Results for Point Group Oh



Symmetric powers of degenerate representation T2u
Vibrational overtones


Characters of symmetric powers
Power
To
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
1 3 0 1 -1 -1 -3 1 0 1 -1
2 6 0 2 0 2 6 0 0 2 2
3 10 1 2 0 -2 -10 0 -1 2 -2
4 15 0 3 1 3 15 1 0 3 3
5 21 0 3 -1 -3 -21 1 0 3 -3
6 28 1 4 0 4 28 0 1 4 4
7 36 0 4 0 -4 -36 0 0 4 -4
8 45 0 5 1 5 45 1 0 5 5
9 55 1 5 -1 -5 -55 1 -1 5 -5
10 66 0 6 0 6 66 0 0 6 6
11 78 0 6 0 -6 -78 0 0 6 -6
12 91 1 7 1 7 91 1 1 7 7
13 105 0 7 -1 -7 -105 1 0 7 -7
14 120 0 8 0 8 120 0 0 8 8
15 136 1 8 0 -8 -136 0 -1 8 -8
16 153 0 9 1 9 153 1 0 9 9
17 171 0 9 -1 -9 -171 1 0 9 -9
18 190 1 10 0 10 190 0 1 10 10
19 210 0 10 0 -10 -210 0 0 10 -10
20 231 0 11 1 11 231 1 0 11 11


Decomposition to irreducible representations
Power
To
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
1 0 0 0 0 0 0 0 0 0 1 T2u
2 1 0 1 0 1 0 0 0 0 0 A1g⊕Eg⊕T2g
3 0 0 0 0 0 1 0 0 1 2 A1u⊕T1u⊕2T2u
4 2 0 2 1 2 0 0 0 0 0 2A1g⊕2Eg⊕T1g⊕2T2g
5 0 0 0 0 0 1 0 1 2 4 A1u⊕Eu⊕2T1u⊕4T2u
6 3 1 3 2 4 0 0 0 0 0 3A1g⊕A2g⊕3Eg⊕2T1g⊕4T2g
7 0 0 0 0 0 2 0 2 4 6 2A1u⊕2Eu⊕4T1u⊕6T2u
8 4 1 5 4 6 0 0 0 0 0 4A1g⊕A2g⊕5Eg⊕4T1g⊕6T2g
9 0 0 0 0 0 3 1 3 6 9 3A1u⊕A2u⊕3Eu⊕6T1u⊕9T2u
10 5 2 7 6 9 0 0 0 0 0 5A1g⊕2A2g⊕7Eg⊕6T1g⊕9T2g
11 0 0 0 0 0 4 1 5 9 12 4A1u⊕A2u⊕5Eu⊕9T1u⊕12T2u
12 7 3 9 9 12 0 0 0 0 0 7A1g⊕3A2g⊕9Eg⊕9T1g⊕12T2g
13 0 0 0 0 0 5 2 7 12 16 5A1u⊕2A2u⊕7Eu⊕12T1u⊕16T2u
14 8 4 12 12 16 0 0 0 0 0 8A1g⊕4A2g⊕12Eg⊕12T1g⊕16T2g
15 0 0 0 0 0 7 3 9 16 20 7A1u⊕3A2u⊕9Eu⊕16T1u⊕20T2u
16 10 5 15 16 20 0 0 0 0 0 10A1g⊕5A2g⊕15Eg⊕16T1g⊕20T2g
17 0 0 0 0 0 8 4 12 20 25 8A1u⊕4A2u⊕12Eu⊕20T1u⊕25T2u
18 12 7 18 20 25 0 0 0 0 0 12A1g⊕7A2g⊕18Eg⊕20T1g⊕25T2g
19 0 0 0 0 0 10 5 15 25 30 10A1u⊕5A2u⊕15Eu⊕25T1u⊕30T2u
20 14 8 22 25 30 0 0 0 0 0 14A1g⊕8A2g⊕22Eg⊕25T1g⊕30T2g



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