Results for Point Group C10h



Symmetric powers of degenerate representation E2g
Vibrational overtones


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


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


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