Results for Point Group D18d



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S36 2C18 2S12 2C9 2(S36)5 2C6 2(S36)7 2(C9)2 2S4 2(C18)5 2(S36)11 2C3 2(S36)13 2(C18)7 2(S12)5 2(C9)4 2(S36)17 C2 18C'2 18σd
1 2 1.732 1.000 0.000 -1.000 -1.732 -2 -1.732 -1.000 0 1.000 1.732 2 1.732 1.000 0.000 -1.000 -1.732 -2 0 0
2 3 2.000 0.000 -1.000 0.000 2.000 3 2.000 0.000 -1 0.000 2.000 3 2.000 0.000 -1.000 0.000 2.000 3 1 1
3 4 1.732 -1.000 0.000 1.000 -1.732 -4 -1.732 1.000 0 -1.000 1.732 4 1.732 -1.000 0.000 1.000 -1.732 -4 0 0
4 5 1.000 -1.000 1.000 -1.000 1.000 5 1.000 -1.000 1 -1.000 1.000 5 1.000 -1.000 1.000 -1.000 1.000 5 1 1
5 6 0.000 0.000 0.000 0.000 0.000 -6 0.000 0.000 0 0.000 0.000 6 0.000 0.000 0.000 0.000 -0.000 -6 0 0
6 7 -1.000 1.000 -1.000 1.000 -1.000 7 -1.000 1.000 -1 1.000 -1.000 7 -1.000 1.000 -1.000 1.000 -1.000 7 1 1
7 8 -1.732 1.000 0.000 -1.000 1.732 -8 1.732 -1.000 0 1.000 -1.732 8 -1.732 1.000 0.000 -1.000 1.732 -8 0 0
8 9 -2.000 0.000 1.000 0.000 -2.000 9 -2.000 0.000 1 0.000 -2.000 9 -2.000 0.000 1.000 0.000 -2.000 9 1 1
9 10 -1.732 -1.000 0.000 1.000 1.732 -10 1.732 1.000 0 -1.000 -1.732 10 -1.732 -1.000 0.000 1.000 1.732 -10 0 0
10 11 -1.000 -1.000 -1.000 -1.000 -1.000 11 -1.000 -1.000 -1 -1.000 -1.000 11 -1.000 -1.000 -1.000 -1.000 -1.000 11 1 1
11 12 -0.000 0.000 0.000 0.000 -0.000 -12 -0.000 0.000 0 0.000 -0.000 12 -0.000 0.000 0.000 0.000 0.000 -12 0 0
12 13 1.000 1.000 1.000 1.000 1.000 13 1.000 1.000 1 1.000 1.000 13 1.000 1.000 1.000 1.000 1.000 13 1 1
13 14 1.732 1.000 0.000 -1.000 -1.732 -14 -1.732 -1.000 0 1.000 1.732 14 1.732 1.000 0.000 -1.000 -1.732 -14 0 0
14 15 2.000 0.000 -1.000 0.000 2.000 15 2.000 0.000 -1 0.000 2.000 15 2.000 0.000 -1.000 0.000 2.000 15 1 1
15 16 1.732 -1.000 0.000 1.000 -1.732 -16 -1.732 1.000 0 -1.000 1.732 16 1.732 -1.000 0.000 1.000 -1.732 -16 0 0
16 17 1.000 -1.000 1.000 -1.000 1.000 17 1.000 -1.000 1 -1.000 1.000 17 1.000 -1.000 1.000 -1.000 1.000 17 1 1
17 18 0.000 0.000 0.000 0.000 0.000 -18 0.000 0.000 0 0.000 0.000 18 0.000 0.000 0.000 0.000 -0.000 -18 0 0
18 19 -1.000 1.000 -1.000 1.000 -1.000 19 -1.000 1.000 -1 1.000 -1.000 19 -1.000 1.000 -1.000 1.000 -1.000 19 1 1
19 20 -1.732 1.000 0.000 -1.000 1.732 -20 1.732 -1.000 0 1.000 -1.732 20 -1.732 1.000 0.000 -1.000 1.732 -20 0 0
20 21 -2.000 0.000 1.000 0.000 -2.000 21 -2.000 0.000 1 0.000 -2.000 21 -2.000 0.000 1.000 0.000 -2.000 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
1 0 0 0 0 0 0 1 0 0 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 0 0 A1⊕E6
3 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 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 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 0 0 E3⊕E9⊕E15
6 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 A1⊕B1⊕B2⊕E6⊕E12
7 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 E3⊕E9⊕2E15
8 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 A1⊕B1⊕B2⊕E6⊕2E12
9 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0 E3⊕2E9⊕2E15
10 1 0 1 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 A1⊕B1⊕B2⊕2E6⊕2E12
11 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2E3⊕2E9⊕2E15
12 2 1 1 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E6⊕2E12
13 0 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 2 0 0 3E3⊕2E9⊕2E15
14 2 1 1 1 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 2A1⊕A2⊕B1⊕B2⊕3E6⊕2E12
15 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 2 0 0 3E3⊕3E9⊕2E15
16 2 1 1 1 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 2A1⊕A2⊕B1⊕B2⊕3E6⊕3E12
17 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 3E3⊕3E9⊕3E15
18 2 1 2 2 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 2A1⊕A2⊕2B1⊕2B2⊕3E6⊕3E12
19 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 4 0 0 3E3⊕3E9⊕4E15
20 2 1 2 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 2A1⊕A2⊕2B1⊕2B2⊕3E6⊕4E12



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement