Results for Point Group D17h



Symmetric powers of degenerate representation E''5
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 σh 2S17 2(S17)15 2(S17)3 2(S17)13 2(S17)5 2(S17)11 2(S17)7 2(S17)9 17σv
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		 A'1 A'2 E'1 E'2 E'3 E'4 E'5 E'6 E'7 E'8 A''1 A''2 E''1 E''2 E''3 E''4 E''5 E''6 E''7 E''8
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 E''5
2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'7
3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 E''2⊕E''5
4 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'3⊕E'7
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 E''2⊕E''5⊕E''8
6 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'3⊕E'4⊕E'7
7 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 E''1⊕E''2⊕E''5⊕E''8
8 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'3⊕E'4⊕E'6⊕E'7
9 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 E''1⊕E''2⊕E''5⊕E''6⊕E''8
10 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'3⊕E'4⊕E'6⊕E'7
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 E''1⊕E''2⊕E''4⊕E''5⊕E''6⊕E''8
12 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'3⊕E'4⊕E'6⊕E'7⊕E'8
13 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''8
14 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'6⊕E'7⊕E'8
15 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8
16 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
17 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 A''1⊕A''2⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8
18 1 0 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕E'6⊕E'7⊕E'8
19 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 1 A''1⊕A''2⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕2E''7⊕E''8
20 1 0 1 2 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕2E'2⊕E'3⊕E'4⊕2E'5⊕E'6⊕E'7⊕E'8


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