Results for Point Group D18d



Symmetric powers of degenerate representation E7
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 0.684 -1.532 -1.732 0.347 1.970 1 -1.286 -1.879 0 1.879 1.286 -1 -1.970 -0.347 1.732 1.532 -0.684 -2 0 0
2 3 -0.532 1.347 2.000 -0.879 2.879 0 0.653 2.532 -1 2.532 0.653 0 2.879 -0.879 2.000 1.347 -0.532 3 1 1
3 4 -1.048 -0.532 -1.732 -0.653 3.702 -1 0.446 -2.879 0 2.879 -0.446 1 -3.702 0.653 1.732 0.532 1.048 -4 0 0
4 5 -0.185 -0.532 1.000 0.653 4.411 -1 -1.227 2.879 1 2.879 -1.227 -1 4.411 0.653 1.000 -0.532 -0.185 5 1 1
5 6 0.922 1.347 0.000 0.879 4.987 0 1.131 -2.532 0 2.532 -1.131 0 -4.987 -0.879 -0.000 -1.347 -0.922 -6 0 0
6 7 0.815 -1.532 -1.000 -0.347 5.411 1 -0.227 1.879 -1 1.879 -0.227 1 5.411 -0.347 -1.000 -1.532 0.815 7 1 1
7 8 -0.364 1.000 1.732 -1.000 5.671 1 -0.839 -1.000 0 1.000 0.839 -1 -5.671 1.000 -1.732 -1.000 0.364 -8 0 0
8 9 -1.064 0.000 -2.000 0.000 5.759 0 1.305 0.000 1 -0.000 1.305 0 5.759 -0.000 -2.000 -0.000 -1.064 9 1 1
9 10 -0.364 -1.000 1.732 1.000 5.671 -1 -0.839 1.000 0 -1.000 0.839 1 -5.671 -1.000 -1.732 1.000 0.364 -10 0 0
10 11 0.815 1.532 -1.000 0.347 5.411 -1 -0.227 -1.879 -1 -1.879 -0.227 -1 5.411 0.347 -1.000 1.532 0.815 11 1 1
11 12 0.922 -1.347 -0.000 -0.879 4.987 0 1.131 2.532 0 -2.532 -1.131 0 -4.987 0.879 0.000 1.347 -0.922 -12 0 0
12 13 -0.185 0.532 1.000 -0.653 4.411 1 -1.227 -2.879 1 -2.879 -1.227 1 4.411 -0.653 1.000 0.532 -0.185 13 1 1
13 14 -1.048 0.532 -1.732 0.653 3.702 1 0.446 2.879 0 -2.879 -0.446 -1 -3.702 -0.653 1.732 -0.532 1.048 -14 0 0
14 15 -0.532 -1.347 2.000 0.879 2.879 0 0.653 -2.532 -1 -2.532 0.653 0 2.879 0.879 2.000 -1.347 -0.532 15 1 1
15 16 0.684 1.532 -1.732 -0.347 1.970 -1 -1.286 1.879 0 -1.879 1.286 1 -1.970 0.347 1.732 -1.532 -0.684 -16 0 0
16 17 1.000 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000 -1 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 0 0.000 0.000 0 0.000 -0.000 0 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 1 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 -1.000 19 1 1
19 20 -0.684 -1.532 1.732 0.347 -1.970 1 1.286 -1.879 0 1.879 -1.286 -1 1.970 -0.347 -1.732 1.532 0.684 -20 0 0
20 21 0.532 1.347 -2.000 -0.879 -2.879 0 -0.653 2.532 1 2.532 -0.653 0 -2.879 -0.879 -2.000 1.347 0.532 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E7
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 A1⊕E14
3 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 E7⊕E15
4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 A1⊕E8⊕E14
5 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 E1⊕E7⊕E15
6 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 A1⊕E6⊕E8⊕E14
7 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 E1⊕E7⊕E13⊕E15
8 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 A1⊕E6⊕E8⊕E14⊕E16
9 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 E1⊕E7⊕E9⊕E13⊕E15
10 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 A1⊕E2⊕E6⊕E8⊕E14⊕E16
11 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 E1⊕E5⊕E7⊕E9⊕E13⊕E15
12 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 A1⊕E2⊕E6⊕E8⊕E12⊕E14⊕E16
13 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 E1⊕E5⊕E7⊕E9⊕E13⊕E15⊕E17
14 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E6⊕E8⊕E10⊕E12⊕E14⊕E16
15 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E13⊕E15⊕E17
16 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12⊕E14⊕E16
17 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13⊕E15⊕E17
18 1 0 1 1 0 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⊕E16
19 0 0 0 0 1 0 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕2E11⊕E13⊕E15⊕E17
20 1 0 1 1 0 1 0 2 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕2E4⊕E6⊕E8⊕E10⊕E12⊕E14⊕E16



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