Results for Point Group D20d



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