Results for Point Group D17h



Symmetric powers of degenerate representation E'2
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 1.478 0.185 -1.205 -1.966 -1.700 -0.547 0.891 1.865 0 2 1.478 0.185 -1.205 -1.966 -1.700 -0.547 0.891 1.865 0
2 3 1.185 -0.966 0.453 2.865 1.891 -0.700 -0.205 2.478 1 3 1.185 -0.966 0.453 2.865 1.891 -0.700 -0.205 2.478 1
3 4 0.273 -0.363 0.660 -3.666 -1.516 0.931 -1.074 2.756 0 4 0.273 -0.363 0.660 -3.666 -1.516 0.931 -1.074 2.756 0
4 5 -0.781 0.899 -1.248 4.343 0.686 0.191 -0.753 2.663 1 5 -0.781 0.899 -1.248 4.343 0.686 0.191 -0.753 2.663 1
5 6 -1.428 0.529 0.844 -4.872 0.349 -1.035 0.404 2.209 0 6 -1.428 0.529 0.844 -4.872 0.349 -1.035 0.404 2.209 0
6 7 -1.329 -0.801 0.230 5.234 -1.280 0.376 1.112 1.457 1 7 -1.329 -0.801 0.230 5.234 -1.280 0.376 1.112 1.457 1
7 8 -0.536 -0.677 -1.122 -5.419 1.827 0.830 0.588 0.509 0 8 -0.536 -0.677 -1.122 -5.419 1.827 0.830 0.588 0.509 0
8 9 0.536 0.677 1.122 5.419 -1.827 -0.830 -0.588 -0.509 1 9 0.536 0.677 1.122 5.419 -1.827 -0.830 -0.588 -0.509 1
9 10 1.329 0.801 -0.230 -5.234 1.280 -0.376 -1.112 -1.457 0 10 1.329 0.801 -0.230 -5.234 1.280 -0.376 -1.112 -1.457 0
10 11 1.428 -0.529 -0.844 4.872 -0.349 1.035 -0.404 -2.209 1 11 1.428 -0.529 -0.844 4.872 -0.349 1.035 -0.404 -2.209 1
11 12 0.781 -0.899 1.248 -4.343 -0.686 -0.191 0.753 -2.663 0 12 0.781 -0.899 1.248 -4.343 -0.686 -0.191 0.753 -2.663 0
12 13 -0.273 0.363 -0.660 3.666 1.516 -0.931 1.074 -2.756 1 13 -0.273 0.363 -0.660 3.666 1.516 -0.931 1.074 -2.756 1
13 14 -1.185 0.966 -0.453 -2.865 -1.891 0.700 0.205 -2.478 0 14 -1.185 0.966 -0.453 -2.865 -1.891 0.700 0.205 -2.478 0
14 15 -1.478 -0.185 1.205 1.966 1.700 0.547 -0.891 -1.865 1 15 -1.478 -0.185 1.205 1.966 1.700 0.547 -0.891 -1.865 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 1.478 0.185 -1.205 -1.966 -1.700 -0.547 0.891 1.865 1 19 1.478 0.185 -1.205 -1.966 -1.700 -0.547 0.891 1.865 1
19 20 1.185 -0.966 0.453 2.865 1.891 -0.700 -0.205 2.478 0 20 1.185 -0.966 0.453 2.865 1.891 -0.700 -0.205 2.478 0
20 21 0.273 -0.363 0.660 -3.666 -1.516 0.931 -1.074 2.756 1 21 0.273 -0.363 0.660 -3.666 -1.516 0.931 -1.074 2.756 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E'2
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'4
3 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'6
4 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'4⊕E'8
5 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'6⊕E'7
6 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'4⊕E'5⊕E'8
7 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'3⊕E'6⊕E'7
8 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'4⊕E'5⊕E'8
9 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'6⊕E'7
10 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'3⊕E'4⊕E'5⊕E'8
11 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'5⊕E'6⊕E'7
12 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'3⊕E'4⊕E'5⊕E'7⊕E'8
13 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'5⊕E'6⊕E'7⊕E'8
14 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
15 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
18 1 0 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕2E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
19 1 1 1 1 1 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6⊕E'7⊕E'8
20 1 0 1 2 1 1 1 2 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕2E'2⊕E'3⊕E'4⊕E'5⊕2E'6⊕E'7⊕E'8



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