Results for Point Group D16h



Symmetric powers of degenerate representation E7g
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 8C'2 8C''2 i 2(S16)7 2(S8)3 2(S16)5 2S4 2(S16)3 2S8 2S16 σh v d
1 2 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -2 0 0 2 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -2 0 0
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 1 1 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 1 1
3 4 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -4 0 0 4 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -4 0 0
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 1 1 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 1 1
5 6 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -6 0 0 6 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -6 0 0
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1 1 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1 1
7 8 0.000 0.000 -0.000 0 0.000 -0.000 0.000 -8 0 0 8 0.000 0.000 -0.000 0 0.000 -0.000 0.000 -8 0 0
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 1 1 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 1 1
9 10 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -10 0 0 10 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -10 0 0
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 1 1 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 1 1
11 12 2.613 -0.000 -1.082 0 1.082 0.000 -2.613 -12 0 0 12 2.613 -0.000 -1.082 0 1.082 0.000 -2.613 -12 0 0
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 1 1 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 1 1
13 14 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -14 0 0 14 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -14 0 0
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 1 1 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 1 1
15 16 -0.000 0.000 0.000 0 -0.000 -0.000 -0.000 -16 0 0 16 -0.000 0.000 0.000 0 -0.000 -0.000 -0.000 -16 0 0
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1 1 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1 1
17 18 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -18 0 0 18 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -18 0 0
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 1 1 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 1 1
19 20 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -20 0 0 20 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -20 0 0
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 1 1 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 1 1


Decomposition to irreducible representations
Power
To
A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u
1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E7g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E5g⊕E7g
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g
5 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E3g⊕E5g⊕E7g
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g
7 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E3g⊕E5g⊕E7g
8 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕E4g⊕E6g
9 0 0 0 0 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕E3g⊕E5g⊕E7g
10 1 0 1 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕E4g⊕2E6g
11 0 0 0 0 2 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕E5g⊕E7g
12 1 0 1 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕E2g⊕2E4g⊕2E6g
13 0 0 0 0 2 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕E7g
14 1 0 1 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕B1g⊕B2g⊕2E2g⊕2E4g⊕2E6g
15 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕2E7g
16 2 1 1 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕2E2g⊕2E4g⊕2E6g
17 0 0 0 0 2 0 2 0 2 0 3 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕2E5g⊕3E7g
18 2 1 1 1 0 3 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕3E2g⊕2E4g⊕2E6g
19 0 0 0 0 2 0 2 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 2E1g⊕2E3g⊕3E5g⊕3E7g
20 2 1 1 1 0 3 0 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕B1g⊕B2g⊕3E2g⊕3E4g⊕2E6g



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