Results for Point Group D12d



Symmetric powers of degenerate representation E11
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2S24 2C12 2S8 2C6 2(S24)5 2C4 2(S24)7 2C3 2(S8)3 2(C12)5 2(S24)11 C2 12C'2 12σd
1 2 -1.932 1.732 -1.414 1 -0.518 0 0.518 -1 1.414 -1.732 1.932 -2 0 0
2 3 2.732 2.000 1.000 0 -0.732 -1 -0.732 0 1.000 2.000 2.732 3 1 1
3 4 -3.346 1.732 0.000 -1 0.897 0 -0.897 1 0.000 -1.732 3.346 -4 0 0
4 5 3.732 1.000 -1.000 -1 0.268 1 0.268 -1 -1.000 1.000 3.732 5 1 1
5 6 -3.864 -0.000 1.414 0 -1.035 0 1.035 0 -1.414 -0.000 3.864 -6 0 0
6 7 3.732 -1.000 -1.000 1 0.268 -1 0.268 1 -1.000 -1.000 3.732 7 1 1
7 8 -3.346 -1.732 -0.000 1 0.897 0 -0.897 -1 -0.000 1.732 3.346 -8 0 0
8 9 2.732 -2.000 1.000 0 -0.732 1 -0.732 0 1.000 -2.000 2.732 9 1 1
9 10 -1.932 -1.732 -1.414 -1 -0.518 0 0.518 1 1.414 1.732 1.932 -10 0 0
10 11 1.000 -1.000 1.000 -1 1.000 -1 1.000 -1 1.000 -1.000 1.000 11 1 1
11 12 0.000 0.000 0.000 0 0.000 0 0.000 0 0.000 0.000 0.000 -12 0 0
12 13 -1.000 1.000 -1.000 1 -1.000 1 -1.000 1 -1.000 1.000 -1.000 13 1 1
13 14 1.932 1.732 1.414 1 0.518 0 -0.518 -1 -1.414 -1.732 -1.932 -14 0 0
14 15 -2.732 2.000 -1.000 0 0.732 -1 0.732 0 -1.000 2.000 -2.732 15 1 1
15 16 3.346 1.732 -0.000 -1 -0.897 0 0.897 1 -0.000 -1.732 -3.346 -16 0 0
16 17 -3.732 1.000 1.000 -1 -0.268 1 -0.268 -1 1.000 1.000 -3.732 17 1 1
17 18 3.864 -0.000 -1.414 0 1.035 0 -1.035 0 1.414 -0.000 -3.864 -18 0 0
18 19 -3.732 -1.000 1.000 1 -0.268 -1 -0.268 1 1.000 -1.000 -3.732 19 1 1
19 20 3.346 -1.732 0.000 1 -0.897 0 0.897 -1 0.000 1.732 -3.346 -20 0 0
20 21 -2.732 -2.000 -1.000 0 0.732 1 0.732 0 -1.000 -2.000 -2.732 21 1 1


Decomposition to irreducible representations
Power
To		 A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E11
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A1⊕E2
3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 E9⊕E11
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 A1⊕E2⊕E4
5 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 E7⊕E9⊕E11
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 A1⊕E2⊕E4⊕E6
7 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 E5⊕E7⊕E9⊕E11
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 A1⊕E2⊕E4⊕E6⊕E8
9 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 E3⊕E5⊕E7⊕E9⊕E11
10 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10
11 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11
12 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10
13 0 0 0 0 2 0 1 0 1 0 1 0 1 0 1 2E1⊕E3⊕E5⊕E7⊕E9⊕E11
14 1 0 1 1 0 1 0 1 0 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕2E10
15 0 0 0 0 2 0 2 0 1 0 1 0 1 0 1 2E1⊕2E3⊕E5⊕E7⊕E9⊕E11
16 1 0 1 1 0 1 0 1 0 1 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕2E8⊕2E10
17 0 0 0 0 2 0 2 0 2 0 1 0 1 0 1 2E1⊕2E3⊕2E5⊕E7⊕E9⊕E11
18 1 0 1 1 0 1 0 1 0 2 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕2E6⊕2E8⊕2E10
19 0 0 0 0 2 0 2 0 2 0 2 0 1 0 1 2E1⊕2E3⊕2E5⊕2E7⊕E9⊕E11
20 1 0 1 1 0 1 0 2 0 2 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕2E4⊕2E6⊕2E8⊕2E10


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