Results for Point Group D17d



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


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