Results for Point Group D11d



Symmetric powers of degenerate representation E3g
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 -0.285 -1.919 0.831 1.683 -1.310 0 2 -0.285 -1.919 0.831 1.683 -1.310 0
2 3 -0.919 2.683 -0.310 1.831 0.715 1 3 -0.919 2.683 -0.310 1.831 0.715 1
3 4 0.546 -3.229 -1.088 1.398 0.373 0 4 0.546 -3.229 -1.088 1.398 0.373 0
4 5 0.764 3.513 -0.594 0.521 -1.204 1 5 0.764 3.513 -0.594 0.521 -1.204 1
5 6 -0.764 -3.513 0.594 -0.521 1.204 0 6 -0.764 -3.513 0.594 -0.521 1.204 0
6 7 -0.546 3.229 1.088 -1.398 -0.373 1 7 -0.546 3.229 1.088 -1.398 -0.373 1
7 8 0.919 -2.683 0.310 -1.831 -0.715 0 8 0.919 -2.683 0.310 -1.831 -0.715 0
8 9 0.285 1.919 -0.831 -1.683 1.310 1 9 0.285 1.919 -0.831 -1.683 1.310 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 -0.285 -1.919 0.831 1.683 -1.310 1 13 -0.285 -1.919 0.831 1.683 -1.310 1
13 14 -0.919 2.683 -0.310 1.831 0.715 0 14 -0.919 2.683 -0.310 1.831 0.715 0
14 15 0.546 -3.229 -1.088 1.398 0.373 1 15 0.546 -3.229 -1.088 1.398 0.373 1
15 16 0.764 3.513 -0.594 0.521 -1.204 0 16 0.764 3.513 -0.594 0.521 -1.204 0
16 17 -0.764 -3.513 0.594 -0.521 1.204 1 17 -0.764 -3.513 0.594 -0.521 1.204 1
17 18 -0.546 3.229 1.088 -1.398 -0.373 0 18 -0.546 3.229 1.088 -1.398 -0.373 0
18 19 0.919 -2.683 0.310 -1.831 -0.715 1 19 0.919 -2.683 0.310 -1.831 -0.715 1
19 20 0.285 1.919 -0.831 -1.683 1.310 0 20 0.285 1.919 -0.831 -1.683 1.310 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 1 0 0 0 0 0 0 0 0 0 E3g
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 A1g⊕E5g
3 0 0 0 1 1 0 0 0 0 0 0 0 0 0 E2g⊕E3g
4 1 0 1 0 0 0 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g
5 0 0 0 1 1 1 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g
6 1 0 1 0 0 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g
7 0 0 1 1 1 1 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g
8 1 0 1 1 0 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g
9 0 0 1 1 1 1 1 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g
11 1 1 1 1 1 1 1 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g
12 1 0 1 1 2 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g
13 1 1 1 1 1 1 2 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕2E5g
14 1 0 1 2 2 1 1 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕E4g⊕E5g
15 1 1 2 1 1 1 2 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g⊕2E5g
16 1 0 1 2 2 2 1 0 0 0 0 0 0 0 A1g⊕E1g⊕2E2g⊕2E3g⊕2E4g⊕E5g
17 1 1 2 1 1 2 2 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕2E4g⊕2E5g
18 1 0 2 2 2 2 1 0 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g⊕2E4g⊕E5g
19 1 1 2 2 1 2 2 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕E3g⊕2E4g⊕2E5g
20 1 0 2 2 2 2 2 0 0 0 0 0 0 0 A1g⊕2E1g⊕2E2g⊕2E3g⊕2E4g⊕2E5g


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