Results for Point Group D7d



Symmetric powers of degenerate representation E3u
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 -1.802 1.247 -0.445 0 -2 1.802 -1.247 0.445 0
2 3 2.247 0.555 -0.802 1 3 2.247 0.555 -0.802 1
3 4 -2.247 -0.555 0.802 0 -4 2.247 0.555 -0.802 0
4 5 1.802 -1.247 0.445 1 5 1.802 -1.247 0.445 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 -1.802 1.247 -0.445 1 9 -1.802 1.247 -0.445 1
9 10 2.247 0.555 -0.802 0 -10 -2.247 -0.555 0.802 0
10 11 -2.247 -0.555 0.802 1 11 -2.247 -0.555 0.802 1
11 12 1.802 -1.247 0.445 0 -12 -1.802 1.247 -0.445 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 -1.802 1.247 -0.445 0 -16 1.802 -1.247 0.445 0
16 17 2.247 0.555 -0.802 1 17 2.247 0.555 -0.802 1
17 18 -2.247 -0.555 0.802 0 -18 2.247 0.555 -0.802 0
18 19 1.802 -1.247 0.445 1 19 1.802 -1.247 0.445 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 0 0 0 0 0 0 1 E3u
2 1 0 1 0 0 0 0 0 0 0 A1g⊕E1g
3 0 0 0 0 0 0 0 0 1 1 E2u⊕E3u
4 1 0 1 1 0 0 0 0 0 0 A1g⊕E1g⊕E2g
5 0 0 0 0 0 0 0 1 1 1 E1u⊕E2u⊕E3u
6 1 0 1 1 1 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
7 0 0 0 0 0 1 1 1 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u
8 1 0 1 1 2 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g
9 0 0 0 0 0 1 1 2 1 1 A1u⊕A2u⊕2E1u⊕E2u⊕E3u
10 1 0 1 2 2 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g
11 0 0 0 0 0 1 1 2 2 1 A1u⊕A2u⊕2E1u⊕2E2u⊕E3u
12 1 0 2 2 2 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g
13 0 0 0 0 0 1 1 2 2 2 A1u⊕A2u⊕2E1u⊕2E2u⊕2E3u
14 2 1 2 2 2 0 0 0 0 0 2A1g⊕A2g⊕2E1g⊕2E2g⊕2E3g
15 0 0 0 0 0 1 1 2 2 3 A1u⊕A2u⊕2E1u⊕2E2u⊕3E3u
16 2 1 3 2 2 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕2E2g⊕2E3g
17 0 0 0 0 0 1 1 2 3 3 A1u⊕A2u⊕2E1u⊕3E2u⊕3E3u
18 2 1 3 3 2 0 0 0 0 0 2A1g⊕A2g⊕3E1g⊕3E2g⊕2E3g
19 0 0 0 0 0 1 1 3 3 3 A1u⊕A2u⊕3E1u⊕3E2u⊕3E3u
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