Results for Point Group C13h



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


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


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