Results for Point Group D7d



Symmetric powers of degenerate representation E1g
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C7 2(C7)2 2(C7)3 7C'2 i 2(S14)5 2(S14)3 2S14 d
1 2 1.247 -0.445 -1.802 0 2 1.247 -0.445 -1.802 0
2 3 0.555 -0.802 2.247 1 3 0.555 -0.802 2.247 1
3 4 -0.555 0.802 -2.247 0 4 -0.555 0.802 -2.247 0
4 5 -1.247 0.445 1.802 1 5 -1.247 0.445 1.802 1
5 6 -1.000 -1.000 -1.000 0 6 -1.000 -1.000 -1.000 0
6 7 -0.000 -0.000 -0.000 1 7 -0.000 -0.000 -0.000 1
7 8 1.000 1.000 1.000 0 8 1.000 1.000 1.000 0
8 9 1.247 -0.445 -1.802 1 9 1.247 -0.445 -1.802 1
9 10 0.555 -0.802 2.247 0 10 0.555 -0.802 2.247 0
10 11 -0.555 0.802 -2.247 1 11 -0.555 0.802 -2.247 1
11 12 -1.247 0.445 1.802 0 12 -1.247 0.445 1.802 0
12 13 -1.000 -1.000 -1.000 1 13 -1.000 -1.000 -1.000 1
13 14 -0.000 -0.000 -0.000 0 14 -0.000 -0.000 -0.000 0
14 15 1.000 1.000 1.000 1 15 1.000 1.000 1.000 1
15 16 1.247 -0.445 -1.802 0 16 1.247 -0.445 -1.802 0
16 17 0.555 -0.802 2.247 1 17 0.555 -0.802 2.247 1
17 18 -0.555 0.802 -2.247 0 18 -0.555 0.802 -2.247 0
18 19 -1.247 0.445 1.802 1 19 -1.247 0.445 1.802 1
19 20 -1.000 -1.000 -1.000 0 20 -1.000 -1.000 -1.000 0
20 21 -0.000 -0.000 -0.000 1 21 -0.000 -0.000 -0.000 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g A1u A2u E1u E2u E3u
1 0 0 1 0 0 0 0 0 0 0 E1g
2 1 0 0 1 0 0 0 0 0 0 A1g⊕E2g
3 0 0 1 0 1 0 0 0 0 0 E1g⊕E3g
4 1 0 0 1 1 0 0 0 0 0 A1g⊕E2g⊕E3g
5 0 0 1 1 1 0 0 0 0 0 E1g⊕E2g⊕E3g
6 1 0 1 1 1 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
7 1 1 1 1 1 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g
8 1 0 2 1 1 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕E3g
9 1 1 1 2 1 0 0 0 0 0 A1g⊕A2g⊕E1g⊕2E2g⊕E3g
10 1 0 2 1 2 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕2E3g
11 1 1 1 2 2 0 0 0 0 0 A1g⊕A2g⊕E1g⊕2E2g⊕2E3g
12 1 0 2 2 2 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g
13 1 1 2 2 2 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g
14 2 1 2 2 2 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g
15 1 1 3 2 2 0 0 0 0 0 A1g⊕A2g⊕3E1g⊕2E2g⊕2E3g
16 2 1 2 3 2 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕3E2g⊕2E3g
17 1 1 3 2 3 0 0 0 0 0 A1g⊕A2g⊕3E1g⊕2E2g⊕3E3g
18 2 1 2 3 3 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕3E2g⊕3E3g
19 1 1 3 3 3 0 0 0 0 0 A1g⊕A2g⊕3E1g⊕3E2g⊕3E3g
20 2 1 3 3 3 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕3E2g⊕3E3g



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