Results for Point Group C14h



Symmetric powers of degenerate representation E3g
Vibrational overtones


Characters of symmetric powers
Power
To
E C14 C7 (C14)3 (C7)2 (C14)5 (C7)3 C2 (C7)4 (C14)9 (C7)5 (C14)11 (C7)6 (C14)13 i (S7)11 (S14)9 (S7)5 (S14)11 (S7)13 (S14)13 σh S14 S7 (S14)3 (S7)9 (S14)5 (S7)3
1 2 0.445 -1.802 -1.247 1.247 1.802 -0.445 -2 -0.445 1.802 1.247 -1.247 -1.802 0.445 2 0.445 -1.802 -1.247 1.247 1.802 -0.445 -2 -0.445 1.802 1.247 -1.247 -1.802 0.445
2 3 -0.802 2.247 0.555 0.555 2.247 -0.802 3 -0.802 2.247 0.555 0.555 2.247 -0.802 3 -0.802 2.247 0.555 0.555 2.247 -0.802 3 -0.802 2.247 0.555 0.555 2.247 -0.802
3 4 -0.802 -2.247 0.555 -0.555 2.247 0.802 -4 0.802 2.247 -0.555 0.555 -2.247 -0.802 4 -0.802 -2.247 0.555 -0.555 2.247 0.802 -4 0.802 2.247 -0.555 0.555 -2.247 -0.802
4 5 0.445 1.802 -1.247 -1.247 1.802 0.445 5 0.445 1.802 -1.247 -1.247 1.802 0.445 5 0.445 1.802 -1.247 -1.247 1.802 0.445 5 0.445 1.802 -1.247 -1.247 1.802 0.445
5 6 1.000 -1.000 1.000 -1.000 1.000 -1.000 -6 -1.000 1.000 -1.000 1.000 -1.000 1.000 6 1.000 -1.000 1.000 -1.000 1.000 -1.000 -6 -1.000 1.000 -1.000 1.000 -1.000 1.000
6 7 0.000 -0.000 -0.000 0.000 0.000 -0.000 7 0.000 -0.000 -0.000 0.000 0.000 -0.000 7 0.000 -0.000 -0.000 0.000 0.000 -0.000 7 0.000 -0.000 -0.000 0.000 0.000 -0.000
7 8 -1.000 1.000 -1.000 1.000 -1.000 1.000 -8 1.000 -1.000 1.000 -1.000 1.000 -1.000 8 -1.000 1.000 -1.000 1.000 -1.000 1.000 -8 1.000 -1.000 1.000 -1.000 1.000 -1.000
8 9 -0.445 -1.802 1.247 1.247 -1.802 -0.445 9 -0.445 -1.802 1.247 1.247 -1.802 -0.445 9 -0.445 -1.802 1.247 1.247 -1.802 -0.445 9 -0.445 -1.802 1.247 1.247 -1.802 -0.445
9 10 0.802 2.247 -0.555 0.555 -2.247 -0.802 -10 -0.802 -2.247 0.555 -0.555 2.247 0.802 10 0.802 2.247 -0.555 0.555 -2.247 -0.802 -10 -0.802 -2.247 0.555 -0.555 2.247 0.802
10 11 0.802 -2.247 -0.555 -0.555 -2.247 0.802 11 0.802 -2.247 -0.555 -0.555 -2.247 0.802 11 0.802 -2.247 -0.555 -0.555 -2.247 0.802 11 0.802 -2.247 -0.555 -0.555 -2.247 0.802
11 12 -0.445 1.802 1.247 -1.247 -1.802 0.445 -12 0.445 -1.802 -1.247 1.247 1.802 -0.445 12 -0.445 1.802 1.247 -1.247 -1.802 0.445 -12 0.445 -1.802 -1.247 1.247 1.802 -0.445
12 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
13 14 -0.000 -0.000 0.000 0.000 -0.000 -0.000 -14 0.000 0.000 -0.000 -0.000 0.000 0.000 14 -0.000 -0.000 0.000 0.000 -0.000 -0.000 -14 0.000 0.000 -0.000 -0.000 0.000 0.000
14 15 1.000 1.000 1.000 1.000 1.000 1.000 15 1.000 1.000 1.000 1.000 1.000 1.000 15 1.000 1.000 1.000 1.000 1.000 1.000 15 1.000 1.000 1.000 1.000 1.000 1.000
15 16 0.445 -1.802 -1.247 1.247 1.802 -0.445 -16 -0.445 1.802 1.247 -1.247 -1.802 0.445 16 0.445 -1.802 -1.247 1.247 1.802 -0.445 -16 -0.445 1.802 1.247 -1.247 -1.802 0.445
16 17 -0.802 2.247 0.555 0.555 2.247 -0.802 17 -0.802 2.247 0.555 0.555 2.247 -0.802 17 -0.802 2.247 0.555 0.555 2.247 -0.802 17 -0.802 2.247 0.555 0.555 2.247 -0.802
17 18 -0.802 -2.247 0.555 -0.555 2.247 0.802 -18 0.802 2.247 -0.555 0.555 -2.247 -0.802 18 -0.802 -2.247 0.555 -0.555 2.247 0.802 -18 0.802 2.247 -0.555 0.555 -2.247 -0.802
18 19 0.445 1.802 -1.247 -1.247 1.802 0.445 19 0.445 1.802 -1.247 -1.247 1.802 0.445 19 0.445 1.802 -1.247 -1.247 1.802 0.445 19 0.445 1.802 -1.247 -1.247 1.802 0.445
19 20 1.000 -1.000 1.000 -1.000 1.000 -1.000 -20 -1.000 1.000 -1.000 1.000 -1.000 1.000 20 1.000 -1.000 1.000 -1.000 1.000 -1.000 -20 -1.000 1.000 -1.000 1.000 -1.000 1.000
20 21 0.000 -0.000 -0.000 0.000 0.000 -0.000 21 0.000 -0.000 -0.000 0.000 0.000 -0.000 21 0.000 -0.000 -0.000 0.000 0.000 -0.000 21 0.000 -0.000 -0.000 0.000 0.000 -0.000


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



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