Results for Point Group Oh



Symmetric powers of degenerate representation T1g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 8C3 6C2 6C4 3C2 i 6S4 8S6 3σh 6σd
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 1 0 0 0 0 0 0 T1g
2 1 0 1 0 1 0 0 0 0 0 A1g⊕Eg⊕T2g
3 0 1 0 2 1 0 0 0 0 0 A2g⊕2T1g⊕T2g
4 2 0 2 1 2 0 0 0 0 0 2A1g⊕2Eg⊕T1g⊕2T2g
5 0 1 1 4 2 0 0 0 0 0 A2g⊕Eg⊕4T1g⊕2T2g
6 3 1 3 2 4 0 0 0 0 0 3A1g⊕A2g⊕3Eg⊕2T1g⊕4T2g
7 0 2 2 6 4 0 0 0 0 0 2A2g⊕2Eg⊕6T1g⊕4T2g
8 4 1 5 4 6 0 0 0 0 0 4A1g⊕A2g⊕5Eg⊕4T1g⊕6T2g
9 1 3 3 9 6 0 0 0 0 0 A1g⊕3A2g⊕3Eg⊕9T1g⊕6T2g
10 5 2 7 6 9 0 0 0 0 0 5A1g⊕2A2g⊕7Eg⊕6T1g⊕9T2g
11 1 4 5 12 9 0 0 0 0 0 A1g⊕4A2g⊕5Eg⊕12T1g⊕9T2g
12 7 3 9 9 12 0 0 0 0 0 7A1g⊕3A2g⊕9Eg⊕9T1g⊕12T2g
13 2 5 7 16 12 0 0 0 0 0 2A1g⊕5A2g⊕7Eg⊕16T1g⊕12T2g
14 8 4 12 12 16 0 0 0 0 0 8A1g⊕4A2g⊕12Eg⊕12T1g⊕16T2g
15 3 7 9 20 16 0 0 0 0 0 3A1g⊕7A2g⊕9Eg⊕20T1g⊕16T2g
16 10 5 15 16 20 0 0 0 0 0 10A1g⊕5A2g⊕15Eg⊕16T1g⊕20T2g
17 4 8 12 25 20 0 0 0 0 0 4A1g⊕8A2g⊕12Eg⊕25T1g⊕20T2g
18 12 7 18 20 25 0 0 0 0 0 12A1g⊕7A2g⊕18Eg⊕20T1g⊕25T2g
19 5 10 15 30 25 0 0 0 0 0 5A1g⊕10A2g⊕15Eg⊕30T1g⊕25T2g
20 14 8 22 25 30 0 0 0 0 0 14A1g⊕8A2g⊕22Eg⊕25T1g⊕30T2g


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