Results for Point Group C13h



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


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 1 0 0 0 0 0 E''1
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'2
3 0 0 0 0 0 0 0 0 1 0 1 0 0 0 E''1⊕E''3
4 1 0 1 0 1 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'4
5 0 0 0 0 0 0 0 0 1 0 1 0 1 0 E''1⊕E''3⊕E''5
6 1 0 1 0 1 0 1 0 0 0 0 0 0 0 A'⊕E'2⊕E'4⊕E'6
7 0 0 0 0 0 0 0 0 1 0 1 0 1 1 E''1⊕E''3⊕E''5⊕E''6
8 1 0 1 0 1 1 1 0 0 0 0 0 0 0 A'⊕E'2⊕E'4⊕E'5⊕E'6
9 0 0 0 0 0 0 0 0 1 0 1 1 1 1 E''1⊕E''3⊕E''4⊕E''5⊕E''6
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕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 2 1 1 1 1 1 0 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
15 0 0 0 0 0 0 0 2 1 2 1 1 1 1 2A''⊕E''1⊕2E''2⊕E''3⊕E''4⊕E''5⊕E''6
16 1 2 1 2 1 1 1 0 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕E'5⊕E'6
17 0 0 0 0 0 0 0 2 1 2 1 2 1 1 2A''⊕E''1⊕2E''2⊕E''3⊕2E''4⊕E''5⊕E''6
18 1 2 1 2 1 2 1 0 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕2E'5⊕E'6
19 0 0 0 0 0 0 0 2 1 2 1 2 1 2 2A''⊕E''1⊕2E''2⊕E''3⊕2E''4⊕E''5⊕2E''6
20 1 2 1 2 1 2 2 0 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕2E'5⊕2E'6



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