Results for Point Group D16d



Symmetric powers of degenerate representation E6
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 0.765 -1.414 -1.848 0.000 1.848 1.414 -0.765 -2 -0.765 1.414 1.848 0.000 -1.848 -1.414 0.765 2 0 0
2 3 -0.414 1.000 2.414 -1.000 2.414 1.000 -0.414 3 -0.414 1.000 2.414 -1.000 2.414 1.000 -0.414 3 1 1
3 4 -1.082 0.000 -2.613 0.000 2.613 0.000 1.082 -4 1.082 -0.000 2.613 0.000 -2.613 -0.000 -1.082 4 0 0
4 5 -0.414 -1.000 2.414 1.000 2.414 -1.000 -0.414 5 -0.414 -1.000 2.414 1.000 2.414 -1.000 -0.414 5 1 1
5 6 0.765 1.414 -1.848 0.000 1.848 -1.414 -0.765 -6 -0.765 -1.414 1.848 0.000 -1.848 1.414 0.765 6 0 0
6 7 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 7 1 1
7 8 0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -8 -0.000 0.000 -0.000 0.000 0.000 0.000 -0.000 8 0 0
8 9 -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 9 1 1
9 10 -0.765 -1.414 1.848 0.000 -1.848 1.414 0.765 -10 0.765 1.414 -1.848 0.000 1.848 -1.414 -0.765 10 0 0
10 11 0.414 1.000 -2.414 -1.000 -2.414 1.000 0.414 11 0.414 1.000 -2.414 -1.000 -2.414 1.000 0.414 11 1 1
11 12 1.082 0.000 2.613 0.000 -2.613 0.000 -1.082 -12 -1.082 -0.000 -2.613 0.000 2.613 -0.000 1.082 12 0 0
12 13 0.414 -1.000 -2.414 1.000 -2.414 -1.000 0.414 13 0.414 -1.000 -2.414 1.000 -2.414 -1.000 0.414 13 1 1
13 14 -0.765 1.414 1.848 0.000 -1.848 -1.414 0.765 -14 0.765 -1.414 -1.848 0.000 1.848 1.414 -0.765 14 0 0
14 15 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 15 -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 -16 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 17 1.000 1.000 1.000 1.000 1.000 1.000 1.000 17 1 1
17 18 0.765 -1.414 -1.848 0.000 1.848 1.414 -0.765 -18 -0.765 1.414 1.848 0.000 -1.848 -1.414 0.765 18 0 0
18 19 -0.414 1.000 2.414 -1.000 2.414 1.000 -0.414 19 -0.414 1.000 2.414 -1.000 2.414 1.000 -0.414 19 1 1
19 20 -1.082 0.000 -2.613 0.000 2.613 0.000 1.082 -20 1.082 -0.000 2.613 0.000 -2.613 -0.000 -1.082 20 0 0
20 21 -0.414 -1.000 2.414 1.000 2.414 -1.000 -0.414 21 -0.414 -1.000 2.414 1.000 2.414 -1.000 -0.414 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 0 0 0 1 0 0 0 0 0 0 0 0 0 E6
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 A1⊕E12
3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 E6⊕E14
4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 A1⊕E8⊕E12
5 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 E2⊕E6⊕E14
6 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 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 E2⊕E6⊕E10⊕E14
8 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 A1⊕B1⊕B2⊕E4⊕E8⊕E12
9 0 0 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 1 0 E2⊕E6⊕2E10⊕E14
10 1 0 1 1 0 0 0 2 0 0 0 1 0 0 0 1 0 0 0 A1⊕B1⊕B2⊕2E4⊕E8⊕E12
11 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 1 0 2E2⊕E6⊕2E10⊕E14
12 1 0 1 1 0 0 0 2 0 0 0 2 0 0 0 1 0 0 0 A1⊕B1⊕B2⊕2E4⊕2E8⊕E12
13 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 2 0 2E2⊕E6⊕2E10⊕2E14
14 1 0 1 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 A1⊕B1⊕B2⊕2E4⊕2E8⊕2E12
15 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 2E2⊕2E6⊕2E10⊕2E14
16 2 1 1 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E4⊕2E8⊕2E12
17 0 0 0 0 0 2 0 0 0 3 0 0 0 2 0 0 0 2 0 2E2⊕3E6⊕2E10⊕2E14
18 2 1 1 1 0 0 0 2 0 0 0 2 0 0 0 3 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E4⊕2E8⊕3E12
19 0 0 0 0 0 2 0 0 0 3 0 0 0 2 0 0 0 3 0 2E2⊕3E6⊕2E10⊕3E14
20 2 1 1 1 0 0 0 2 0 0 0 3 0 0 0 3 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E4⊕3E8⊕3E12


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