Results for Point Group D16



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C16 2C8 2(C16)3 2C4 2(C16)5 2(C8)3 2(C16)7 C2 8C'2 8C''2
1 2 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -2 0 0
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 1 1
3 4 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -4 0 0
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 1 1
5 6 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -6 0 0
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1 1
7 8 0.000 -0.000 0.000 0 0.000 -0.000 0.000 -8 0 0
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 1 1
9 10 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -10 0 0
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 1 1
11 12 -2.613 0.000 1.082 0 -1.082 0.000 2.613 -12 0 0
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 1 1
13 14 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -14 0 0
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 1 1
15 16 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -16 0 0
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1 1
17 18 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -18 0 0
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 1 1
19 20 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -20 0 0
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7
1 0 0 0 0 1 0 0 0 0 0 0 E1
2 1 0 0 0 0 1 0 0 0 0 0 A1⊕E2
3 0 0 0 0 1 0 1 0 0 0 0 E1⊕E3
4 1 0 0 0 0 1 0 1 0 0 0 A1⊕E2⊕E4
5 0 0 0 0 1 0 1 0 1 0 0 E1⊕E3⊕E5
6 1 0 0 0 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6
7 0 0 0 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7
8 1 0 1 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6
9 0 0 0 0 1 0 1 0 1 0 2 E1⊕E3⊕E5⊕2E7
10 1 0 1 1 0 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕2E6
11 0 0 0 0 1 0 1 0 2 0 2 E1⊕E3⊕2E5⊕2E7
12 1 0 1 1 0 1 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕2E4⊕2E6
13 0 0 0 0 1 0 2 0 2 0 2 E1⊕2E3⊕2E5⊕2E7
14 1 0 1 1 0 2 0 2 0 2 0 A1⊕B1⊕B2⊕2E2⊕2E4⊕2E6
15 0 0 0 0 2 0 2 0 2 0 2 2E1⊕2E3⊕2E5⊕2E7
16 2 1 1 1 0 2 0 2 0 2 0 2A1⊕A2⊕B1⊕B2⊕2E2⊕2E4⊕2E6
17 0 0 0 0 3 0 2 0 2 0 2 3E1⊕2E3⊕2E5⊕2E7
18 2 1 1 1 0 3 0 2 0 2 0 2A1⊕A2⊕B1⊕B2⊕3E2⊕2E4⊕2E6
19 0 0 0 0 3 0 3 0 2 0 2 3E1⊕3E3⊕2E5⊕2E7
20 2 1 1 1 0 3 0 3 0 2 0 2A1⊕A2⊕B1⊕B2⊕3E2⊕3E4⊕2E6



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