Results for Point Group C10h



Symmetric powers of degenerate representation E1g
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 1.618 0.618 -0.618 -1.618 -2 2 1.618 0.618 -0.618 -1.618 -2
2 3 1.618 -0.618 -0.618 1.618 3 3 1.618 -0.618 -0.618 1.618 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 -1.618 0.618 0.618 -1.618 7 7 -1.618 0.618 0.618 -1.618 7
7 8 -1.618 -0.618 0.618 1.618 -8 8 -1.618 -0.618 0.618 1.618 -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 1.618 0.618 -0.618 -1.618 -12 12 1.618 0.618 -0.618 -1.618 -12
12 13 1.618 -0.618 -0.618 1.618 13 13 1.618 -0.618 -0.618 1.618 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 -1.618 0.618 0.618 -1.618 17 17 -1.618 0.618 0.618 -1.618 17
17 18 -1.618 -0.618 0.618 1.618 -18 18 -1.618 -0.618 0.618 1.618 -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 1 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 1 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 1 0 1 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 0 1 0 1 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 2 1 0 1 0 0 0 0 0 0 0 2Bg⊕E1g⊕E3g
6 1 0 0 1 0 2 0 0 0 0 0 0 Ag⊕E2g⊕2E4g
7 0 2 1 0 2 0 0 0 0 0 0 0 2Bg⊕E1g⊕2E3g
8 1 0 0 2 0 2 0 0 0 0 0 0 Ag⊕2E2g⊕2E4g
9 0 2 2 0 2 0 0 0 0 0 0 0 2Bg⊕2E1g⊕2E3g
10 3 0 0 2 0 2 0 0 0 0 0 0 3Ag⊕2E2g⊕2E4g
11 0 2 3 0 2 0 0 0 0 0 0 0 2Bg⊕3E1g⊕2E3g
12 3 0 0 3 0 2 0 0 0 0 0 0 3Ag⊕3E2g⊕2E4g
13 0 2 3 0 3 0 0 0 0 0 0 0 2Bg⊕3E1g⊕3E3g
14 3 0 0 3 0 3 0 0 0 0 0 0 3Ag⊕3E2g⊕3E4g
15 0 4 3 0 3 0 0 0 0 0 0 0 4Bg⊕3E1g⊕3E3g
16 3 0 0 3 0 4 0 0 0 0 0 0 3Ag⊕3E2g⊕4E4g
17 0 4 3 0 4 0 0 0 0 0 0 0 4Bg⊕3E1g⊕4E3g
18 3 0 0 4 0 4 0 0 0 0 0 0 3Ag⊕4E2g⊕4E4g
19 0 4 4 0 4 0 0 0 0 0 0 0 4Bg⊕4E1g⊕4E3g
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