Results for Point Group D11h



Symmetric powers of degenerate representation E''1
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 1.683 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		 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 0 0 0 1 0 0 0 0 E''1
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2
3 0 0 0 0 0 0 0 0 0 1 0 1 0 0 E''1⊕E''3
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'4
5 0 0 0 0 0 0 0 0 0 1 0 1 0 1 E''1⊕E''3⊕E''5
6 1 0 0 1 0 1 1 0 0 0 0 0 0 0 A'1⊕E'2⊕E'4⊕E'5
7 0 0 0 0 0 0 0 0 0 1 0 1 1 1 E''1⊕E''3⊕E''4⊕E''5
8 1 0 0 1 1 1 1 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'4⊕E'5
9 0 0 0 0 0 0 0 0 0 1 1 1 1 1 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 0 0 0 0 0 0 0 1 1 1 1 1 1 1 A''1⊕A''2⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5
12 1 0 2 1 1 1 1 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5
13 0 0 0 0 0 0 0 1 1 1 2 1 1 1 A''1⊕A''2⊕E''1⊕2E''2⊕E''3⊕E''4⊕E''5
14 1 0 2 1 2 1 1 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕2E'3⊕E'4⊕E'5
15 0 0 0 0 0 0 0 1 1 1 2 1 2 1 A''1⊕A''2⊕E''1⊕2E''2⊕E''3⊕2E''4⊕E''5
16 1 0 2 1 2 1 2 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕2E'3⊕E'4⊕2E'5
17 0 0 0 0 0 0 0 1 1 1 2 1 2 2 A''1⊕A''2⊕E''1⊕2E''2⊕E''3⊕2E''4⊕2E''5
18 1 0 2 1 2 2 2 0 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5
19 0 0 0 0 0 0 0 1 1 1 2 2 2 2 A''1⊕A''2⊕E''1⊕2E''2⊕2E''3⊕2E''4⊕2E''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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement