Results for Point Group D13d



Symmetric powers of degenerate representation E3g
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 0.241 -1.942 -0.709 1.771 1.136 -1.497 0 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 -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 -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 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 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 -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 -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 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 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 -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 -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 0.241 -1.942 -0.709 1.771 1.136 -1.497 1 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 -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 -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 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 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 -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 21 -0.829 -3.907 0.256 -1.427 1.206 0.701 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 1 0 0 0 0 0 0 0 0 0 0 0 E3g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 A1g⊕E6g
3 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 E3g⊕E4g
4 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E6g
5 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g
6 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g⊕E6g
7 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E5g
8 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E5g⊕E6g
9 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g
10 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g⊕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 2 1 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕E6g
15 1 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕2E6g
16 1 0 1 1 2 2 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕2E4g⊕E5g⊕E6g
17 1 1 2 1 1 1 1 2 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕2E6g
18 1 0 1 2 2 2 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕2E4g⊕E5g⊕E6g
19 1 1 2 1 1 1 2 2 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g⊕2E5g⊕2E6g
20 1 0 1 2 2 2 2 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕2E4g⊕2E5g⊕E6g


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