Results for Point Group D16d



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2S32 2C16 2(S32)3 2C8 2(S32)5 2(C16)3 2(S32)7 2C4 2(S32)9 2(C16)5 2(S32)11 2(C8)3 2(S32)13 2(C16)7 2(S32)15 C2 16C'2 16σd
1 2 1.663 0.765 -0.390 -1.414 -1.962 -1.848 -1.111 0 1.111 1.848 1.962 1.414 0.390 -0.765 -1.663 -2 0 0
2 3 1.765 -0.414 -0.848 1.000 2.848 2.414 0.235 -1 0.235 2.414 2.848 1.000 -0.848 -0.414 1.765 3 1 1
3 4 1.273 -1.082 0.721 0.000 -3.625 -2.613 0.850 0 -0.850 2.613 3.625 0.000 -0.721 1.082 -1.273 -4 0 0
4 5 0.351 -0.414 0.566 -1.000 4.262 2.414 -1.180 1 -1.180 2.414 4.262 -1.000 0.566 -0.414 0.351 5 1 1
5 6 -0.689 0.765 -0.942 1.414 -4.736 -1.848 0.460 0 -0.460 1.848 4.736 -1.414 0.942 -0.765 0.689 -6 0 0
6 7 -1.497 1.000 -0.199 -1.000 5.027 1.000 0.668 -1 0.668 1.000 5.027 -1.000 -0.199 1.000 -1.497 7 1 1
7 8 -1.800 0.000 1.020 -0.000 -5.126 -0.000 -1.203 0 1.203 -0.000 5.126 -0.000 -1.020 -0.000 1.800 -8 0 0
8 9 -1.497 -1.000 -0.199 1.000 5.027 -1.000 0.668 1 0.668 -1.000 5.027 1.000 -0.199 -1.000 -1.497 9 1 1
9 10 -0.689 -0.765 -0.942 -1.414 -4.736 1.848 0.460 0 -0.460 -1.848 4.736 1.414 0.942 0.765 0.689 -10 0 0
10 11 0.351 0.414 0.566 1.000 4.262 -2.414 -1.180 -1 -1.180 -2.414 4.262 1.000 0.566 0.414 0.351 11 1 1
11 12 1.273 1.082 0.721 0.000 -3.625 2.613 0.850 0 -0.850 -2.613 3.625 0.000 -0.721 -1.082 -1.273 -12 0 0
12 13 1.765 0.414 -0.848 -1.000 2.848 -2.414 0.235 1 0.235 -2.414 2.848 -1.000 -0.848 0.414 1.765 13 1 1
13 14 1.663 -0.765 -0.390 1.414 -1.962 1.848 -1.111 0 1.111 -1.848 1.962 -1.414 0.390 0.765 -1.663 -14 0 0
14 15 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 15 1 1
15 16 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 -16 0 0
16 17 -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 17 1 1
17 18 -1.663 0.765 0.390 -1.414 1.962 -1.848 1.111 0 -1.111 1.848 -1.962 1.414 -0.390 -0.765 1.663 -18 0 0
18 19 -1.765 -0.414 0.848 1.000 -2.848 2.414 -0.235 -1 -0.235 2.414 -2.848 1.000 0.848 -0.414 -1.765 19 1 1
19 20 -1.273 -1.082 -0.721 0.000 3.625 -2.613 -0.850 0 0.850 2.613 -3.625 0.000 0.721 1.082 1.273 -20 0 0
20 21 -0.351 -0.414 -0.566 -1.000 -4.262 2.414 1.180 1 1.180 2.414 -4.262 -1.000 -0.566 -0.414 -0.351 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
1 0 0 0 0 0 0 1 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 A1⊕E6
3 0 0 0 0 0 0 1 0 0 0 0 0 1 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 A1⊕E6⊕E12
5 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 E3⊕E9⊕E15
6 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 A1⊕E6⊕E12⊕E14
7 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 E3⊕E9⊕E11⊕E15
8 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 A1⊕E6⊕E8⊕E12⊕E14
9 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 E3⊕E5⊕E9⊕E11⊕E15
10 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 A1⊕E2⊕E6⊕E8⊕E12⊕E14
11 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 E1⊕E3⊕E5⊕E9⊕E11⊕E15
12 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E12⊕E14
13 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E15
14 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕E14
15 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13⊕E15
16 1 0 1 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
17 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 2 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕2E13⊕E15
18 1 0 1 1 0 1 0 1 0 1 0 1 0 2 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕2E10⊕E12⊕E14
19 0 0 0 0 1 0 1 0 1 0 2 0 1 0 1 0 2 0 1 E1⊕E3⊕E5⊕2E7⊕E9⊕E11⊕2E13⊕E15
20 1 0 1 1 0 1 0 2 0 1 0 1 0 2 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕2E4⊕E6⊕E8⊕2E10⊕E12⊕E14


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement