Results for Point Group D13h



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


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