Results for Point Group S14



Symmetric powers of degenerate representation E3u
Vibrational overtones


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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement