Results for Point Group D20d



Symmetric powers of degenerate representation E3
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 1.782 1.176 0.313 -0.618 -1.414 -1.902 -1.975 -1.618 -0.908 0 0.908 1.618 1.975 1.902 1.414 0.618 -0.313 -1.176 -1.782 -2 0 0
2 3 2.176 0.382 -0.902 -0.618 1.000 2.618 2.902 1.618 -0.176 -1 -0.176 1.618 2.902 2.618 1.000 -0.618 -0.902 0.382 2.176 3 1 1
3 4 2.095 -0.727 -0.595 1.000 0.000 -3.078 -3.757 -1.000 1.067 0 -1.067 1.000 3.757 3.078 0.000 -1.000 0.595 0.727 -2.095 -4 0 0
4 5 1.558 -1.236 0.716 0.000 -1.000 3.236 4.520 0.000 -0.794 1 -0.794 0.000 4.520 3.236 -1.000 -0.000 0.716 -1.236 1.558 5 1 1
5 6 0.681 -0.727 0.819 -1.000 1.414 -3.078 -5.172 1.000 -0.347 0 0.347 -1.000 5.172 3.078 -1.414 1.000 -0.819 0.727 -0.681 -6 0 0
6 7 -0.345 0.382 -0.460 0.618 -1.000 2.618 5.696 -1.618 1.109 -1 1.109 -1.618 5.696 2.618 -1.000 0.618 -0.460 0.382 -0.345 7 1 1
7 8 -1.295 1.176 -0.963 0.618 -0.000 -1.902 -6.080 1.618 -0.660 0 0.660 -1.618 6.080 1.902 -0.000 -0.618 0.963 -1.176 1.295 -8 0 0
8 9 -1.963 1.000 0.158 -1.000 1.000 1.000 6.314 -1.000 -0.510 1 -0.510 -1.000 6.314 1.000 1.000 -1.000 0.158 1.000 -1.963 9 1 1
9 10 -2.203 0.000 1.012 -0.000 -1.414 0.000 -6.392 0.000 1.122 0 -1.122 -0.000 6.392 0.000 1.414 -0.000 -1.012 0.000 2.203 -10 0 0
10 11 -1.963 -1.000 0.158 1.000 1.000 -1.000 6.314 1.000 -0.510 -1 -0.510 1.000 6.314 -1.000 1.000 1.000 0.158 -1.000 -1.963 11 1 1
11 12 -1.295 -1.176 -0.963 -0.618 0.000 1.902 -6.080 -1.618 -0.660 0 0.660 1.618 6.080 -1.902 0.000 0.618 0.963 1.176 1.295 -12 0 0
12 13 -0.345 -0.382 -0.460 -0.618 -1.000 -2.618 5.696 1.618 1.109 1 1.109 1.618 5.696 -2.618 -1.000 -0.618 -0.460 -0.382 -0.345 13 1 1
13 14 0.681 0.727 0.819 1.000 1.414 3.078 -5.172 -1.000 -0.347 0 0.347 1.000 5.172 -3.078 -1.414 -1.000 -0.819 -0.727 -0.681 -14 0 0
14 15 1.558 1.236 0.716 0.000 -1.000 -3.236 4.520 0.000 -0.794 -1 -0.794 0.000 4.520 -3.236 -1.000 -0.000 0.716 1.236 1.558 15 1 1
15 16 2.095 0.727 -0.595 -1.000 -0.000 3.078 -3.757 1.000 1.067 0 -1.067 -1.000 3.757 -3.078 -0.000 1.000 0.595 -0.727 -2.095 -16 0 0
16 17 2.176 -0.382 -0.902 0.618 1.000 -2.618 2.902 -1.618 -0.176 1 -0.176 -1.618 2.902 -2.618 1.000 0.618 -0.902 -0.382 2.176 17 1 1
17 18 1.782 -1.176 0.313 0.618 -1.414 1.902 -1.975 1.618 -0.908 0 0.908 -1.618 1.975 -1.902 1.414 -0.618 -0.313 1.176 -1.782 -18 0 0
18 19 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1 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 0 -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 1 -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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E3
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1⊕E6
3 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E3⊕E9
4 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 A1⊕E6⊕E12
5 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 E3⊕E9⊕E15
6 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 A1⊕E6⊕E12⊕E18
7 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 E3⊕E9⊕E15⊕E19
8 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 A1⊕E6⊕E12⊕E16⊕E18
9 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 E3⊕E9⊕E13⊕E15⊕E19
10 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 A1⊕E6⊕E10⊕E12⊕E16⊕E18
11 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 E3⊕E7⊕E9⊕E13⊕E15⊕E19
12 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 A1⊕E4⊕E6⊕E10⊕E12⊕E16⊕E18
13 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 E1⊕E3⊕E7⊕E9⊕E13⊕E15⊕E19
14 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E10⊕E12⊕E16⊕E18
15 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E13⊕E15⊕E19
16 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕E16⊕E18
17 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13⊕E15⊕E19
18 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕E14⊕E16⊕E18
19 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13⊕E15⊕E17⊕E19
20 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕E14⊕E16⊕E18



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