Results for Point Group D16h



Symmetric powers of degenerate representation E2g
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 i 2(S16)7 2(S8)3 2(S16)5 2S4 2(S16)3 2S8 2S16 σh v d
1 2 1.414 0.000 -1.414 -2 -1.414 0.000 1.414 2 0 0 2 1.414 0.000 -1.414 -2 -1.414 0.000 1.414 2 0 0
2 3 1.000 -1.000 1.000 3 1.000 -1.000 1.000 3 1 1 3 1.000 -1.000 1.000 3 1.000 -1.000 1.000 3 1 1
3 4 0.000 0.000 0.000 -4 -0.000 0.000 -0.000 4 0 0 4 0.000 0.000 0.000 -4 -0.000 0.000 -0.000 4 0 0
4 5 -1.000 1.000 -1.000 5 -1.000 1.000 -1.000 5 1 1 5 -1.000 1.000 -1.000 5 -1.000 1.000 -1.000 5 1 1
5 6 -1.414 0.000 1.414 -6 1.414 0.000 -1.414 6 0 0 6 -1.414 0.000 1.414 -6 1.414 0.000 -1.414 6 0 0
6 7 -1.000 -1.000 -1.000 7 -1.000 -1.000 -1.000 7 1 1 7 -1.000 -1.000 -1.000 7 -1.000 -1.000 -1.000 7 1 1
7 8 -0.000 0.000 -0.000 -8 0.000 0.000 0.000 8 0 0 8 -0.000 0.000 -0.000 -8 0.000 0.000 0.000 8 0 0
8 9 1.000 1.000 1.000 9 1.000 1.000 1.000 9 1 1 9 1.000 1.000 1.000 9 1.000 1.000 1.000 9 1 1
9 10 1.414 0.000 -1.414 -10 -1.414 0.000 1.414 10 0 0 10 1.414 0.000 -1.414 -10 -1.414 0.000 1.414 10 0 0
10 11 1.000 -1.000 1.000 11 1.000 -1.000 1.000 11 1 1 11 1.000 -1.000 1.000 11 1.000 -1.000 1.000 11 1 1
11 12 0.000 0.000 0.000 -12 -0.000 0.000 -0.000 12 0 0 12 0.000 0.000 0.000 -12 -0.000 0.000 -0.000 12 0 0
12 13 -1.000 1.000 -1.000 13 -1.000 1.000 -1.000 13 1 1 13 -1.000 1.000 -1.000 13 -1.000 1.000 -1.000 13 1 1
13 14 -1.414 0.000 1.414 -14 1.414 0.000 -1.414 14 0 0 14 -1.414 0.000 1.414 -14 1.414 0.000 -1.414 14 0 0
14 15 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 15 1 1 15 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 15 1 1
15 16 -0.000 0.000 0.000 -16 0.000 0.000 0.000 16 0 0 16 -0.000 0.000 0.000 -16 0.000 0.000 0.000 16 0 0
16 17 1.000 1.000 1.000 17 1.000 1.000 1.000 17 1 1 17 1.000 1.000 1.000 17 1.000 1.000 1.000 17 1 1
17 18 1.414 0.000 -1.414 -18 -1.414 0.000 1.414 18 0 0 18 1.414 0.000 -1.414 -18 -1.414 0.000 1.414 18 0 0
18 19 1.000 -1.000 1.000 19 1.000 -1.000 1.000 19 1 1 19 1.000 -1.000 1.000 19 1.000 -1.000 1.000 19 1 1
19 20 0.000 0.000 -0.000 -20 -0.000 0.000 -0.000 20 0 0 20 0.000 0.000 -0.000 -20 -0.000 0.000 -0.000 20 0 0
20 21 -1.000 1.000 -1.000 21 -1.000 1.000 -1.000 21 1 1 21 -1.000 1.000 -1.000 21 -1.000 1.000 -1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u
1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g
3 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E6g
4 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E4g
5 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕2E6g
6 1 0 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕2E4g
7 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2E2g⊕2E6g
8 2 1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕2E4g
9 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3E2g⊕2E6g
10 2 1 1 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕3E4g
11 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3E2g⊕3E6g
12 2 1 2 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g⊕3E4g
13 0 0 0 0 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3E2g⊕4E6g
14 2 1 2 2 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2B1g⊕2B2g⊕4E4g
15 0 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4E2g⊕4E6g
16 3 2 2 2 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g⊕4E4g
17 0 0 0 0 0 5 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 5E2g⊕4E6g
18 3 2 2 2 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕2B1g⊕2B2g⊕5E4g
19 0 0 0 0 0 5 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5E2g⊕5E6g
20 3 2 3 3 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕3B1g⊕3B2g⊕5E4g



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