Results for Point Group D20d



Symmetric powers of degenerate representation E2
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S40 2C20 2(S40)3 2C10 2S8 2(C20)3 2(S40)7 2C5 2(S40)9 2C4 2(S40)11 2(C10)3 2(S40)13 2(C20)7 2(S8)3 2(C5)2 2(S40)17 2(C20)9 2(S40)19 C2 20C'2 20σd
1 2 1.902 1.618 1.176 0.618 0.000 -0.618 -1.176 -1.618 -1.902 -2 -1.902 -1.618 -1.176 -0.618 0.000 0.618 1.176 1.618 1.902 2 0 0
2 3 2.618 1.618 0.382 -0.618 -1.000 -0.618 0.382 1.618 2.618 3 2.618 1.618 0.382 -0.618 -1.000 -0.618 0.382 1.618 2.618 3 1 1
3 4 3.078 1.000 -0.727 -1.000 0.000 1.000 0.727 -1.000 -3.078 -4 -3.078 -1.000 0.727 1.000 0.000 -1.000 -0.727 1.000 3.078 4 0 0
4 5 3.236 0.000 -1.236 -0.000 1.000 0.000 -1.236 -0.000 3.236 5 3.236 0.000 -1.236 -0.000 1.000 0.000 -1.236 -0.000 3.236 5 1 1
5 6 3.078 -1.000 -0.727 1.000 0.000 -1.000 0.727 1.000 -3.078 -6 -3.078 1.000 0.727 -1.000 0.000 1.000 -0.727 -1.000 3.078 6 0 0
6 7 2.618 -1.618 0.382 0.618 -1.000 0.618 0.382 -1.618 2.618 7 2.618 -1.618 0.382 0.618 -1.000 0.618 0.382 -1.618 2.618 7 1 1
7 8 1.902 -1.618 1.176 -0.618 0.000 0.618 -1.176 1.618 -1.902 -8 -1.902 1.618 -1.176 0.618 0.000 -0.618 1.176 -1.618 1.902 8 0 0
8 9 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 9 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 9 1 1
9 10 0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 -10 0.000 0.000 -0.000 0.000 0.000 0.000 -0.000 0.000 -0.000 10 0 0
10 11 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 11 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 11 1 1
11 12 -1.902 1.618 -1.176 0.618 0.000 -0.618 1.176 -1.618 1.902 -12 1.902 -1.618 1.176 -0.618 0.000 0.618 -1.176 1.618 -1.902 12 0 0
12 13 -2.618 1.618 -0.382 -0.618 1.000 -0.618 -0.382 1.618 -2.618 13 -2.618 1.618 -0.382 -0.618 1.000 -0.618 -0.382 1.618 -2.618 13 1 1
13 14 -3.078 1.000 0.727 -1.000 0.000 1.000 -0.727 -1.000 3.078 -14 3.078 -1.000 -0.727 1.000 0.000 -1.000 0.727 1.000 -3.078 14 0 0
14 15 -3.236 0.000 1.236 -0.000 -1.000 0.000 1.236 -0.000 -3.236 15 -3.236 0.000 1.236 -0.000 -1.000 0.000 1.236 -0.000 -3.236 15 1 1
15 16 -3.078 -1.000 0.727 1.000 0.000 -1.000 -0.727 1.000 3.078 -16 3.078 1.000 -0.727 -1.000 0.000 1.000 0.727 -1.000 -3.078 16 0 0
16 17 -2.618 -1.618 -0.382 0.618 1.000 0.618 -0.382 -1.618 -2.618 17 -2.618 -1.618 -0.382 0.618 1.000 0.618 -0.382 -1.618 -2.618 17 1 1
17 18 -1.902 -1.618 -1.176 -0.618 0.000 0.618 1.176 1.618 1.902 -18 1.902 1.618 1.176 0.618 0.000 -0.618 -1.176 -1.618 -1.902 18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 0.000 -20 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 20 0 0
20 21 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1⊕E4
3 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E2⊕E6
4 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1⊕E4⊕E8
5 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 E2⊕E6⊕E10
6 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 A1⊕E4⊕E8⊕E12
7 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 E2⊕E6⊕E10⊕E14
8 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 A1⊕E4⊕E8⊕E12⊕E16
9 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 E2⊕E6⊕E10⊕E14⊕E18
10 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 A1⊕B1⊕B2⊕E4⊕E8⊕E12⊕E16
11 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0 E2⊕E6⊕E10⊕E14⊕2E18
12 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 A1⊕B1⊕B2⊕E4⊕E8⊕E12⊕2E16
13 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 2 0 E2⊕E6⊕E10⊕2E14⊕2E18
14 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 2 0 0 0 A1⊕B1⊕B2⊕E4⊕E8⊕2E12⊕2E16
15 0 0 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 2 0 0 0 2 0 E2⊕E6⊕2E10⊕2E14⊕2E18
16 1 0 1 1 0 0 0 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 A1⊕B1⊕B2⊕E4⊕2E8⊕2E12⊕2E16
17 0 0 0 0 0 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 E2⊕2E6⊕2E10⊕2E14⊕2E18
18 1 0 1 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 A1⊕B1⊕B2⊕2E4⊕2E8⊕2E12⊕2E16
19 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 2E2⊕2E6⊕2E10⊕2E14⊕2E18
20 2 1 1 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E4⊕2E8⊕2E12⊕2E16



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