Results for Point Group C16h



Symmetric powers of degenerate representation E7g
Vibrational overtones


Characters of symmetric powers
Power
To
E C16 C8 (C16)3 C4 (C16)5 (C8)3 (C16)7 C2 (C16)9 (C8)5 (C16)11 (C4)3 (C16)13 (C8)7 (C16)15 i (S16)9 (S8)5 (S16)11 (S4)3 (S16)13 (S8)7 (S16)15 σh S16 S8 (S16)3 S4 (S16)5 (S8)3 (S16)7
1 2 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -2 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 2 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -2 1.848 -1.414 0.765 0 -0.765 1.414 -1.848
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414
3 4 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -4 2.613 0.000 -1.082 0 1.082 0.000 -2.613 4 -2.613 0.000 1.082 0 -1.082 -0.000 2.613 -4 2.613 0.000 -1.082 0 1.082 0.000 -2.613
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414
5 6 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -6 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 6 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -6 1.848 1.414 0.765 0 -0.765 -1.414 -1.848
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000
7 8 0.000 0.000 -0.000 0 0.000 0.000 0.000 -8 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 8 0.000 0.000 0.000 0 0.000 0.000 0.000 -8 -0.000 -0.000 0.000 0 -0.000 -0.000 -0.000
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000
9 10 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -10 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 10 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -10 -1.848 -1.414 -0.765 0 0.765 1.414 1.848
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414
11 12 2.613 -0.000 -1.082 0 1.082 -0.000 -2.613 -12 -2.613 0.000 1.082 0 -1.082 0.000 2.613 12 2.613 -0.000 -1.082 0 1.082 -0.000 -2.613 -12 -2.613 0.000 1.082 0 -1.082 0.000 2.613
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414
13 14 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -14 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 14 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -14 -1.848 1.414 -0.765 0 0.765 -1.414 1.848
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000
15 16 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 -16 0.000 -0.000 0.000 0 0.000 -0.000 0.000 16 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 -16 0.000 -0.000 0.000 0 0.000 -0.000 0.000
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1.000 1.000 1.000 1 1.000 1.000 1.000
17 18 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -18 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 18 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -18 1.848 -1.414 0.765 0 -0.765 1.414 -1.848
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414
19 20 -2.613 -0.000 1.082 0 -1.082 -0.000 2.613 -20 2.613 0.000 -1.082 0 1.082 0.000 -2.613 20 -2.613 -0.000 1.082 0 -1.082 -0.000 2.613 -20 2.613 0.000 -1.082 0 1.082 0.000 -2.613
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414


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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 E7g
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ag⊕E2g
3 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 E5g⊕E7g
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 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 E3g⊕E5g⊕E7g
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 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 2E1g⊕E3g⊕E5g⊕E7g
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 2 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕E5g⊕E7g
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 2 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕E7g
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 2 0 2 0 2 0 3 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕3E7g
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 2 0 2 0 3 0 3 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕3E5g⊕3E7g
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