Results for Point Group C18h



Symmetric powers of degenerate representation E8u
Vibrational overtones


Characters of symmetric powers
Power
To
E C18 C9 C6 (C9)2 (C18)5 C3 (C18)7 (C9)4 C2 (C9)5 (C18)11 (C3)2 (C18)13 (C9)7 (C6)5 (C9)8 (C18)17 i (S9)5 (S18)11 (S3)5 (S18)13 (S9)7 (S6)5 (S9)17 (S18)17 σh S18 S9 S6 (S9)11 (S18)5 S3 (S18)7 (S9)13
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 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 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 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 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 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 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 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 -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 -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 -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 -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 -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 -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 -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 -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 -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 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 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 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 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 Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u*
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E8u
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 E6u⊕E8u
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 E4u⊕E6u⊕E8u
6 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 E2u⊕E4u⊕E6u⊕E8u
8 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g⊕E8g
9 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 1 0 1 0 1 2Au⊕E2u⊕E4u⊕E6u⊕E8u
10 1 0 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g⊕2E8g
11 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 1 0 1 0 1 2Au⊕2E2u⊕E4u⊕E6u⊕E8u
12 1 0 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕2E6g⊕2E8g
13 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 1 0 1 2Au⊕2E2u⊕2E4u⊕E6u⊕E8u
14 1 0 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕2E4g⊕2E6g⊕2E8g
15 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 1 2Au⊕2E2u⊕2E4u⊕2E6u⊕E8u
16 1 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕2E4g⊕2E6g⊕2E8g
17 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 2 2Au⊕2E2u⊕2E4u⊕2E6u⊕2E8u
18 3 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 3 2Au⊕2E2u⊕2E4u⊕2E6u⊕3E8u
20 3 0 0 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕3E2g⊕2E4g⊕2E6g⊕2E8g



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement