Results for Point Group D17d



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


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