Results for Point Group D11h



Symmetric powers of degenerate representation E'5
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C11 2(C11)2 2(C11)3 2(C11)4 2(C11)5 11C'2 σh 2S11 2(S11)9 2(S11)3 2(S11)7 2(S11)5 11σv
1 2 -1.919 1.683 -1.310 0.831 -0.285 0 2 -1.919 1.683 -1.310 0.831 -0.285 0
2 3 2.683 1.831 0.715 -0.310 -0.919 1 3 2.683 1.831 0.715 -0.310 -0.919 1
3 4 -3.229 1.398 0.373 -1.088 0.546 0 4 -3.229 1.398 0.373 -1.088 0.546 0
4 5 3.513 0.521 -1.204 -0.594 0.764 1 5 3.513 0.521 -1.204 -0.594 0.764 1
5 6 -3.513 -0.521 1.204 0.594 -0.764 0 6 -3.513 -0.521 1.204 0.594 -0.764 0
6 7 3.229 -1.398 -0.373 1.088 -0.546 1 7 3.229 -1.398 -0.373 1.088 -0.546 1
7 8 -2.683 -1.831 -0.715 0.310 0.919 0 8 -2.683 -1.831 -0.715 0.310 0.919 0
8 9 1.919 -1.683 1.310 -0.831 0.285 1 9 1.919 -1.683 1.310 -0.831 0.285 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 -1.919 1.683 -1.310 0.831 -0.285 1 13 -1.919 1.683 -1.310 0.831 -0.285 1
13 14 2.683 1.831 0.715 -0.310 -0.919 0 14 2.683 1.831 0.715 -0.310 -0.919 0
14 15 -3.229 1.398 0.373 -1.088 0.546 1 15 -3.229 1.398 0.373 -1.088 0.546 1
15 16 3.513 0.521 -1.204 -0.594 0.764 0 16 3.513 0.521 -1.204 -0.594 0.764 0
16 17 -3.513 -0.521 1.204 0.594 -0.764 1 17 -3.513 -0.521 1.204 0.594 -0.764 1
17 18 3.229 -1.398 -0.373 1.088 -0.546 0 18 3.229 -1.398 -0.373 1.088 -0.546 0
18 19 -2.683 -1.831 -0.715 0.310 0.919 1 19 -2.683 -1.831 -0.715 0.310 0.919 1
19 20 1.919 -1.683 1.310 -0.831 0.285 0 20 1.919 -1.683 1.310 -0.831 0.285 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
A'1 A'2 E'1 E'2 E'3 E'4 E'5 A''1 A''2 E''1 E''2 E''3 E''4 E''5
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 E'5
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1
3 0 0 0 0 0 1 1 0 0 0 0 0 0 0 E'4⊕E'5
4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2
5 0 0 0 0 1 1 1 0 0 0 0 0 0 0 E'3⊕E'4⊕E'5
6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3
7 0 0 0 1 1 1 1 0 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5
8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4
9 0 0 1 1 1 1 1 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
11 1 1 1 1 1 1 1 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
12 1 0 1 1 1 1 2 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5
13 1 1 2 1 1 1 1 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5
14 1 0 1 1 1 2 2 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕2E'4⊕2E'5
15 1 1 2 2 1 1 1 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕2E'2⊕E'3⊕E'4⊕E'5
16 1 0 1 1 2 2 2 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5
17 1 1 2 2 2 1 1 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕2E'2⊕2E'3⊕E'4⊕E'5
18 1 0 1 2 2 2 2 0 0 0 0 0 0 0 A'1⊕E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5
19 1 1 2 2 2 2 1 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕E'5
20 1 0 2 2 2 2 2 0 0 0 0 0 0 0 A'1⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5



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