Results for Point Group D17h



Symmetric powers of degenerate representation E''3
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 0.891 -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
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 1 0 0 0 0 0 E''3
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'6
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 E''3⊕E''8
4 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'5⊕E'6
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 E''2⊕E''3⊕E''8
6 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'5⊕E'6
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 E''2⊕E''3⊕E''4⊕E''8
8 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'5⊕E'6⊕E'7
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 E''2⊕E''3⊕E''4⊕E''7⊕E''8
10 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'4⊕E'5⊕E'6⊕E'7
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''7⊕E''8
12 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7
13 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''7⊕E''8
14 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'4⊕E'5⊕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 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'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 2 1 1 A''1⊕A''2⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕2E''6⊕E''7⊕E''8
20 1 0 1 1 2 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕2E'8



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