 0 4A1g⊕3A2g⊕6Eg
19 3 3 7 0 0 0 0 0 0 0 3A1g⊕3A2g⊕7Eg
20 4 3 7 0 0 0 0 0 0 0 4A1g⊕3A2g⊕7Eg


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