Results for Point Group D11d



Symmetric powers of degenerate representation E1u
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C11 2(C11)2 2(C11)3 2(C11)4 2(C11)5 11C'2 i 2(S22)9 2(S22)7 2(S22)5 2(S22)3 2S22 11σd
1 2 1.683 0.831 -0.285 -1.310 -1.919 0 -2 -1.683 -0.831 0.285 1.310 1.919 0
2 3 1.831 -0.310 -0.919 0.715 2.683 1 3 1.831 -0.310 -0.919 0.715 2.683 1
3 4 1.398 -1.088 0.546 0.373 -3.229 0 -4 -1.398 1.088 -0.546 -0.373 3.229 0
4 5 0.521 -0.594 0.764 -1.204 3.513 1 5 0.521 -0.594 0.764 -1.204 3.513 1
5 6 -0.521 0.594 -0.764 1.204 -3.513 0 -6 0.521 -0.594 0.764 -1.204 3.513 0
6 7 -1.398 1.088 -0.546 -0.373 3.229 1 7 -1.398 1.088 -0.546 -0.373 3.229 1
7 8 -1.831 0.310 0.919 -0.715 -2.683 0 -8 1.831 -0.310 -0.919 0.715 2.683 0
8 9 -1.683 -0.831 0.285 1.310 1.919 1 9 -1.683 -0.831 0.285 1.310 1.919 1
9 10 -1.000 -1.000 -1.000 -1.000 -1.000 0 -10 1.000 1.000 1.000 1.000 1.000 0
10 11 -0.000 0.000 -0.000 0.000 0.000 1 11 -0.000 0.000 -0.000 0.000 0.000 1
11 12 1.000 1.000 1.000 1.000 1.000 0 -12 -1.000 -1.000 -1.000 -1.000 -1.000 0
12 13 1.683 0.831 -0.285 -1.310 -1.919 1 13 1.683 0.831 -0.285 -1.310 -1.919 1
13 14 1.831 -0.310 -0.919 0.715 2.683 0 -14 -1.831 0.310 0.919 -0.715 -2.683 0
14 15 1.398 -1.088 0.546 0.373 -3.229 1 15 1.398 -1.088 0.546 0.373 -3.229 1
15 16 0.521 -0.594 0.764 -1.204 3.513 0 -16 -0.521 0.594 -0.764 1.204 -3.513 0
16 17 -0.521 0.594 -0.764 1.204 -3.513 1 17 -0.521 0.594 -0.764 1.204 -3.513 1
17 18 -1.398 1.088 -0.546 -0.373 3.229 0 -18 1.398 -1.088 0.546 0.373 -3.229 0
18 19 -1.831 0.310 0.919 -0.715 -2.683 1 19 -1.831 0.310 0.919 -0.715 -2.683 1
19 20 -1.683 -0.831 0.285 1.310 1.919 0 -20 1.683 0.831 -0.285 -1.310 -1.919 0
20 21 -1.000 -1.000 -1.000 -1.000 -1.000 1 21 -1.000 -1.000 -1.000 -1.000 -1.000 1


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



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