Results for Point Group D13d



Symmetric powers of degenerate representation E5g
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 i 2(S26)11 2(S26)9 2(S26)7 2(S26)5 2(S26)3 2S26 13σd
1 2 -1.497 0.241 1.136 -1.942 1.771 -0.709 0 2 -1.497 0.241 1.136 -1.942 1.771 -0.709 0
2 3 1.241 -0.942 0.291 2.771 2.136 -0.497 1 3 1.241 -0.942 0.291 2.771 2.136 -0.497 1
3 4 -0.361 -0.468 -0.806 -3.439 2.012 1.062 0 4 -0.361 -0.468 -0.806 -3.439 2.012 1.062 0
4 5 -0.701 0.829 -1.206 3.907 1.427 -0.256 1 5 -0.701 0.829 -1.206 3.907 1.427 -0.256 1
5 6 1.410 0.668 -0.565 -4.148 0.515 -0.880 0 6 1.410 0.668 -0.565 -4.148 0.515 -0.880 0
6 7 -1.410 -0.668 0.565 4.148 -0.515 0.880 1 7 -1.410 -0.668 0.565 4.148 -0.515 0.880 1
7 8 0.701 -0.829 1.206 -3.907 -1.427 0.256 0 8 0.701 -0.829 1.206 -3.907 -1.427 0.256 0
8 9 0.361 0.468 0.806 3.439 -2.012 -1.062 1 9 0.361 0.468 0.806 3.439 -2.012 -1.062 1
9 10 -1.241 0.942 -0.291 -2.771 -2.136 0.497 0 10 -1.241 0.942 -0.291 -2.771 -2.136 0.497 0
10 11 1.497 -0.241 -1.136 1.942 -1.771 0.709 1 11 1.497 -0.241 -1.136 1.942 -1.771 0.709 1
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0 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 -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 1.000 1.000 1.000 1.000 1.000 1.000 0
14 15 -1.497 0.241 1.136 -1.942 1.771 -0.709 1 15 -1.497 0.241 1.136 -1.942 1.771 -0.709 1
15 16 1.241 -0.942 0.291 2.771 2.136 -0.497 0 16 1.241 -0.942 0.291 2.771 2.136 -0.497 0
16 17 -0.361 -0.468 -0.806 -3.439 2.012 1.062 1 17 -0.361 -0.468 -0.806 -3.439 2.012 1.062 1
17 18 -0.701 0.829 -1.206 3.907 1.427 -0.256 0 18 -0.701 0.829 -1.206 3.907 1.427 -0.256 0
18 19 1.410 0.668 -0.565 -4.148 0.515 -0.880 1 19 1.410 0.668 -0.565 -4.148 0.515 -0.880 1
19 20 -1.410 -0.668 0.565 4.148 -0.515 0.880 0 20 -1.410 -0.668 0.565 4.148 -0.515 0.880 0
20 21 0.701 -0.829 1.206 -3.907 -1.427 0.256 1 21 0.701 -0.829 1.206 -3.907 -1.427 0.256 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g E5g E6g A1u A2u E1u E2u E3u E4u E5u E6u
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 E5g
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g
3 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 E2g⊕E5g
4 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E6g
5 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E5g
6 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E4g⊕E6g
7 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E4g⊕E5g
8 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E6g
9 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E4g⊕E5g⊕E6g
10 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E6g
11 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g
12 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g
13 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g
14 1 0 1 1 1 1 2 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕2E5g⊕E6g
15 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕E6g
16 1 0 1 2 1 1 2 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕E3g⊕E4g⊕2E5g⊕E6g
17 1 1 1 1 2 1 1 2 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕2E6g
18 1 0 2 2 1 1 2 1 0 0 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕E3g⊕E4g⊕2E5g⊕E6g
19 1 1 1 1 2 2 1 2 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕2E3g⊕2E4g⊕E5g⊕2E6g
20 1 0 2 2 1 2 2 1 0 0 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕E3g⊕2E4g⊕2E5g⊕E6g



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