Results for Point Group D13h



Symmetric powers of degenerate representation E'6
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 -1.942 1.771 -1.497 1.136 -0.709 0.241 0 2 -1.942 1.771 -1.497 1.136 -0.709 0.241 0
2 3 2.771 2.136 1.241 0.291 -0.497 -0.942 1 3 2.771 2.136 1.241 0.291 -0.497 -0.942 1
3 4 -3.439 2.012 -0.361 -0.806 1.062 -0.468 0 4 -3.439 2.012 -0.361 -0.806 1.062 -0.468 0
4 5 3.907 1.427 -0.701 -1.206 -0.256 0.829 1 5 3.907 1.427 -0.701 -1.206 -0.256 0.829 1
5 6 -4.148 0.515 1.410 -0.565 -0.880 0.668 0 6 -4.148 0.515 1.410 -0.565 -0.880 0.668 0
6 7 4.148 -0.515 -1.410 0.565 0.880 -0.668 1 7 4.148 -0.515 -1.410 0.565 0.880 -0.668 1
7 8 -3.907 -1.427 0.701 1.206 0.256 -0.829 0 8 -3.907 -1.427 0.701 1.206 0.256 -0.829 0
8 9 3.439 -2.012 0.361 0.806 -1.062 0.468 1 9 3.439 -2.012 0.361 0.806 -1.062 0.468 1
9 10 -2.771 -2.136 -1.241 -0.291 0.497 0.942 0 10 -2.771 -2.136 -1.241 -0.291 0.497 0.942 0
10 11 1.942 -1.771 1.497 -1.136 0.709 -0.241 1 11 1.942 -1.771 1.497 -1.136 0.709 -0.241 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 -1.942 1.771 -1.497 1.136 -0.709 0.241 1 15 -1.942 1.771 -1.497 1.136 -0.709 0.241 1
15 16 2.771 2.136 1.241 0.291 -0.497 -0.942 0 16 2.771 2.136 1.241 0.291 -0.497 -0.942 0
16 17 -3.439 2.012 -0.361 -0.806 1.062 -0.468 1 17 -3.439 2.012 -0.361 -0.806 1.062 -0.468 1
17 18 3.907 1.427 -0.701 -1.206 -0.256 0.829 0 18 3.907 1.427 -0.701 -1.206 -0.256 0.829 0
18 19 -4.148 0.515 1.410 -0.565 -0.880 0.668 1 19 -4.148 0.515 1.410 -0.565 -0.880 0.668 1
19 20 4.148 -0.515 -1.410 0.565 0.880 -0.668 0 20 4.148 -0.515 -1.410 0.565 0.880 -0.668 0
20 21 -3.907 -1.427 0.701 1.206 0.256 -0.829 1 21 -3.907 -1.427 0.701 1.206 0.256 -0.829 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 0 0 1 0 0 0 0 0 0 0 0 E'6
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1
3 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 E'5⊕E'6
4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2
5 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 E'4⊕E'5⊕E'6
6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3
7 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 E'3⊕E'4⊕E'5⊕E'6
8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4
9 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5⊕E'6
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
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 1 1 2 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕2E'6
15 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
16 1 0 1 1 1 1 2 2 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕2E'6
17 1 1 2 2 1 1 1 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕2E'2⊕E'3⊕E'4⊕E'5⊕E'6
18 1 0 1 1 1 2 2 2 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕2E'4⊕2E'5⊕2E'6
19 1 1 2 2 2 1 1 1 0 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕2E'2⊕2E'3⊕E'4⊕E'5⊕E'6
20 1 0 1 1 2 2 2 2 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5⊕2E'6



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