Results for Point Group C11h



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