Results for Point Group C20h



Symmetric powers of degenerate representation E1g
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 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -2 2 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -2
2 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3
3 4 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -4 4 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -4
4 5 3.236 0.000 -1.236 -0.000 1 0.000 -1.236 -0.000 3.236 5 5 3.236 0.000 -1.236 -0.000 1 0.000 -1.236 -0.000 3.236 5
5 6 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -6 6 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -6
6 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7
7 8 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -8 8 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -8
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9
9 10 0.000 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 0.000 -10 10 0.000 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 0.000 -10
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11
11 12 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -12 12 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -12
12 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13
13 14 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -14 14 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -14
14 15 -3.236 0.000 1.236 -0.000 -1 0.000 1.236 -0.000 -3.236 15 15 -3.236 0.000 1.236 -0.000 -1 0.000 1.236 -0.000 -3.236 15
15 16 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -16 16 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -16
16 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17
17 18 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -18 18 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -18
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19
19 20 -0.000 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -0.000 -20 20 -0.000 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -0.000 -20
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 21 1.000 1.000 1.000 1.000 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g
6 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g
7 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g
8 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g⊕E8g
9 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g⊕E9g
10 1 2 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g⊕E6g⊕E8g
11 0 0 1 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g⊕2E9g
12 1 2 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g⊕E6g⊕2E8g
13 0 0 1 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕2E7g⊕2E9g
14 1 2 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g⊕2E6g⊕2E8g
15 0 0 1 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕2E5g⊕2E7g⊕2E9g
16 1 2 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕2E4g⊕2E6g⊕2E8g
17 0 0 1 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 E1g⊕2E3g⊕2E5g⊕2E7g⊕2E9g
18 1 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 0 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕2E7g⊕2E9g
20 3 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕2E2g⊕2E4g⊕2E6g⊕2E8g


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