Results for Point Group C20h



Symmetric powers of degenerate representation E3g
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 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176 -2 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176 2 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176 -2 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176
2 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382
3 4 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727 -4 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727 4 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727 -4 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727
4 5 -1.236 0.000 3.236 0.000 1 -0.000 3.236 -0.000 -1.236 5 -1.236 0.000 3.236 0.000 1 -0.000 3.236 -0.000 -1.236 5 -1.236 0.000 3.236 0.000 1 -0.000 3.236 -0.000 -1.236 5 -1.236 0.000 3.236 0.000 1 -0.000 3.236 -0.000 -1.236
5 6 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727 -6 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727 6 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727 -6 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727
6 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382
7 8 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176 -8 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176 8 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176 -8 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000
9 10 0.000 -0.000 0.000 0.000 0 0.000 0.000 -0.000 0.000 -10 -0.000 0.000 -0.000 -0.000 0 -0.000 -0.000 0.000 -0.000 10 -0.000 -0.000 0.000 0.000 0 0.000 0.000 -0.000 0.000 -10 -0.000 0.000 -0.000 -0.000 0 -0.000 -0.000 0.000 -0.000
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000
11 12 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176 -12 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176 12 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176 -12 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176
12 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382
13 14 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727 -14 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727 14 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727 -14 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727
14 15 1.236 0.000 -3.236 0.000 -1 -0.000 -3.236 -0.000 1.236 15 1.236 0.000 -3.236 0.000 -1 -0.000 -3.236 -0.000 1.236 15 1.236 0.000 -3.236 0.000 -1 -0.000 -3.236 -0.000 1.236 15 1.236 0.000 -3.236 0.000 -1 -0.000 -3.236 -0.000 1.236
15 16 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727 -16 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727 16 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727 -16 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727
16 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382
17 18 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176 -18 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176 18 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176 -18 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 -0.000 -0.000 0.000 0 0.000 -0.000 -0.000 -0.000 -20 0.000 0.000 0.000 -0.000 0 -0.000 0.000 0.000 0.000 20 0.000 -0.000 -0.000 0.000 0 0.000 -0.000 -0.000 -0.000 -20 0.000 0.000 0.000 -0.000 0 -0.000 0.000 0.000 0.000
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E3g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E6g
3 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E3g⊕E9g
4 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E6g⊕E8g
5 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E3g⊕E5g⊕E9g
6 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E6g⊕E8g
7 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E9g
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 2 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕2E7g⊕E9g
12 1 2 0 1 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕2E4g⊕E6g⊕E8g
13 0 0 2 0 1 0 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕E3g⊕E5g⊕2E7g⊕E9g
14 1 2 0 2 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g⊕2E4g⊕E6g⊕E8g
15 0 0 2 0 1 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕E3g⊕2E5g⊕2E7g⊕E9g
16 1 2 0 2 0 2 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g⊕2E4g⊕E6g⊕2E8g
17 0 0 2 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕E3g⊕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 January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement