Results for Point Group C18h



Symmetric powers of degenerate representation E4u
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 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 2 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 -2 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 -2 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
2 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879
3 4 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 4 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 -4 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 -4 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653
4 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653
5 6 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 6 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 -6 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 -6 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879
6 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
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 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347
11 12 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 12 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 -12 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 -12 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879
12 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653
13 14 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 14 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 -14 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 -14 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653
14 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879
15 16 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 16 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 -16 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 -16 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347
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 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 20 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 -20 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 -20 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
20 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879


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 1 0 0 0 0 E4u
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E8g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 E4u⊕E6u
4 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E8g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 E2u⊕E4u⊕E6u
6 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E6g⊕E8g
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 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕2E4g⊕E6g⊕E8g
11 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 1 0 1 0 2 2Au⊕E2u⊕E4u⊕E6u⊕2E8u
12 1 0 0 1 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕2E4g⊕2E6g⊕E8g
13 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 1 0 1 0 2 2Au⊕2E2u⊕E4u⊕E6u⊕2E8u
14 1 0 0 2 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕2E2g⊕2E4g⊕2E6g⊕E8g
15 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 1 0 2 0 2 2Au⊕2E2u⊕E4u⊕2E6u⊕2E8u
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 3 0 2 0 2 2Au⊕2E2u⊕3E4u⊕2E6u⊕2E8u
20 3 0 0 2 0 2 0 2 0 3 0 0 0 0 0 0 0 0 0 0 3Ag⊕2E2g⊕2E4g⊕2E6g⊕3E8g


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