Results for Point Group D8



Symmetric powers of degenerate representation E3
Vibrational overtones


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


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



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