Results for Point Group D7d



Symmetric powers of degenerate representation E2g
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 7σd
1 2 -0.445 -1.802 1.247 0 2 -0.445 -1.802 1.247 0
2 3 -0.802 2.247 0.555 1 3 -0.802 2.247 0.555 1
3 4 0.802 -2.247 -0.555 0 4 0.802 -2.247 -0.555 0
4 5 0.445 1.802 -1.247 1 5 0.445 1.802 -1.247 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 -0.445 -1.802 1.247 1 9 -0.445 -1.802 1.247 1
9 10 -0.802 2.247 0.555 0 10 -0.802 2.247 0.555 0
10 11 0.802 -2.247 -0.555 1 11 0.802 -2.247 -0.555 1
11 12 0.445 1.802 -1.247 0 12 0.445 1.802 -1.247 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 -0.445 -1.802 1.247 0 16 -0.445 -1.802 1.247 0
16 17 -0.802 2.247 0.555 1 17 -0.802 2.247 0.555 1
17 18 0.802 -2.247 -0.555 0 18 0.802 -2.247 -0.555 0
18 19 0.445 1.802 -1.247 1 19 0.445 1.802 -1.247 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 0 1 0 0 0 0 0 0 E2g
2 1 0 0 0 1 0 0 0 0 0 A1g⊕E3g
3 0 0 1 1 0 0 0 0 0 0 E1g⊕E2g
4 1 0 1 0 1 0 0 0 0 0 A1g⊕E1g⊕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 1 2 1 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕E3g
9 1 1 1 1 2 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕2E3g
10 1 0 2 2 1 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕E3g
11 1 1 2 1 2 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕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 2 3 2 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕3E2g⊕2E3g
16 2 1 2 2 3 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕2E2g⊕3E3g
17 1 1 3 3 2 0 0 0 0 0 A1g⊕A2g⊕3E1g⊕3E2g⊕2E3g
18 2 1 3 2 3 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕2E2g⊕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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement