Results for Point Group D17d



Symmetric powers of degenerate representation E3u
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 0.891 -1.205 -1.966 -0.547 1.478 1.865 0.185 -1.700 0 -2 -0.891 1.205 1.966 0.547 -1.478 -1.865 -0.185 1.700 0
2 3 -0.205 0.453 2.865 -0.700 1.185 2.478 -0.966 1.891 1 3 -0.205 0.453 2.865 -0.700 1.185 2.478 -0.966 1.891 1
3 4 -1.074 0.660 -3.666 0.931 0.273 2.756 -0.363 -1.516 0 -4 1.074 -0.660 3.666 -0.931 -0.273 -2.756 0.363 1.516 0
4 5 -0.753 -1.248 4.343 0.191 -0.781 2.663 0.899 0.686 1 5 -0.753 -1.248 4.343 0.191 -0.781 2.663 0.899 0.686 1
5 6 0.404 0.844 -4.872 -1.035 -1.428 2.209 0.529 0.349 0 -6 -0.404 -0.844 4.872 1.035 1.428 -2.209 -0.529 -0.349 0
6 7 1.112 0.230 5.234 0.376 -1.329 1.457 -0.801 -1.280 1 7 1.112 0.230 5.234 0.376 -1.329 1.457 -0.801 -1.280 1
7 8 0.588 -1.122 -5.419 0.830 -0.536 0.509 -0.677 1.827 0 -8 -0.588 1.122 5.419 -0.830 0.536 -0.509 0.677 -1.827 0
8 9 -0.588 1.122 5.419 -0.830 0.536 -0.509 0.677 -1.827 1 9 -0.588 1.122 5.419 -0.830 0.536 -0.509 0.677 -1.827 1
9 10 -1.112 -0.230 -5.234 -0.376 1.329 -1.457 0.801 1.280 0 -10 1.112 0.230 5.234 0.376 -1.329 1.457 -0.801 -1.280 0
10 11 -0.404 -0.844 4.872 1.035 1.428 -2.209 -0.529 -0.349 1 11 -0.404 -0.844 4.872 1.035 1.428 -2.209 -0.529 -0.349 1
11 12 0.753 1.248 -4.343 -0.191 0.781 -2.663 -0.899 -0.686 0 -12 -0.753 -1.248 4.343 0.191 -0.781 2.663 0.899 0.686 0
12 13 1.074 -0.660 3.666 -0.931 -0.273 -2.756 0.363 1.516 1 13 1.074 -0.660 3.666 -0.931 -0.273 -2.756 0.363 1.516 1
13 14 0.205 -0.453 -2.865 0.700 -1.185 -2.478 0.966 -1.891 0 -14 -0.205 0.453 2.865 -0.700 1.185 2.478 -0.966 1.891 0
14 15 -0.891 1.205 1.966 0.547 -1.478 -1.865 -0.185 1.700 1 15 -0.891 1.205 1.966 0.547 -1.478 -1.865 -0.185 1.700 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 0.891 -1.205 -1.966 -0.547 1.478 1.865 0.185 -1.700 1 19 0.891 -1.205 -1.966 -0.547 1.478 1.865 0.185 -1.700 1
19 20 -0.205 0.453 2.865 -0.700 1.185 2.478 -0.966 1.891 0 -20 0.205 -0.453 -2.865 0.700 -1.185 -2.478 0.966 -1.891 0
20 21 -1.074 0.660 -3.666 0.931 0.273 2.756 -0.363 -1.516 1 21 -1.074 0.660 -3.666 0.931 0.273 2.756 -0.363 -1.516 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 0 0 0 0 0 1 0 0 0 0 0 E3u
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E6g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 E3u⊕E8u
4 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E5g⊕E6g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 E2u⊕E3u⊕E8u
6 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g⊕E6g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 E2u⊕E3u⊕E4u⊕E8u
8 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g⊕E6g⊕E7g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 E2u⊕E3u⊕E4u⊕E7u⊕E8u
10 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g⊕E6g⊕E7g
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E7u⊕E8u
12 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E7g
13 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E7u⊕E8u
14 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
15 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u
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 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u
18 1 0 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
19 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕2E6u⊕E7u⊕E8u
20 1 0 1 1 2 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕2E8g



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