Results for Point Group C11h



Symmetric powers of degenerate representation E''3
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 -0.285 -1.919 0.831 1.683 -1.310 -1.310 1.683 0.831 -1.919 -0.285 -2 0.285 1.919 -0.831 -1.683 1.310 1.310 -1.683 -0.831 1.919 0.285
2 3 -0.919 2.683 -0.310 1.831 0.715 0.715 1.831 -0.310 2.683 -0.919 3 -0.919 2.683 -0.310 1.831 0.715 0.715 1.831 -0.310 2.683 -0.919
3 4 0.546 -3.229 -1.088 1.398 0.373 0.373 1.398 -1.088 -3.229 0.546 -4 -0.546 3.229 1.088 -1.398 -0.373 -0.373 -1.398 1.088 3.229 -0.546
4 5 0.764 3.513 -0.594 0.521 -1.204 -1.204 0.521 -0.594 3.513 0.764 5 0.764 3.513 -0.594 0.521 -1.204 -1.204 0.521 -0.594 3.513 0.764
5 6 -0.764 -3.513 0.594 -0.521 1.204 1.204 -0.521 0.594 -3.513 -0.764 -6 0.764 3.513 -0.594 0.521 -1.204 -1.204 0.521 -0.594 3.513 0.764
6 7 -0.546 3.229 1.088 -1.398 -0.373 -0.373 -1.398 1.088 3.229 -0.546 7 -0.546 3.229 1.088 -1.398 -0.373 -0.373 -1.398 1.088 3.229 -0.546
7 8 0.919 -2.683 0.310 -1.831 -0.715 -0.715 -1.831 0.310 -2.683 0.919 -8 -0.919 2.683 -0.310 1.831 0.715 0.715 1.831 -0.310 2.683 -0.919
8 9 0.285 1.919 -0.831 -1.683 1.310 1.310 -1.683 -0.831 1.919 0.285 9 0.285 1.919 -0.831 -1.683 1.310 1.310 -1.683 -0.831 1.919 0.285
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 -0.285 -1.919 0.831 1.683 -1.310 -1.310 1.683 0.831 -1.919 -0.285 13 -0.285 -1.919 0.831 1.683 -1.310 -1.310 1.683 0.831 -1.919 -0.285
13 14 -0.919 2.683 -0.310 1.831 0.715 0.715 1.831 -0.310 2.683 -0.919 -14 0.919 -2.683 0.310 -1.831 -0.715 -0.715 -1.831 0.310 -2.683 0.919
14 15 0.546 -3.229 -1.088 1.398 0.373 0.373 1.398 -1.088 -3.229 0.546 15 0.546 -3.229 -1.088 1.398 0.373 0.373 1.398 -1.088 -3.229 0.546
15 16 0.764 3.513 -0.594 0.521 -1.204 -1.204 0.521 -0.594 3.513 0.764 -16 -0.764 -3.513 0.594 -0.521 1.204 1.204 -0.521 0.594 -3.513 -0.764
16 17 -0.764 -3.513 0.594 -0.521 1.204 1.204 -0.521 0.594 -3.513 -0.764 17 -0.764 -3.513 0.594 -0.521 1.204 1.204 -0.521 0.594 -3.513 -0.764
17 18 -0.546 3.229 1.088 -1.398 -0.373 -0.373 -1.398 1.088 3.229 -0.546 -18 0.546 -3.229 -1.088 1.398 0.373 0.373 1.398 -1.088 -3.229 0.546
18 19 0.919 -2.683 0.310 -1.831 -0.715 -0.715 -1.831 0.310 -2.683 0.919 19 0.919 -2.683 0.310 -1.831 -0.715 -0.715 -1.831 0.310 -2.683 0.919
19 20 0.285 1.919 -0.831 -1.683 1.310 1.310 -1.683 -0.831 1.919 0.285 -20 -0.285 -1.919 0.831 1.683 -1.310 -1.310 1.683 0.831 -1.919 -0.285
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 0 0 0 0 0 1 0 0 E''3
2 1 0 0 0 0 1 0 0 0 0 0 0 A'⊕E'5
3 0 0 0 0 0 0 0 0 1 1 0 0 E''2⊕E''3
4 1 1 0 0 0 1 0 0 0 0 0 0 A'⊕E'1⊕E'5
5 0 0 0 0 0 0 0 0 1 1 1 0 E''2⊕E''3⊕E''4
6 1 1 0 0 1 1 0 0 0 0 0 0 A'⊕E'1⊕E'4⊕E'5
7 0 0 0 0 0 0 0 1 1 1 1 0 E''1⊕E''2⊕E''3⊕E''4
8 1 1 1 0 1 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'4⊕E'5
9 0 0 0 0 0 0 0 1 1 1 1 1 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 0 0 0 0 0 0 2 1 1 1 1 1 2A''⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5
12 1 1 1 2 1 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5
13 0 0 0 0 0 0 2 1 1 1 1 2 2A''⊕E''1⊕E''2⊕E''3⊕E''4⊕2E''5
14 1 1 2 2 1 1 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕2E'3⊕E'4⊕E'5
15 0 0 0 0 0 0 2 2 1 1 1 2 2A''⊕2E''1⊕E''2⊕E''3⊕E''4⊕2E''5
16 1 1 2 2 2 1 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕2E'3⊕2E'4⊕E'5
17 0 0 0 0 0 0 2 2 1 1 2 2 2A''⊕2E''1⊕E''2⊕E''3⊕2E''4⊕2E''5
18 1 2 2 2 2 1 0 0 0 0 0 0 A'⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕E'5
19 0 0 0 0 0 0 2 2 2 1 2 2 2A''⊕2E''1⊕2E''2⊕E''3⊕2E''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