Results for Point Group D16d



Symmetric powers of degenerate representation E1
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 1.962 1.848 1.663 1.414 1.111 0.765 0.390 0 -0.390 -0.765 -1.111 -1.414 -1.663 -1.848 -1.962 -2 0 0
2 3 2.848 2.414 1.765 1.000 0.235 -0.414 -0.848 -1 -0.848 -0.414 0.235 1.000 1.765 2.414 2.848 3 1 1
3 4 3.625 2.613 1.273 0.000 -0.850 -1.082 -0.721 0 0.721 1.082 0.850 0.000 -1.273 -2.613 -3.625 -4 0 0
4 5 4.262 2.414 0.351 -1.000 -1.180 -0.414 0.566 1 0.566 -0.414 -1.180 -1.000 0.351 2.414 4.262 5 1 1
5 6 4.736 1.848 -0.689 -1.414 -0.460 0.765 0.942 0 -0.942 -0.765 0.460 1.414 0.689 -1.848 -4.736 -6 0 0
6 7 5.027 1.000 -1.497 -1.000 0.668 1.000 -0.199 -1 -0.199 1.000 0.668 -1.000 -1.497 1.000 5.027 7 1 1
7 8 5.126 0.000 -1.800 -0.000 1.203 0.000 -1.020 0 1.020 0.000 -1.203 -0.000 1.800 0.000 -5.126 -8 0 0
8 9 5.027 -1.000 -1.497 1.000 0.668 -1.000 -0.199 1 -0.199 -1.000 0.668 1.000 -1.497 -1.000 5.027 9 1 1
9 10 4.736 -1.848 -0.689 1.414 -0.460 -0.765 0.942 0 -0.942 0.765 0.460 -1.414 0.689 1.848 -4.736 -10 0 0
10 11 4.262 -2.414 0.351 1.000 -1.180 0.414 0.566 -1 0.566 0.414 -1.180 1.000 0.351 -2.414 4.262 11 1 1
11 12 3.625 -2.613 1.273 0.000 -0.850 1.082 -0.721 0 0.721 -1.082 0.850 0.000 -1.273 2.613 -3.625 -12 0 0
12 13 2.848 -2.414 1.765 -1.000 0.235 0.414 -0.848 1 -0.848 0.414 0.235 -1.000 1.765 -2.414 2.848 13 1 1
13 14 1.962 -1.848 1.663 -1.414 1.111 -0.765 0.390 0 -0.390 0.765 -1.111 1.414 -1.663 1.848 -1.962 -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 -1.962 1.848 -1.663 1.414 -1.111 0.765 -0.390 0 0.390 -0.765 1.111 -1.414 1.663 -1.848 1.962 -18 0 0
18 19 -2.848 2.414 -1.765 1.000 -0.235 -0.414 0.848 -1 0.848 -0.414 -0.235 1.000 -1.765 2.414 -2.848 19 1 1
19 20 -3.625 2.613 -1.273 0.000 0.850 -1.082 0.721 0 -0.721 1.082 -0.850 0.000 1.273 -2.613 3.625 -20 0 0
20 21 -4.262 2.414 -0.351 -1.000 1.180 -0.414 -0.566 1 -0.566 -0.414 1.180 -1.000 -0.351 2.414 -4.262 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1⊕E2
3 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E1⊕E3
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1⊕E2⊕E4
5 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 E1⊕E3⊕E5
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 A1⊕E2⊕E4⊕E6
7 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 E1⊕E3⊕E5⊕E7
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 A1⊕E2⊕E4⊕E6⊕E8
9 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 E1⊕E3⊕E5⊕E7⊕E9
10 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10
11 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 E1⊕E3⊕E5⊕E7⊕E9⊕E11
12 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12
13 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13
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 1 0 2 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13⊕2E15
18 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕2E14
19 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 2 0 2 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕2E13⊕2E15
20 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10⊕2E12⊕2E14


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