Results for Point Group D13



Symmetric powers of degenerate representation E2
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
1 2 1.136 -0.709 -1.942 -1.497 0.241 1.771 0
2 3 0.291 -0.497 2.771 1.241 -0.942 2.136 1
3 4 -0.806 1.062 -3.439 -0.361 -0.468 2.012 0
4 5 -1.206 -0.256 3.907 -0.701 0.829 1.427 1
5 6 -0.565 -0.880 -4.148 1.410 0.668 0.515 0
6 7 0.565 0.880 4.148 -1.410 -0.668 -0.515 1
7 8 1.206 0.256 -3.907 0.701 -0.829 -1.427 0
8 9 0.806 -1.062 3.439 0.361 0.468 -2.012 1
9 10 -0.291 0.497 -2.771 -1.241 0.942 -2.136 0
10 11 -1.136 0.709 1.942 1.497 -0.241 -1.771 1
11 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 14 1.000 1.000 1.000 1.000 1.000 1.000 0
14 15 1.136 -0.709 -1.942 -1.497 0.241 1.771 1
15 16 0.291 -0.497 2.771 1.241 -0.942 2.136 0
16 17 -0.806 1.062 -3.439 -0.361 -0.468 2.012 1
17 18 -1.206 -0.256 3.907 -0.701 0.829 1.427 0
18 19 -0.565 -0.880 -4.148 1.410 0.668 0.515 1
19 20 0.565 0.880 4.148 -1.410 -0.668 -0.515 0
20 21 1.206 0.256 -3.907 0.701 -0.829 -1.427 1


Decomposition to irreducible representations
Power
To
A1 A2 E1 E2 E3 E4 E5 E6
1 0 0 0 1 0 0 0 0 E2
2 1 0 0 0 0 1 0 0 A1⊕E4
3 0 0 0 1 0 0 0 1 E2⊕E6
4 1 0 0 0 0 1 1 0 A1⊕E4⊕E5
5 0 0 0 1 1 0 0 1 E2⊕E3⊕E6
6 1 0 1 0 0 1 1 0 A1⊕E1⊕E4⊕E5
7 0 0 1 1 1 0 0 1 E1⊕E2⊕E3⊕E6
8 1 0 1 0 1 1 1 0 A1⊕E1⊕E3⊕E4⊕E5
9 0 0 1 1 1 0 1 1 E1⊕E2⊕E3⊕E5⊕E6
10 1 0 1 0 1 1 1 1 A1⊕E1⊕E3⊕E4⊕E5⊕E6
11 0 0 1 1 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E5⊕E6
12 1 0 1 1 1 1 1 1 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
13 1 1 1 1 1 1 1 1 A1⊕A2⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
14 1 0 1 2 1 1 1 1 A1⊕E1⊕2E2⊕E3⊕E4⊕E5⊕E6
15 1 1 1 1 1 2 1 1 A1⊕A2⊕E1⊕E2⊕E3⊕2E4⊕E5⊕E6
16 1 0 1 2 1 1 1 2 A1⊕E1⊕2E2⊕E3⊕E4⊕E5⊕2E6
17 1 1 1 1 1 2 2 1 A1⊕A2⊕E1⊕E2⊕E3⊕2E4⊕2E5⊕E6
18 1 0 1 2 2 1 1 2 A1⊕E1⊕2E2⊕2E3⊕E4⊕E5⊕2E6
19 1 1 2 1 1 2 2 1 A1⊕A2⊕2E1⊕E2⊕E3⊕2E4⊕2E5⊕E6
20 1 0 2 2 2 1 1 2 A1⊕2E1⊕2E2⊕2E3⊕E4⊕E5⊕2E6



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