Results for Point Group D17d



Symmetric powers of degenerate representation E5g
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C17 2(C17)2 2(C17)3 2(C17)4 2(C17)5 2(C17)6 2(C17)7 2(C17)8 17C'2 i 2(S34)15 2(S34)13 2(S34)11 2(S34)9 2(S34)7 2(S34)5 2(S34)3 2S34 17σd
1 2 -0.547 -1.700 1.478 0.891 -1.966 0.185 1.865 -1.205 0 2 -0.547 -1.700 1.478 0.891 -1.966 0.185 1.865 -1.205 0
2 3 -0.700 1.891 1.185 -0.205 2.865 -0.966 2.478 0.453 1 3 -0.700 1.891 1.185 -0.205 2.865 -0.966 2.478 0.453 1
3 4 0.931 -1.516 0.273 -1.074 -3.666 -0.363 2.756 0.660 0 4 0.931 -1.516 0.273 -1.074 -3.666 -0.363 2.756 0.660 0
4 5 0.191 0.686 -0.781 -0.753 4.343 0.899 2.663 -1.248 1 5 0.191 0.686 -0.781 -0.753 4.343 0.899 2.663 -1.248 1
5 6 -1.035 0.349 -1.428 0.404 -4.872 0.529 2.209 0.844 0 6 -1.035 0.349 -1.428 0.404 -4.872 0.529 2.209 0.844 0
6 7 0.376 -1.280 -1.329 1.112 5.234 -0.801 1.457 0.230 1 7 0.376 -1.280 -1.329 1.112 5.234 -0.801 1.457 0.230 1
7 8 0.830 1.827 -0.536 0.588 -5.419 -0.677 0.509 -1.122 0 8 0.830 1.827 -0.536 0.588 -5.419 -0.677 0.509 -1.122 0
8 9 -0.830 -1.827 0.536 -0.588 5.419 0.677 -0.509 1.122 1 9 -0.830 -1.827 0.536 -0.588 5.419 0.677 -0.509 1.122 1
9 10 -0.376 1.280 1.329 -1.112 -5.234 0.801 -1.457 -0.230 0 10 -0.376 1.280 1.329 -1.112 -5.234 0.801 -1.457 -0.230 0
10 11 1.035 -0.349 1.428 -0.404 4.872 -0.529 -2.209 -0.844 1 11 1.035 -0.349 1.428 -0.404 4.872 -0.529 -2.209 -0.844 1
11 12 -0.191 -0.686 0.781 0.753 -4.343 -0.899 -2.663 1.248 0 12 -0.191 -0.686 0.781 0.753 -4.343 -0.899 -2.663 1.248 0
12 13 -0.931 1.516 -0.273 1.074 3.666 0.363 -2.756 -0.660 1 13 -0.931 1.516 -0.273 1.074 3.666 0.363 -2.756 -0.660 1
13 14 0.700 -1.891 -1.185 0.205 -2.865 0.966 -2.478 -0.453 0 14 0.700 -1.891 -1.185 0.205 -2.865 0.966 -2.478 -0.453 0
14 15 0.547 1.700 -1.478 -0.891 1.966 -0.185 -1.865 1.205 1 15 0.547 1.700 -1.478 -0.891 1.966 -0.185 -1.865 1.205 1
15 16 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0 16 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0
16 17 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 1 17 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 1
17 18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0 18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0
18 19 -0.547 -1.700 1.478 0.891 -1.966 0.185 1.865 -1.205 1 19 -0.547 -1.700 1.478 0.891 -1.966 0.185 1.865 -1.205 1
19 20 -0.700 1.891 1.185 -0.205 2.865 -0.966 2.478 0.453 0 20 -0.700 1.891 1.185 -0.205 2.865 -0.966 2.478 0.453 0
20 21 0.931 -1.516 0.273 -1.074 -3.666 -0.363 2.756 0.660 1 21 0.931 -1.516 0.273 -1.074 -3.666 -0.363 2.756 0.660 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g E5g E6g E7g E8g A1u A2u E1u E2u E3u E4u E5u E6u E7u E8u
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E5g
2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E7g
3 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E5g
4 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E7g
5 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E5g⊕E8g
6 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E4g⊕E7g
7 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E5g⊕E8g
8 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E4g⊕E6g⊕E7g
9 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E5g⊕E6g⊕E8g
10 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E6g⊕E7g
11 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E8g
12 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E6g⊕E7g⊕E8g
13 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E8g
14 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E6g⊕E7g⊕E8g
15 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
16 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
17 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
18 1 0 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕2E5g⊕E6g⊕E7g⊕E8g
19 1 1 1 1 1 1 1 1 2 1 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕2E7g⊕E8g
20 1 0 1 2 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕E3g⊕E4g⊕2E5g⊕E6g⊕E7g⊕E8g



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