Results for Point Group S18



Symmetric powers of degenerate representation E1g
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 2 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532
2 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347
3 4 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 4 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532
4 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532
5 6 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 6 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347
6 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532
11 12 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 12 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347
12 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532
13 14 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 14 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532
14 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347
15 16 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 16 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 20 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532
20 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347


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


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