Results for Point Group C20h



Symmetric powers of degenerate representation E2g
Vibrational overtones


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


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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g
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 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E6g
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 2 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E2g⊕E6g
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 2 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕E2g⊕2E6g
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 2 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕2E2g⊕2E6g
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 2 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕3E2g⊕2E6g
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 2 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2Bg⊕3E2g⊕3E6g
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 4 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4Bg⊕3E2g⊕3E6g
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 4 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4Bg⊕3E2g⊕4E6g
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 4 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4Bg⊕4E2g⊕4E6g
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