Results for Point Group C11h



Symmetric powers of degenerate representation E'4
Vibrational overtones


Characters of symmetric powers
Power
To
E C11 (C11)2 (C11)3 (C11)4 (C11)5 (C11)6 (C11)7 (C11)8 (C11)9 (C11)10 σh S11 (S11)13 (S11)3 (S11)15 (S11)5 (S11)17 (S11)7 (S11)19 (S11)9 (S11)21
1 2 -1.310 -0.285 1.683 -1.919 0.831 0.831 -1.919 1.683 -0.285 -1.310 2 -1.310 -0.285 1.683 -1.919 0.831 0.831 -1.919 1.683 -0.285 -1.310
2 3 0.715 -0.919 1.831 2.683 -0.310 -0.310 2.683 1.831 -0.919 0.715 3 0.715 -0.919 1.831 2.683 -0.310 -0.310 2.683 1.831 -0.919 0.715
3 4 0.373 0.546 1.398 -3.229 -1.088 -1.088 -3.229 1.398 0.546 0.373 4 0.373 0.546 1.398 -3.229 -1.088 -1.088 -3.229 1.398 0.546 0.373
4 5 -1.204 0.764 0.521 3.513 -0.594 -0.594 3.513 0.521 0.764 -1.204 5 -1.204 0.764 0.521 3.513 -0.594 -0.594 3.513 0.521 0.764 -1.204
5 6 1.204 -0.764 -0.521 -3.513 0.594 0.594 -3.513 -0.521 -0.764 1.204 6 1.204 -0.764 -0.521 -3.513 0.594 0.594 -3.513 -0.521 -0.764 1.204
6 7 -0.373 -0.546 -1.398 3.229 1.088 1.088 3.229 -1.398 -0.546 -0.373 7 -0.373 -0.546 -1.398 3.229 1.088 1.088 3.229 -1.398 -0.546 -0.373
7 8 -0.715 0.919 -1.831 -2.683 0.310 0.310 -2.683 -1.831 0.919 -0.715 8 -0.715 0.919 -1.831 -2.683 0.310 0.310 -2.683 -1.831 0.919 -0.715
8 9 1.310 0.285 -1.683 1.919 -0.831 -0.831 1.919 -1.683 0.285 1.310 9 1.310 0.285 -1.683 1.919 -0.831 -0.831 1.919 -1.683 0.285 1.310
9 10 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 10 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
10 11 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 11 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000
11 12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
12 13 -1.310 -0.285 1.683 -1.919 0.831 0.831 -1.919 1.683 -0.285 -1.310 13 -1.310 -0.285 1.683 -1.919 0.831 0.831 -1.919 1.683 -0.285 -1.310
13 14 0.715 -0.919 1.831 2.683 -0.310 -0.310 2.683 1.831 -0.919 0.715 14 0.715 -0.919 1.831 2.683 -0.310 -0.310 2.683 1.831 -0.919 0.715
14 15 0.373 0.546 1.398 -3.229 -1.088 -1.088 -3.229 1.398 0.546 0.373 15 0.373 0.546 1.398 -3.229 -1.088 -1.088 -3.229 1.398 0.546 0.373
15 16 -1.204 0.764 0.521 3.513 -0.594 -0.594 3.513 0.521 0.764 -1.204 16 -1.204 0.764 0.521 3.513 -0.594 -0.594 3.513 0.521 0.764 -1.204
16 17 1.204 -0.764 -0.521 -3.513 0.594 0.594 -3.513 -0.521 -0.764 1.204 17 1.204 -0.764 -0.521 -3.513 0.594 0.594 -3.513 -0.521 -0.764 1.204
17 18 -0.373 -0.546 -1.398 3.229 1.088 1.088 3.229 -1.398 -0.546 -0.373 18 -0.373 -0.546 -1.398 3.229 1.088 1.088 3.229 -1.398 -0.546 -0.373
18 19 -0.715 0.919 -1.831 -2.683 0.310 0.310 -2.683 -1.831 0.919 -0.715 19 -0.715 0.919 -1.831 -2.683 0.310 0.310 -2.683 -1.831 0.919 -0.715
19 20 1.310 0.285 -1.683 1.919 -0.831 -0.831 1.919 -1.683 0.285 1.310 20 1.310 0.285 -1.683 1.919 -0.831 -0.831 1.919 -1.683 0.285 1.310
20 21 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 21 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000


Decomposition to irreducible representations
Power
To
A' E'1* E'2* E'3* E'4* E'5* A'' E''1* E''2* E''3* E''4* E''5*
1 0 0 0 0 1 0 0 0 0 0 0 0 E'4
2 1 0 0 1 0 0 0 0 0 0 0 0 A'⊕E'3
3 0 1 0 0 1 0 0 0 0 0 0 0 E'1⊕E'4
4 1 0 0 1 0 1 0 0 0 0 0 0 A'⊕E'3⊕E'5
5 0 1 1 0 1 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4
6 1 0 1 1 0 1 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕E'5
7 0 1 1 0 1 1 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5
8 1 1 1 1 0 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'5
9 0 1 1 1 1 1 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5
10 1 1 1 1 1 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
11 2 1 1 1 1 1 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
12 1 1 1 1 2 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5
13 2 1 1 2 1 1 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5
14 1 2 1 1 2 1 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕E'3⊕2E'4⊕E'5
15 2 1 1 2 1 2 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕2E'5
16 1 2 2 1 2 1 0 0 0 0 0 0 A'⊕2E'1⊕2E'2⊕E'3⊕2E'4⊕E'5
17 2 1 2 2 1 2 0 0 0 0 0 0 2A'⊕E'1⊕2E'2⊕2E'3⊕E'4⊕2E'5
18 1 2 2 1 2 2 0 0 0 0 0 0 A'⊕2E'1⊕2E'2⊕E'3⊕2E'4⊕2E'5
19 2 2 2 2 1 2 0 0 0 0 0 0 2A'⊕2E'1⊕2E'2⊕2E'3⊕E'4⊕2E'5
20 1 2 2 2 2 2 0 0 0 0 0 0 A'⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5



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