Results for Point Group C20h



Symmetric powers of degenerate representation E6u
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 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618 2 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618 -2 0.618 1.618 -1.618 -0.618 2 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618 2 -0.618 -1.618 1.618 0.618
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618
3 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 -4 -1.000 1.000 -1.000 1.000 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4 1.000 -1.000 1.000 -1.000
4 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 -0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 0.000 -0.000 5 0.000 0.000 -0.000 -0.000
5 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 -6 1.000 -1.000 1.000 -1.000 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6 -1.000 1.000 -1.000 1.000
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618
7 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618 -8 -0.618 -1.618 1.618 0.618 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618 8 0.618 1.618 -1.618 -0.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 -10 -0.000 -0.000 -0.000 0.000 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 10 -0.000 0.000 0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618 -12 0.618 1.618 -1.618 -0.618 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618 12 -0.618 -1.618 1.618 0.618
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618
13 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 -14 -1.000 1.000 -1.000 1.000 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14 1.000 -1.000 1.000 -1.000
14 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 -0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000
15 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 -16 1.000 -1.000 1.000 -1.000 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16 -1.000 1.000 -1.000 1.000
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618
17 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618 -18 -0.618 -1.618 1.618 0.618 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618 18 0.618 1.618 -1.618 -0.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000 -20 -0.000 -0.000 -0.000 0.000 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000 20 -0.000 0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 E6u
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E8g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 E2u⊕E6u
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 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 1 0 0 0 2Bu⊕E2u⊕E6u
6 1 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2E4g⊕E8g
7 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 1 0 0 0 2Bu⊕2E2u⊕E6u
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 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 0 0 0 2Bu⊕2E2u⊕2E6u
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 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 3 0 0 0 2Bu⊕2E2u⊕3E6u
12 3 0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E4g⊕3E8g
13 0 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0 0 3 0 0 0 2Bu⊕3E2u⊕3E6u
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 0 0 0 0 0 0 0 0 0 0 0 4 0 3 0 0 0 3 0 0 0 4Bu⊕3E2u⊕3E6u
16 3 0 0 0 0 4 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕4E4g⊕3E8g
17 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 3 0 0 0 4Bu⊕4E2u⊕3E6u
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 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 4 0 0 0 4Bu⊕4E2u⊕4E6u
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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement