Results for Point Group D18d



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


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