Results for Point Group Oh



Symmetric powers of degenerate representation Eu
Vibrational overtones


Characters of symmetric powers
Power
To
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
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 0 0 0 0 0 1 0 0 Eu
2 1 0 1 0 0 0 0 0 0 0 A1g⊕Eg
3 0 0 0 0 0 1 1 1 0 0 A1u⊕A2u⊕Eu
4 1 0 2 0 0 0 0 0 0 0 A1g⊕2Eg
5 0 0 0 0 0 1 1 2 0 0 A1u⊕A2u⊕2Eu
6 2 1 2 0 0 0 0 0 0 0 2A1g⊕A2g⊕2Eg
7 0 0 0 0 0 1 1 3 0 0 A1u⊕A2u⊕3Eu
8 2 1 3 0 0 0 0 0 0 0 2A1g⊕A2g⊕3Eg
9 0 0 0 0 0 2 2 3 0 0 2A1u⊕2A2u⊕3Eu
10 2 1 4 0 0 0 0 0 0 0 2A1g⊕A2g⊕4Eg
11 0 0 0 0 0 2 2 4 0 0 2A1u⊕2A2u⊕4Eu
12 3 2 4 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4Eg
13 0 0 0 0 0 2 2 5 0 0 2A1u⊕2A2u⊕5Eu
14 3 2 5 0 0 0 0 0 0 0 3A1g⊕2A2g⊕5Eg
15 0 0 0 0 0 3 3 5 0 0 3A1u⊕3A2u⊕5Eu
16 3 2 6 0 0 0 0 0 0 0 3A1g⊕2A2g⊕6Eg
17 0 0 0 0 0 3 3 6 0 0 3A1u⊕3A2u⊕6Eu
18 4 3 6 0 0 0 0 0 0 0 4A1g⊕3A2g⊕6Eg
19 0 0 0 0 0 3 3 7 0 0 3A1u⊕3A2u⊕7Eu
20 4 3 7 0 0 0 0 0 0 0 4A1g⊕3A2g⊕7Eg



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement