Results for Point Group S18



Symmetric powers of degenerate representation E4g
Vibrational overtones


Characters of symmetric powers
Power
To		 E C9 (C9)2 C3 (C9)4 (C9)5 (C3)2 (C9)7 (C9)8 i (S18)11 (S18)13 (S6)5 (S18)17 S18 S6 (S18)5 (S18)7
1 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
2 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532
3 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879
4 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879
5 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532
6 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
8 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000
10 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
11 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532
12 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879
13 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879
14 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532
15 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
17 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000
19 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
20 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532


Decomposition to irreducible representations
Power
To		 Ag E1g* E2g* E3g* E4g* Au E1u* E2u* E3u* E4u*
1 0 0 0 0 1 0 0 0 0 0 E4g
2 1 1 0 0 0 0 0 0 0 0 Ag⊕E1g
3 0 0 0 1 1 0 0 0 0 0 E3g⊕E4g
4 1 1 1 0 0 0 0 0 0 0 Ag⊕E1g⊕E2g
5 0 0 1 1 1 0 0 0 0 0 E2g⊕E3g⊕E4g
6 1 1 1 1 0 0 0 0 0 0 Ag⊕E1g⊕E2g⊕E3g
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 1 1 2 0 0 0 0 0 Ag⊕E1g⊕E2g⊕E3g⊕2E4g
11 2 2 1 1 1 0 0 0 0 0 2Ag⊕2E1g⊕E2g⊕E3g⊕E4g
12 1 1 1 2 2 0 0 0 0 0 Ag⊕E1g⊕E2g⊕2E3g⊕2E4g
13 2 2 2 1 1 0 0 0 0 0 2Ag⊕2E1g⊕2E2g⊕E3g⊕E4g
14 1 1 2 2 2 0 0 0 0 0 Ag⊕E1g⊕2E2g⊕2E3g⊕2E4g
15 2 2 2 2 1 0 0 0 0 0 2Ag⊕2E1g⊕2E2g⊕2E3g⊕E4g
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 2 2 3 0 0 0 0 0 2Ag⊕2E1g⊕2E2g⊕2E3g⊕3E4g
20 3 3 2 2 2 0 0 0 0 0 3Ag⊕3E1g⊕2E2g⊕2E3g⊕2E4g


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