Results for Point Group Ih



Symmetric powers of degenerate representation T1g
Vibrational overtones


Characters of symmetric powers
Power
To
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
1 3 1.618 -0.618 0 -1 3 -0.618 1.618 0 -1
2 6 1.000 1.000 0 2 6 1.000 1.000 0 2
3 10 -0.000 -0.000 1 -2 10 -0.000 -0.000 1 -2
4 15 -0.000 0.000 0 3 15 0.000 -0.000 0 3
5 21 1.000 1.000 0 -3 21 1.000 1.000 0 -3
6 28 1.618 -0.618 1 4 28 -0.618 1.618 1 4
7 36 1.000 1.000 0 -4 36 1.000 1.000 0 -4
8 45 -0.000 -0.000 0 5 45 -0.000 -0.000 0 5
9 55 -0.000 -0.000 1 -5 55 -0.000 -0.000 1 -5
10 66 1.000 1.000 0 6 66 1.000 1.000 0 6
11 78 1.618 -0.618 0 -6 78 -0.618 1.618 0 -6
12 91 1.000 1.000 1 7 91 1.000 1.000 1 7
13 105 -0.000 -0.000 0 -7 105 -0.000 -0.000 0 -7
14 120 -0.000 -0.000 0 8 120 -0.000 -0.000 0 8
15 136 1.000 1.000 1 -8 136 1.000 1.000 1 -8
16 153 1.618 -0.618 0 9 153 -0.618 1.618 0 9
17 171 1.000 1.000 0 -9 171 1.000 1.000 0 -9
18 190 -0.000 -0.000 1 10 190 -0.000 -0.000 1 10
19 210 -0.000 -0.000 0 -10 210 -0.000 -0.000 0 -10
20 231 1.000 1.000 0 11 231 1.000 1.000 0 11


Decomposition to irreducible representations
Power
To
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 0 1 0 0 0 0 0 0 0 0 T1g
2 1 0 0 0 1 0 0 0 0 0 Ag⊕Hg
3 0 1 1 1 0 0 0 0 0 0 T1g⊕T2g⊕Gg
4 1 0 0 1 2 0 0 0 0 0 Ag⊕Gg⊕2Hg
5 0 2 2 1 1 0 0 0 0 0 2T1g⊕2T2g⊕Gg⊕Hg
6 2 1 0 2 3 0 0 0 0 0 2Ag⊕T1g⊕2Gg⊕3Hg
7 0 3 3 2 2 0 0 0 0 0 3T1g⊕3T2g⊕2Gg⊕2Hg
8 2 1 1 3 5 0 0 0 0 0 2Ag⊕T1g⊕T2g⊕3Gg⊕5Hg
9 0 4 4 4 3 0 0 0 0 0 4T1g⊕4T2g⊕4Gg⊕3Hg
10 3 2 2 4 7 0 0 0 0 0 3Ag⊕2T1g⊕2T2g⊕4Gg⊕7Hg
11 0 6 5 5 5 0 0 0 0 0 6T1g⊕5T2g⊕5Gg⊕5Hg
12 4 3 3 6 9 0 0 0 0 0 4Ag⊕3T1g⊕3T2g⊕6Gg⊕9Hg
13 0 7 7 7 7 0 0 0 0 0 7T1g⊕7T2g⊕7Gg⊕7Hg
14 4 4 4 8 12 0 0 0 0 0 4Ag⊕4T1g⊕4T2g⊕8Gg⊕12Hg
15 1 9 9 9 9 0 0 0 0 0 Ag⊕9T1g⊕9T2g⊕9Gg⊕9Hg
16 5 6 5 10 15 0 0 0 0 0 5Ag⊕6T1g⊕5T2g⊕10Gg⊕15Hg
17 1 11 11 11 12 0 0 0 0 0 Ag⊕11T1g⊕11T2g⊕11Gg⊕12Hg
18 6 7 7 13 18 0 0 0 0 0 6Ag⊕7T1g⊕7T2g⊕13Gg⊕18Hg
19 1 13 13 14 15 0 0 0 0 0 Ag⊕13T1g⊕13T2g⊕14Gg⊕15Hg
20 7 9 9 15 22 0 0 0 0 0 7Ag⊕9T1g⊕9T2g⊕15Gg⊕22Hg



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