Results for Point Group C20h



Symmetric powers of degenerate representation E8u
Vibrational overtones


Characters of symmetric powers
Power
To
E C20 C10 (C20)3 C5 C4 (C10)3 (C20)7 (C5)2 (C20)9 C2 (C20)11 (C5)3 (C20)13 (C10)7 (C4)3 (C5)4 (C20)17 (C10)9 (C20)19 i (S20)11 (S5)3 (S20)13 (S10)7 (S4)3 (S5)9 (S20)17 (S10)9 (S20)19 σh S20 S10 (S20)3 S5 S4 (S10)3 (S20)7 (S5)7 (S20)9
1 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 -2 1.618 -0.618 -0.618 1.618 -2 1.618 -0.618 -0.618 1.618 -2 1.618 -0.618 -0.618 1.618 -2 1.618 -0.618 -0.618 1.618
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 1.000 1.000
4 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 -1.000 -1.000
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618
7 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 -8 -1.618 0.618 0.618 -1.618 -8 -1.618 0.618 0.618 -1.618 -8 -1.618 0.618 0.618 -1.618 -8 -1.618 0.618 0.618 -1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 -0.000 0.000 10 -0.000 0.000 -0.000 0.000 10 -0.000 0.000 -0.000 0.000 10 -0.000 0.000 -0.000 0.000 -10 0.000 -0.000 0.000 -0.000 -10 0.000 -0.000 0.000 -0.000 -10 0.000 -0.000 0.000 -0.000 -10 0.000 -0.000 0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 -12 1.618 -0.618 -0.618 1.618 -12 1.618 -0.618 -0.618 1.618 -12 1.618 -0.618 -0.618 1.618 -12 1.618 -0.618 -0.618 1.618
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 1.000 1.000
14 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 -1.000 -1.000
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618
17 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 -18 -1.618 0.618 0.618 -1.618 -18 -1.618 0.618 0.618 -1.618 -18 -1.618 0.618 0.618 -1.618 -18 -1.618 0.618 0.618 -1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 -0.000 0.000 20 -0.000 0.000 -0.000 0.000 20 -0.000 0.000 -0.000 0.000 20 -0.000 0.000 -0.000 0.000 -20 0.000 -0.000 0.000 -0.000 -20 0.000 -0.000 0.000 -0.000 -20 0.000 -0.000 0.000 -0.000 -20 0.000 -0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000


Decomposition to irreducible representations
Power
To
Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* E9g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u* E9u*
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 E8u
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 E4u⊕E8u
4 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g⊕E8g
5 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 1 0 2Au⊕E4u⊕E8u
6 1 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g⊕2E8g
7 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 1 0 2Au⊕2E4u⊕E8u
8 1 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2E4g⊕2E8g
9 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 0 2Au⊕2E4u⊕2E8u
10 3 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E4g⊕2E8g
11 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 3 0 2Au⊕2E4u⊕3E8u
12 3 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕3E4g⊕2E8g
13 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 3 0 0 0 3 0 2Au⊕3E4u⊕3E8u
14 3 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕3E4g⊕3E8g
15 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 0 0 0 3 0 4Au⊕3E4u⊕3E8u
16 3 0 0 0 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕3E4g⊕4E8g
17 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 0 0 0 3 0 4Au⊕4E4u⊕3E8u
18 3 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕4E4g⊕4E8g
19 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 0 0 0 4 0 4Au⊕4E4u⊕4E8u
20 5 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕4E4g⊕4E8g



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