Results for Point Group D13d



Symmetric powers of degenerate representation E2u
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 1.136 -0.709 -1.942 -1.497 0.241 1.771 0 -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 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 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 -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 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 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 -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 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 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 -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 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 1.136 -0.709 -1.942 -1.497 0.241 1.771 1 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 -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 -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 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 -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 -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 21 1.206 0.256 -3.907 0.701 -0.829 -1.427 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 0 0 0 0 0 1 0 0 0 0 E2u
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g
3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 E2u⊕E6u
4 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕E5g
5 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 E2u⊕E3u⊕E6u
6 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g
7 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 E1u⊕E2u⊕E3u⊕E6u
8 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E5g
9 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 E1u⊕E2u⊕E3u⊕E5u⊕E6u
10 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E5g⊕E6g
11 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u
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 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u
14 1 0 1 2 1 1 1 1 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕E3g⊕E4g⊕E5g⊕E6g
15 0 0 0 0 0 0 0 0 1 1 1 1 1 2 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕2E4u⊕E5u⊕E6u
16 1 0 1 2 1 1 1 2 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕E3g⊕E4g⊕E5g⊕2E6g
17 0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕2E4u⊕2E5u⊕E6u
18 1 0 1 2 2 1 1 2 0 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕E4g⊕E5g⊕2E6g
19 0 0 0 0 0 0 0 0 1 1 2 1 1 2 2 1 A1u⊕A2u⊕2E1u⊕E2u⊕E3u⊕2E4u⊕2E5u⊕E6u
20 1 0 2 2 2 1 1 2 0 0 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g⊕E4g⊕E5g⊕2E6g


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