Results for Point Group C13h



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


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 1 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 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 1 1 1 0 0 0 0 0 0 0 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 1 1 1 1 0 0 0 0 0 0 0 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 1 1 1 1 1 0 0 0 0 0 0 0 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 1 1 1 1 1 1 0 0 0 0 0 0 0 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 2 1 1 1 1 1 1 0 0 0 0 0 0 0 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 2 1 1 1 1 1 2 0 0 0 0 0 0 0 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 2 2 1 1 1 1 2 0 0 0 0 0 0 0 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 2 2 1 1 1 2 2 0 0 0 0 0 0 0 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