Results for Point Group D13



Symmetric powers of degenerate representation E3
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 0.241 -1.942 -0.709 1.771 1.136 -1.497 0
2 3 -0.942 2.771 -0.497 2.136 0.291 1.241 1
3 4 -0.468 -3.439 1.062 2.012 -0.806 -0.361 0
4 5 0.829 3.907 -0.256 1.427 -1.206 -0.701 1
5 6 0.668 -4.148 -0.880 0.515 -0.565 1.410 0
6 7 -0.668 4.148 0.880 -0.515 0.565 -1.410 1
7 8 -0.829 -3.907 0.256 -1.427 1.206 0.701 0
8 9 0.468 3.439 -1.062 -2.012 0.806 0.361 1
9 10 0.942 -2.771 0.497 -2.136 -0.291 -1.241 0
10 11 -0.241 1.942 0.709 -1.771 -1.136 1.497 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 0.241 -1.942 -0.709 1.771 1.136 -1.497 1
15 16 -0.942 2.771 -0.497 2.136 0.291 1.241 0
16 17 -0.468 -3.439 1.062 2.012 -0.806 -0.361 1
17 18 0.829 3.907 -0.256 1.427 -1.206 -0.701 0
18 19 0.668 -4.148 -0.880 0.515 -0.565 1.410 1
19 20 -0.668 4.148 0.880 -0.515 0.565 -1.410 0
20 21 -0.829 -3.907 0.256 -1.427 1.206 0.701 1


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


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