Results for Point Group D13h



Symmetric powers of degenerate representation E'4
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C13 2(C13)2 2(C13)3 2(C13)4 2(C13)5 2(C13)6 13C'2 σh 2S13 2(S13)11 2(S13)3 2(S13)9 2(S13)5 2(S13)7 13σv
1 2 -0.709 -1.497 1.771 0.241 -1.942 1.136 0 2 -0.709 -1.497 1.771 0.241 -1.942 1.136 0
2 3 -0.497 1.241 2.136 -0.942 2.771 0.291 1 3 -0.497 1.241 2.136 -0.942 2.771 0.291 1
3 4 1.062 -0.361 2.012 -0.468 -3.439 -0.806 0 4 1.062 -0.361 2.012 -0.468 -3.439 -0.806 0
4 5 -0.256 -0.701 1.427 0.829 3.907 -1.206 1 5 -0.256 -0.701 1.427 0.829 3.907 -1.206 1
5 6 -0.880 1.410 0.515 0.668 -4.148 -0.565 0 6 -0.880 1.410 0.515 0.668 -4.148 -0.565 0
6 7 0.880 -1.410 -0.515 -0.668 4.148 0.565 1 7 0.880 -1.410 -0.515 -0.668 4.148 0.565 1
7 8 0.256 0.701 -1.427 -0.829 -3.907 1.206 0 8 0.256 0.701 -1.427 -0.829 -3.907 1.206 0
8 9 -1.062 0.361 -2.012 0.468 3.439 0.806 1 9 -1.062 0.361 -2.012 0.468 3.439 0.806 1
9 10 0.497 -1.241 -2.136 0.942 -2.771 -0.291 0 10 0.497 -1.241 -2.136 0.942 -2.771 -0.291 0
10 11 0.709 1.497 -1.771 -0.241 1.942 -1.136 1 11 0.709 1.497 -1.771 -0.241 1.942 -1.136 1
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0
12 13 -0.000 0.000 -0.000 -0.000 0.000 -0.000 1 13 -0.000 0.000 -0.000 -0.000 0.000 -0.000 1
13 14 1.000 1.000 1.000 1.000 1.000 1.000 0 14 1.000 1.000 1.000 1.000 1.000 1.000 0
14 15 -0.709 -1.497 1.771 0.241 -1.942 1.136 1 15 -0.709 -1.497 1.771 0.241 -1.942 1.136 1
15 16 -0.497 1.241 2.136 -0.942 2.771 0.291 0 16 -0.497 1.241 2.136 -0.942 2.771 0.291 0
16 17 1.062 -0.361 2.012 -0.468 -3.439 -0.806 1 17 1.062 -0.361 2.012 -0.468 -3.439 -0.806 1
17 18 -0.256 -0.701 1.427 0.829 3.907 -1.206 0 18 -0.256 -0.701 1.427 0.829 3.907 -1.206 0
18 19 -0.880 1.410 0.515 0.668 -4.148 -0.565 1 19 -0.880 1.410 0.515 0.668 -4.148 -0.565 1
19 20 0.880 -1.410 -0.515 -0.668 4.148 0.565 0 20 0.880 -1.410 -0.515 -0.668 4.148 0.565 0
20 21 0.256 0.701 -1.427 -0.829 -3.907 1.206 1 21 0.256 0.701 -1.427 -0.829 -3.907 1.206 1


Decomposition to irreducible representations
Power
To
A'1 A'2 E'1 E'2 E'3 E'4 E'5 E'6 A''1 A''2 E''1 E''2 E''3 E''4 E''5 E''6
1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 E'4
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A'1⊕E'5
3 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'4
4 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 A'1⊕E'3⊕E'5
5 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 E'1⊕E'4⊕E'6
6 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'5
7 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'6
8 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'5⊕E'6
9 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'6
10 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'5⊕E'6
11 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
12 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
13 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
14 1 0 1 1 1 2 1 1 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6
15 1 1 1 1 1 1 2 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕E'6
16 1 0 2 1 1 2 1 1 0 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6
17 1 1 1 1 2 1 2 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕2E'3⊕E'4⊕2E'5⊕E'6
18 1 0 2 1 1 2 1 2 0 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕2E'6
19 1 1 1 2 2 1 2 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕2E'2⊕2E'3⊕E'4⊕2E'5⊕E'6
20 1 0 2 2 1 2 1 2 0 0 0 0 0 0 0 0 A'1⊕2E'1⊕2E'2⊕E'3⊕2E'4⊕E'5⊕2E'6



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