Results for Point Group Ih



Symmetric powers of degenerate representation Hu
Vibrational overtones


Characters of symmetric powers
Power
To
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
1 5 0.000 0.000 -1 1 -5 0.000 0.000 1 -1
2 15 0.000 0.000 0 3 15 0.000 0.000 0 3
3 35 0.000 0.000 2 3 -35 0.000 0.000 -2 -3
4 70 0.000 0.000 -2 6 70 0.000 0.000 -2 6
5 126 1.000 1.000 0 6 -126 -1.000 -1.000 0 -6
6 210 0.000 0.000 3 10 210 0.000 0.000 3 10
7 330 0.000 0.000 -3 10 -330 0.000 0.000 3 -10
8 495 0.000 0.000 0 15 495 0.000 0.000 0 15
9 715 0.000 0.000 4 15 -715 0.000 0.000 -4 -15
10 1.001 1.000 1.000 -4 21 1.001 1.000 1.000 -4 21
11 1.365 0.000 0.000 0 21 -1.365 0.000 0.000 0 -21
12 1.820 0.000 0.000 5 28 1.820 0.000 0.000 5 28
13 2.380 0.000 0.000 -5 28 -2.380 0.000 0.000 5 -28
14 3.060 0.000 0.000 0 36 3.060 0.000 0.000 0 36
15 3.876 1.000 1.000 6 36 -3.876 -1.000 -1.000 -6 -36
16 4.845 0.000 0.000 -6 45 4.845 0.000 0.000 -6 45
17 5.985 0.000 0.000 0 45 -5.985 0.000 0.000 0 -45
18 7.315 0.000 0.000 7 55 7.315 0.000 0.000 7 55
19 8.855 0.000 0.000 -7 55 -8.855 0.000 0.000 7 -55
20 10.626 1.000 1.000 0 66 10.626 1.000 1.000 0 66


Decomposition to irreducible representations
Power
To
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 0 0 0 0 0 0 0 0 0 1 Hu
2 1 0 0 1 2 0 0 0 0 0 Ag⊕Gg⊕2Hg
3 0 0 0 0 0 2 1 1 3 3 2Au⊕T1u⊕T2u⊕3Gu⊕3Hu
4 2 2 2 4 8 0 0 0 0 0 2Ag⊕2T1g⊕2T2g⊕4Gg⊕8Hg
5 0 0 0 0 0 4 5 5 8 12 4Au⊕5T1u⊕5T2u⊕8Gu⊕12Hu
6 7 8 8 15 19 0 0 0 0 0 7Ag⊕8T1g⊕8T2g⊕15Gg⊕19Hg
7 0 0 0 0 0 7 14 14 21 31 7Au⊕14T1u⊕14T2u⊕21Gu⊕31Hu
8 12 21 21 33 45 0 0 0 0 0 12Ag⊕21T1g⊕21T2g⊕33Gg⊕45Hg
9 0 0 0 0 0 17 32 32 49 62 17Au⊕32T1u⊕32T2u⊕49Gu⊕62Hu
10 21 45 45 65 90 0 0 0 0 0 21Ag⊕45T1g⊕45T2g⊕65Gg⊕90Hg
11 0 0 0 0 0 28 63 63 91 119 28Au⊕63T1u⊕63T2u⊕91Gu⊕119Hu
12 39 84 84 123 157 0 0 0 0 0 39Ag⊕84T1g⊕84T2g⊕123Gg⊕157Hg
13 0 0 0 0 0 45 112 112 157 207 45Au⊕112T1u⊕112T2u⊕157Gu⊕207Hu
14 60 144 144 204 264 0 0 0 0 0 60Ag⊕144T1g⊕144T2g⊕204Gg⊕264Hg
15 0 0 0 0 0 76 185 185 260 330 76Au⊕185T1u⊕185T2u⊕260Gu⊕330Hu
16 90 231 231 321 417 0 0 0 0 0 90Ag⊕231T1g⊕231T2g⊕321Gg⊕417Hg
17 0 0 0 0 0 111 288 288 399 510 111Au⊕288T1u⊕288T2u⊕399Gu⊕510Hu
18 138 352 352 490 621 0 0 0 0 0 138Ag⊕352T1g⊕352T2g⊕490Gg⊕621Hg
19 0 0 0 0 0 159 429 429 588 754 159Au⊕429T1u⊕429T2u⊕588Gu⊕754Hu
20 194 515 515 708 902 0 0 0 0 0 194Ag⊕515T1g⊕515T2g⊕708Gg⊕902Hg



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