Results for Point Group C16h



Symmetric powers of degenerate representation E1g
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 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -2 2 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -2
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3
3 4 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -4 4 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -4
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5
5 6 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -6 6 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -6
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7
7 8 0.000 -0.000 0.000 0 0.000 -0.000 0.000 -8 8 0.000 -0.000 0.000 0 0.000 -0.000 0.000 -8
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9
9 10 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -10 10 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -10
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11
11 12 -2.613 0.000 1.082 0 -1.082 0.000 2.613 -12 12 -2.613 0.000 1.082 0 -1.082 0.000 2.613 -12
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13
13 14 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -14 14 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -14
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15
15 16 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -16 16 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -16
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17
17 18 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -18 18 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -18
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19
19 20 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -20 20 2.613 0.000 -1.082 0 1.082 0.000 -2.613 -20
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g
5 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g
6 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g⊕E4g⊕E6g
7 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g
8 1 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g⊕E6g
9 0 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕2E7g
10 1 2 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕E4g⊕2E6g
11 0 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕2E5g⊕2E7g
12 1 2 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕E2g⊕2E4g⊕2E6g
13 0 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 E1g⊕2E3g⊕2E5g⊕2E7g
14 1 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 Ag⊕2Bg⊕2E2g⊕2E4g⊕2E6g
15 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕2E7g
16 3 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕2E2g⊕2E4g⊕2E6g
17 0 0 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 3E1g⊕2E3g⊕2E5g⊕2E7g
18 3 2 0 3 0 2 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕3E2g⊕2E4g⊕2E6g
19 0 0 3 0 3 0 2 0 2 0 0 0 0 0 0 0 0 0 3E1g⊕3E3g⊕2E5g⊕2E7g
20 3 2 0 3 0 3 0 2 0 0 0 0 0 0 0 0 0 0 3Ag⊕2Bg⊕3E2g⊕3E4g⊕2E6g



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