Results for Point Group S18



Symmetric powers of degenerate representation E2g
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 0.347 -1.879 -1 1.532 2 0.347 -1.879 -1 1.532
2 3 -0.879 2.532 0 1.347 3 -0.879 2.532 0 1.347
3 4 -0.653 -2.879 1 0.532 4 -0.653 -2.879 1 0.532
4 5 0.653 2.879 -1 -0.532 5 0.653 2.879 -1 -0.532
5 6 0.879 -2.532 0 -1.347 6 0.879 -2.532 0 -1.347
6 7 -0.347 1.879 1 -1.532 7 -0.347 1.879 1 -1.532
7 8 -1.000 -1.000 -1 -1.000 8 -1.000 -1.000 -1 -1.000
8 9 -0.000 -0.000 0 0.000 9 -0.000 -0.000 0 0.000
9 10 1.000 1.000 1 1.000 10 1.000 1.000 1 1.000
10 11 0.347 -1.879 -1 1.532 11 0.347 -1.879 -1 1.532
11 12 -0.879 2.532 0 1.347 12 -0.879 2.532 0 1.347
12 13 -0.653 -2.879 1 0.532 13 -0.653 -2.879 1 0.532
13 14 0.653 2.879 -1 -0.532 14 0.653 2.879 -1 -0.532
14 15 0.879 -2.532 0 -1.347 15 0.879 -2.532 0 -1.347
15 16 -0.347 1.879 1 -1.532 16 -0.347 1.879 1 -1.532
16 17 -1.000 -1.000 -1 -1.000 17 -1.000 -1.000 -1 -1.000
17 18 -0.000 -0.000 0 0.000 18 -0.000 -0.000 0 0.000
18 19 1.000 1.000 1 1.000 19 1.000 1.000 1 1.000
19 20 0.347 -1.879 -1 1.532 20 0.347 -1.879 -1 1.532
20 21 -0.879 2.532 0 1.347 21 -0.879 2.532 0 1.347


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


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