Results for Point Group D3d



Symmetric powers of degenerate representation Eu
Vibrational overtones


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


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



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