Results for Point Group D20h



Symmetric powers of degenerate representation E2u
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 10C'2 10C''2 i 2(S20)9 2(S5)3 2(S20)7 2(S10)3 2S4 2S5 2(S20)3 2S10 2S20 σh 10σv 10σd
1 2 1.618 0.618 -0.618 -1.618 -2 -1.618 -0.618 0.618 1.618 2 0 0 -2 -1.618 -0.618 0.618 1.618 2 1.618 0.618 -0.618 -1.618 -2 0 0
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1 1 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1 1
3 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4 0 0 -4 -1.000 1.000 -1.000 1.000 4 1.000 -1.000 1.000 -1.000 -4 0 0
4 5 0.000 -0.000 0.000 -0.000 5 0.000 -0.000 0.000 -0.000 5 1 1 5 0.000 -0.000 0.000 -0.000 5 0.000 -0.000 0.000 -0.000 5 1 1
5 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6 0 0 -6 1.000 -1.000 1.000 -1.000 6 -1.000 1.000 -1.000 1.000 -6 0 0
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 1 1 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 1 1
7 8 -1.618 -0.618 0.618 1.618 -8 1.618 0.618 -0.618 -1.618 8 0 0 -8 1.618 0.618 -0.618 -1.618 8 -1.618 -0.618 0.618 1.618 -8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 1 1 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 -0.000 -0.000 -0.000 -10 0.000 0.000 0.000 0.000 10 0 0 -10 0.000 0.000 0.000 0.000 10 -0.000 -0.000 -0.000 -0.000 -10 0 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1 1 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1 1
11 12 1.618 0.618 -0.618 -1.618 -12 -1.618 -0.618 0.618 1.618 12 0 0 -12 -1.618 -0.618 0.618 1.618 12 1.618 0.618 -0.618 -1.618 -12 0 0
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1 1 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1 1
13 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14 0 0 -14 -1.000 1.000 -1.000 1.000 14 1.000 -1.000 1.000 -1.000 -14 0 0
14 15 0.000 -0.000 0.000 -0.000 15 0.000 -0.000 0.000 -0.000 15 1 1 15 0.000 -0.000 0.000 -0.000 15 0.000 -0.000 0.000 -0.000 15 1 1
15 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16 0 0 -16 1.000 -1.000 1.000 -1.000 16 -1.000 1.000 -1.000 1.000 -16 0 0
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 1 1 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 1 1
17 18 -1.618 -0.618 0.618 1.618 -18 1.618 0.618 -0.618 -1.618 18 0 0 -18 1.618 0.618 -0.618 -1.618 18 -1.618 -0.618 0.618 1.618 -18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 1 1 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 -0.000 -0.000 -0.000 -20 0.000 0.000 0.000 0.000 20 0 0 -20 0.000 0.000 0.000 0.000 20 -0.000 -0.000 -0.000 -0.000 -20 0 0
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1 1 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g E9g A1u A2u B1u B2u 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 0 0 0 0 E2u
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g
3 0 0 0 0 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 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕E8g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 B1u⊕B2u⊕E2u⊕E6u
6 1 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕2E8g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 2 0 0 0 B1u⊕B2u⊕E2u⊕2E6u
8 1 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E4g⊕2E8g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 0 0 0 2 0 0 0 B1u⊕B2u⊕2E2u⊕2E6u
10 2 1 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E4g⊕2E8g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 3 0 0 0 2 0 0 0 B1u⊕B2u⊕3E2u⊕2E6u
12 2 1 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E4g⊕2E8g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 3 0 0 0 3 0 0 0 B1u⊕B2u⊕3E2u⊕3E6u
14 2 1 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E4g⊕3E8g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 3 0 0 0 3 0 0 0 2B1u⊕2B2u⊕3E2u⊕3E6u
16 2 1 0 0 0 0 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E4g⊕4E8g
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 3 0 0 0 4 0 0 0 2B1u⊕2B2u⊕3E2u⊕4E6u
18 2 1 0 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E4g⊕4E8g
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 4 0 0 0 4 0 0 0 2B1u⊕2B2u⊕4E2u⊕4E6u
20 3 2 0 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4E4g⊕4E8g



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement