Results for Point Group S16



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2S16 2C8 2(S16)3 2C4 2(S16)5 2(C8)3 2(S16)7 C2
1 2 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -2
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3
3 4 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -4
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5
5 6 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -6
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7
7 8 0.000 -0.000 0.000 0 0.000 -0.000 0.000 -8
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9
9 10 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -10
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11
11 12 -2.613 0.000 1.082 0 -1.082 0.000 2.613 -12
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13
13 14 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -14
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15
15 16 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -16
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17
17 18 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -18
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19
19 20 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -20
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21


Decomposition to irreducible representations
Power
To		 A B E1* E2* E3* E4* E5* E6* E7*
1 0 0 1 0 0 0 0 0 0 E1
2 1 0 0 1 0 0 0 0 0 A⊕E2
3 0 0 1 0 1 0 0 0 0 E1⊕E3
4 1 0 0 1 0 1 0 0 0 A⊕E2⊕E4
5 0 0 1 0 1 0 1 0 0 E1⊕E3⊕E5
6 1 0 0 1 0 1 0 1 0 A⊕E2⊕E4⊕E6
7 0 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7
8 1 2 0 1 0 1 0 1 0 A⊕2B⊕E2⊕E4⊕E6
9 0 0 1 0 1 0 1 0 2 E1⊕E3⊕E5⊕2E7
10 1 2 0 1 0 1 0 2 0 A⊕2B⊕E2⊕E4⊕2E6
11 0 0 1 0 1 0 2 0 2 E1⊕E3⊕2E5⊕2E7
12 1 2 0 1 0 2 0 2 0 A⊕2B⊕E2⊕2E4⊕2E6
13 0 0 1 0 2 0 2 0 2 E1⊕2E3⊕2E5⊕2E7
14 1 2 0 2 0 2 0 2 0 A⊕2B⊕2E2⊕2E4⊕2E6
15 0 0 2 0 2 0 2 0 2 2E1⊕2E3⊕2E5⊕2E7
16 3 2 0 2 0 2 0 2 0 3A⊕2B⊕2E2⊕2E4⊕2E6
17 0 0 3 0 2 0 2 0 2 3E1⊕2E3⊕2E5⊕2E7
18 3 2 0 3 0 2 0 2 0 3A⊕2B⊕3E2⊕2E4⊕2E6
19 0 0 3 0 3 0 2 0 2 3E1⊕3E3⊕2E5⊕2E7
20 3 2 0 3 0 3 0 2 0 3A⊕2B⊕3E2⊕3E4⊕2E6


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