Results for Point Group C16h



Symmetric powers of degenerate representation E2g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C16 2C8 2(C16)3 2C4 2(C16)5 2(C8)3 2(C16)7 C2 i 2(S16)7 2(S8)3 2(S16)5 2S4 2(S16)3 2S8 2S16 σh
1 2 1.414 0.000 -1.414 -2 -1.414 0.000 1.414 2 2 1.414 0.000 -1.414 -2 -1.414 0.000 1.414 2
2 3 1.000 -1.000 1.000 3 1.000 -1.000 1.000 3 3 1.000 -1.000 1.000 3 1.000 -1.000 1.000 3
3 4 0.000 0.000 0.000 -4 -0.000 0.000 -0.000 4 4 0.000 0.000 0.000 -4 -0.000 0.000 -0.000 4
4 5 -1.000 1.000 -1.000 5 -1.000 1.000 -1.000 5 5 -1.000 1.000 -1.000 5 -1.000 1.000 -1.000 5
5 6 -1.414 0.000 1.414 -6 1.414 0.000 -1.414 6 6 -1.414 0.000 1.414 -6 1.414 0.000 -1.414 6
6 7 -1.000 -1.000 -1.000 7 -1.000 -1.000 -1.000 7 7 -1.000 -1.000 -1.000 7 -1.000 -1.000 -1.000 7
7 8 -0.000 0.000 -0.000 -8 0.000 0.000 0.000 8 8 -0.000 0.000 -0.000 -8 0.000 0.000 0.000 8
8 9 1.000 1.000 1.000 9 1.000 1.000 1.000 9 9 1.000 1.000 1.000 9 1.000 1.000 1.000 9
9 10 1.414 0.000 -1.414 -10 -1.414 0.000 1.414 10 10 1.414 0.000 -1.414 -10 -1.414 0.000 1.414 10
10 11 1.000 -1.000 1.000 11 1.000 -1.000 1.000 11 11 1.000 -1.000 1.000 11 1.000 -1.000 1.000 11
11 12 0.000 0.000 0.000 -12 -0.000 0.000 -0.000 12 12 0.000 0.000 0.000 -12 -0.000 0.000 -0.000 12
12 13 -1.000 1.000 -1.000 13 -1.000 1.000 -1.000 13 13 -1.000 1.000 -1.000 13 -1.000 1.000 -1.000 13
13 14 -1.414 0.000 1.414 -14 1.414 0.000 -1.414 14 14 -1.414 0.000 1.414 -14 1.414 0.000 -1.414 14
14 15 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 15 15 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 15
15 16 -0.000 0.000 -0.000 -16 0.000 0.000 0.000 16 16 -0.000 0.000 -0.000 -16 0.000 0.000 0.000 16
16 17 1.000 1.000 1.000 17 1.000 1.000 1.000 17 17 1.000 1.000 1.000 17 1.000 1.000 1.000 17
17 18 1.414 0.000 -1.414 -18 -1.414 0.000 1.414 18 18 1.414 0.000 -1.414 -18 -1.414 0.000 1.414 18
18 19 1.000 -1.000 1.000 19 1.000 -1.000 1.000 19 19 1.000 -1.000 1.000 19 1.000 -1.000 1.000 19
19 20 0.000 0.000 0.000 -20 -0.000 0.000 -0.000 20 20 0.000 0.000 0.000 -20 -0.000 0.000 -0.000 20
20 21 -1.000 1.000 -1.000 21 -1.000 1.000 -1.000 21 21 -1.000 1.000 -1.000 21 -1.000 1.000 -1.000 21


Decomposition to irreducible representations
Power
To		 Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u*
1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E4g
3 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E6g
4 1 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E4g
5 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 E2g⊕2E6g
6 1 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E4g
7 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2E2g⊕2E6g
8 3 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕2E4g
9 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 3E2g⊕2E6g
10 3 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕3E4g
11 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3E2g⊕3E6g
12 3 4 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕4Bg⊕3E4g
13 0 0 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3E2g⊕4E6g
14 3 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3Ag⊕4Bg⊕4E4g
15 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4E2g⊕4E6g
16 5 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕4Bg⊕4E4g
17 0 0 0 5 0 0 0 4 0 0 0 0 0 0 0 0 0 0 5E2g⊕4E6g
18 5 4 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕4Bg⊕5E4g
19 0 0 0 5 0 0 0 5 0 0 0 0 0 0 0 0 0 0 5E2g⊕5E6g
20 5 6 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5Ag⊕6Bg⊕5E4g


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