Results for Point Group D17h



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


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