Results for Point Group D17d



Symmetric powers of degenerate representation E8g
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 -1.966 1.865 -1.700 1.478 -1.205 0.891 -0.547 0.185 0 2 -1.966 1.865 -1.700 1.478 -1.205 0.891 -0.547 0.185 0
2 3 2.865 2.478 1.891 1.185 0.453 -0.205 -0.700 -0.966 1 3 2.865 2.478 1.891 1.185 0.453 -0.205 -0.700 -0.966 1
3 4 -3.666 2.756 -1.516 0.273 0.660 -1.074 0.931 -0.363 0 4 -3.666 2.756 -1.516 0.273 0.660 -1.074 0.931 -0.363 0
4 5 4.343 2.663 0.686 -0.781 -1.248 -0.753 0.191 0.899 1 5 4.343 2.663 0.686 -0.781 -1.248 -0.753 0.191 0.899 1
5 6 -4.872 2.209 0.349 -1.428 0.844 0.404 -1.035 0.529 0 6 -4.872 2.209 0.349 -1.428 0.844 0.404 -1.035 0.529 0
6 7 5.234 1.457 -1.280 -1.329 0.230 1.112 0.376 -0.801 1 7 5.234 1.457 -1.280 -1.329 0.230 1.112 0.376 -0.801 1
7 8 -5.419 0.509 1.827 -0.536 -1.122 0.588 0.830 -0.677 0 8 -5.419 0.509 1.827 -0.536 -1.122 0.588 0.830 -0.677 0
8 9 5.419 -0.509 -1.827 0.536 1.122 -0.588 -0.830 0.677 1 9 5.419 -0.509 -1.827 0.536 1.122 -0.588 -0.830 0.677 1
9 10 -5.234 -1.457 1.280 1.329 -0.230 -1.112 -0.376 0.801 0 10 -5.234 -1.457 1.280 1.329 -0.230 -1.112 -0.376 0.801 0
10 11 4.872 -2.209 -0.349 1.428 -0.844 -0.404 1.035 -0.529 1 11 4.872 -2.209 -0.349 1.428 -0.844 -0.404 1.035 -0.529 1
11 12 -4.343 -2.663 -0.686 0.781 1.248 0.753 -0.191 -0.899 0 12 -4.343 -2.663 -0.686 0.781 1.248 0.753 -0.191 -0.899 0
12 13 3.666 -2.756 1.516 -0.273 -0.660 1.074 -0.931 0.363 1 13 3.666 -2.756 1.516 -0.273 -0.660 1.074 -0.931 0.363 1
13 14 -2.865 -2.478 -1.891 -1.185 -0.453 0.205 0.700 0.966 0 14 -2.865 -2.478 -1.891 -1.185 -0.453 0.205 0.700 0.966 0
14 15 1.966 -1.865 1.700 -1.478 1.205 -0.891 0.547 -0.185 1 15 1.966 -1.865 1.700 -1.478 1.205 -0.891 0.547 -0.185 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 -1.966 1.865 -1.700 1.478 -1.205 0.891 -0.547 0.185 1 19 -1.966 1.865 -1.700 1.478 -1.205 0.891 -0.547 0.185 1
19 20 2.865 2.478 1.891 1.185 0.453 -0.205 -0.700 -0.966 0 20 2.865 2.478 1.891 1.185 0.453 -0.205 -0.700 -0.966 0
20 21 -3.666 2.756 -1.516 0.273 0.660 -1.074 0.931 -0.363 1 21 -3.666 2.756 -1.516 0.273 0.660 -1.074 0.931 -0.363 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E8g
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g
3 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 E7g⊕E8g
4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g
5 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 E6g⊕E7g⊕E8g
6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
7 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E5g⊕E6g⊕E7g⊕E8g
8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g
9 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E4g⊕E5g⊕E6g⊕E7g⊕E8g
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g
11 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
12 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g
13 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
14 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
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 1 1 1 2 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕2E8g
19 1 1 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
20 1 0 1 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕2E7g⊕2E8g


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement