Results for Point Group C13h



Symmetric powers of degenerate representation E''3
Vibrational overtones


Characters of symmetric powers
Power
To		 E C13 (C13)2 (C13)3 (C13)4 (C13)5 (C13)6 (C13)7 (C13)8 (C13)9 (C13)10 (C13)11 (C13)12 σh S13 (S13)15 (S13)3 (S13)17 (S13)5 (S13)19 (S13)7 (S13)21 (S13)9 (S13)23 (S13)11 (S13)25
1 2 0.241 -1.942 -0.709 1.771 1.136 -1.497 -1.497 1.136 1.771 -0.709 -1.942 0.241 -2 -0.241 1.942 0.709 -1.771 -1.136 1.497 1.497 -1.136 -1.771 0.709 1.942 -0.241
2 3 -0.942 2.771 -0.497 2.136 0.291 1.241 1.241 0.291 2.136 -0.497 2.771 -0.942 3 -0.942 2.771 -0.497 2.136 0.291 1.241 1.241 0.291 2.136 -0.497 2.771 -0.942
3 4 -0.468 -3.439 1.062 2.012 -0.806 -0.361 -0.361 -0.806 2.012 1.062 -3.439 -0.468 -4 0.468 3.439 -1.062 -2.012 0.806 0.361 0.361 0.806 -2.012 -1.062 3.439 0.468
4 5 0.829 3.907 -0.256 1.427 -1.206 -0.701 -0.701 -1.206 1.427 -0.256 3.907 0.829 5 0.829 3.907 -0.256 1.427 -1.206 -0.701 -0.701 -1.206 1.427 -0.256 3.907 0.829
5 6 0.668 -4.148 -0.880 0.515 -0.565 1.410 1.410 -0.565 0.515 -0.880 -4.148 0.668 -6 -0.668 4.148 0.880 -0.515 0.565 -1.410 -1.410 0.565 -0.515 0.880 4.148 -0.668
6 7 -0.668 4.148 0.880 -0.515 0.565 -1.410 -1.410 0.565 -0.515 0.880 4.148 -0.668 7 -0.668 4.148 0.880 -0.515 0.565 -1.410 -1.410 0.565 -0.515 0.880 4.148 -0.668
7 8 -0.829 -3.907 0.256 -1.427 1.206 0.701 0.701 1.206 -1.427 0.256 -3.907 -0.829 -8 0.829 3.907 -0.256 1.427 -1.206 -0.701 -0.701 -1.206 1.427 -0.256 3.907 0.829
8 9 0.468 3.439 -1.062 -2.012 0.806 0.361 0.361 0.806 -2.012 -1.062 3.439 0.468 9 0.468 3.439 -1.062 -2.012 0.806 0.361 0.361 0.806 -2.012 -1.062 3.439 0.468
9 10 0.942 -2.771 0.497 -2.136 -0.291 -1.241 -1.241 -0.291 -2.136 0.497 -2.771 0.942 -10 -0.942 2.771 -0.497 2.136 0.291 1.241 1.241 0.291 2.136 -0.497 2.771 -0.942
10 11 -0.241 1.942 0.709 -1.771 -1.136 1.497 1.497 -1.136 -1.771 0.709 1.942 -0.241 11 -0.241 1.942 0.709 -1.771 -1.136 1.497 1.497 -1.136 -1.771 0.709 1.942 -0.241
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
12 13 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 13 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000
13 14 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 -14 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
14 15 0.241 -1.942 -0.709 1.771 1.136 -1.497 -1.497 1.136 1.771 -0.709 -1.942 0.241 15 0.241 -1.942 -0.709 1.771 1.136 -1.497 -1.497 1.136 1.771 -0.709 -1.942 0.241
15 16 -0.942 2.771 -0.497 2.136 0.291 1.241 1.241 0.291 2.136 -0.497 2.771 -0.942 -16 0.942 -2.771 0.497 -2.136 -0.291 -1.241 -1.241 -0.291 -2.136 0.497 -2.771 0.942
16 17 -0.468 -3.439 1.062 2.012 -0.806 -0.361 -0.361 -0.806 2.012 1.062 -3.439 -0.468 17 -0.468 -3.439 1.062 2.012 -0.806 -0.361 -0.361 -0.806 2.012 1.062 -3.439 -0.468
17 18 0.829 3.907 -0.256 1.427 -1.206 -0.701 -0.701 -1.206 1.427 -0.256 3.907 0.829 -18 -0.829 -3.907 0.256 -1.427 1.206 0.701 0.701 1.206 -1.427 0.256 -3.907 -0.829
18 19 0.668 -4.148 -0.880 0.515 -0.565 1.410 1.410 -0.565 0.515 -0.880 -4.148 0.668 19 0.668 -4.148 -0.880 0.515 -0.565 1.410 1.410 -0.565 0.515 -0.880 -4.148 0.668
19 20 -0.668 4.148 0.880 -0.515 0.565 -1.410 -1.410 0.565 -0.515 0.880 4.148 -0.668 -20 0.668 -4.148 -0.880 0.515 -0.565 1.410 1.410 -0.565 0.515 -0.880 -4.148 0.668
20 21 -0.829 -3.907 0.256 -1.427 1.206 0.701 0.701 1.206 -1.427 0.256 -3.907 -0.829 21 -0.829 -3.907 0.256 -1.427 1.206 0.701 0.701 1.206 -1.427 0.256 -3.907 -0.829


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


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