Results for Point Group S18



Symmetric powers of degenerate representation E3g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C9 2(C9)2 2C3 2(C9)4 i 2(S18)7 2(S18)5 2S6 2S18
1 2 -1.000 -1.000 2 -1.000 2 -1.000 -1.000 2 -1.000
2 3 0.000 0.000 3 0.000 3 0.000 0.000 3 0.000
3 4 1.000 1.000 4 1.000 4 1.000 1.000 4 1.000
4 5 -1.000 -1.000 5 -1.000 5 -1.000 -1.000 5 -1.000
5 6 0.000 0.000 6 0.000 6 0.000 0.000 6 0.000
6 7 1.000 1.000 7 1.000 7 1.000 1.000 7 1.000
7 8 -1.000 -1.000 8 -1.000 8 -1.000 -1.000 8 -1.000
8 9 0.000 0.000 9 0.000 9 0.000 0.000 9 0.000
9 10 1.000 1.000 10 1.000 10 1.000 1.000 10 1.000
10 11 -1.000 -1.000 11 -1.000 11 -1.000 -1.000 11 -1.000
11 12 0.000 0.000 12 0.000 12 0.000 0.000 12 0.000
12 13 1.000 1.000 13 1.000 13 1.000 1.000 13 1.000
13 14 -1.000 -1.000 14 -1.000 14 -1.000 -1.000 14 -1.000
14 15 0.000 0.000 15 0.000 15 0.000 0.000 15 0.000
15 16 1.000 1.000 16 1.000 16 1.000 1.000 16 1.000
16 17 -1.000 -1.000 17 -1.000 17 -1.000 -1.000 17 -1.000
17 18 0.000 0.000 18 0.000 18 0.000 0.000 18 0.000
18 19 1.000 1.000 19 1.000 19 1.000 1.000 19 1.000
19 20 -1.000 -1.000 20 -1.000 20 -1.000 -1.000 20 -1.000
20 21 0.000 0.000 21 0.000 21 0.000 0.000 21 0.000


Decomposition to irreducible representations
Power
To		 Ag E1g* E2g* E3g* E4g* Au E1u* E2u* E3u* E4u*
1 0 0 0 1 0 0 0 0 0 0 E3g
2 1 0 0 1 0 0 0 0 0 0 Ag⊕E3g
3 2 0 0 1 0 0 0 0 0 0 2Ag⊕E3g
4 1 0 0 2 0 0 0 0 0 0 Ag⊕2E3g
5 2 0 0 2 0 0 0 0 0 0 2Ag⊕2E3g
6 3 0 0 2 0 0 0 0 0 0 3Ag⊕2E3g
7 2 0 0 3 0 0 0 0 0 0 2Ag⊕3E3g
8 3 0 0 3 0 0 0 0 0 0 3Ag⊕3E3g
9 4 0 0 3 0 0 0 0 0 0 4Ag⊕3E3g
10 3 0 0 4 0 0 0 0 0 0 3Ag⊕4E3g
11 4 0 0 4 0 0 0 0 0 0 4Ag⊕4E3g
12 5 0 0 4 0 0 0 0 0 0 5Ag⊕4E3g
13 4 0 0 5 0 0 0 0 0 0 4Ag⊕5E3g
14 5 0 0 5 0 0 0 0 0 0 5Ag⊕5E3g
15 6 0 0 5 0 0 0 0 0 0 6Ag⊕5E3g
16 5 0 0 6 0 0 0 0 0 0 5Ag⊕6E3g
17 6 0 0 6 0 0 0 0 0 0 6Ag⊕6E3g
18 7 0 0 6 0 0 0 0 0 0 7Ag⊕6E3g
19 6 0 0 7 0 0 0 0 0 0 6Ag⊕7E3g
20 7 0 0 7 0 0 0 0 0 0 7Ag⊕7E3g


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