Results for Point Group C11h



Symmetric powers of degenerate representation E'5
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 -1.919 1.683 -1.310 0.831 -0.285 -0.285 0.831 -1.310 1.683 -1.919 2 -1.919 1.683 -1.310 0.831 -0.285 -0.285 0.831 -1.310 1.683 -1.919
2 3 2.683 1.831 0.715 -0.310 -0.919 -0.919 -0.310 0.715 1.831 2.683 3 2.683 1.831 0.715 -0.310 -0.919 -0.919 -0.310 0.715 1.831 2.683
3 4 -3.229 1.398 0.373 -1.088 0.546 0.546 -1.088 0.373 1.398 -3.229 4 -3.229 1.398 0.373 -1.088 0.546 0.546 -1.088 0.373 1.398 -3.229
4 5 3.513 0.521 -1.204 -0.594 0.764 0.764 -0.594 -1.204 0.521 3.513 5 3.513 0.521 -1.204 -0.594 0.764 0.764 -0.594 -1.204 0.521 3.513
5 6 -3.513 -0.521 1.204 0.594 -0.764 -0.764 0.594 1.204 -0.521 -3.513 6 -3.513 -0.521 1.204 0.594 -0.764 -0.764 0.594 1.204 -0.521 -3.513
6 7 3.229 -1.398 -0.373 1.088 -0.546 -0.546 1.088 -0.373 -1.398 3.229 7 3.229 -1.398 -0.373 1.088 -0.546 -0.546 1.088 -0.373 -1.398 3.229
7 8 -2.683 -1.831 -0.715 0.310 0.919 0.919 0.310 -0.715 -1.831 -2.683 8 -2.683 -1.831 -0.715 0.310 0.919 0.919 0.310 -0.715 -1.831 -2.683
8 9 1.919 -1.683 1.310 -0.831 0.285 0.285 -0.831 1.310 -1.683 1.919 9 1.919 -1.683 1.310 -0.831 0.285 0.285 -0.831 1.310 -1.683 1.919
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 -1.919 1.683 -1.310 0.831 -0.285 -0.285 0.831 -1.310 1.683 -1.919 13 -1.919 1.683 -1.310 0.831 -0.285 -0.285 0.831 -1.310 1.683 -1.919
13 14 2.683 1.831 0.715 -0.310 -0.919 -0.919 -0.310 0.715 1.831 2.683 14 2.683 1.831 0.715 -0.310 -0.919 -0.919 -0.310 0.715 1.831 2.683
14 15 -3.229 1.398 0.373 -1.088 0.546 0.546 -1.088 0.373 1.398 -3.229 15 -3.229 1.398 0.373 -1.088 0.546 0.546 -1.088 0.373 1.398 -3.229
15 16 3.513 0.521 -1.204 -0.594 0.764 0.764 -0.594 -1.204 0.521 3.513 16 3.513 0.521 -1.204 -0.594 0.764 0.764 -0.594 -1.204 0.521 3.513
16 17 -3.513 -0.521 1.204 0.594 -0.764 -0.764 0.594 1.204 -0.521 -3.513 17 -3.513 -0.521 1.204 0.594 -0.764 -0.764 0.594 1.204 -0.521 -3.513
17 18 3.229 -1.398 -0.373 1.088 -0.546 -0.546 1.088 -0.373 -1.398 3.229 18 3.229 -1.398 -0.373 1.088 -0.546 -0.546 1.088 -0.373 -1.398 3.229
18 19 -2.683 -1.831 -0.715 0.310 0.919 0.919 0.310 -0.715 -1.831 -2.683 19 -2.683 -1.831 -0.715 0.310 0.919 0.919 0.310 -0.715 -1.831 -2.683
19 20 1.919 -1.683 1.310 -0.831 0.285 0.285 -0.831 1.310 -1.683 1.919 20 1.919 -1.683 1.310 -0.831 0.285 0.285 -0.831 1.310 -1.683 1.919
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 1 0 0 0 0 0 0 E'5
2 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1
3 0 0 0 0 1 1 0 0 0 0 0 0 E'4⊕E'5
4 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2
5 0 0 0 1 1 1 0 0 0 0 0 0 E'3⊕E'4⊕E'5
6 1 1 1 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3
7 0 0 1 1 1 1 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5
8 1 1 1 1 1 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4
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 1 2 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5
13 2 2 1 1 1 1 0 0 0 0 0 0 2A'⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5
14 1 1 1 1 2 2 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕2E'4⊕2E'5
15 2 2 2 1 1 1 0 0 0 0 0 0 2A'⊕2E'1⊕2E'2⊕E'3⊕E'4⊕E'5
16 1 1 1 2 2 2 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5
17 2 2 2 2 1 1 0 0 0 0 0 0 2A'⊕2E'1⊕2E'2⊕2E'3⊕E'4⊕E'5
18 1 1 2 2 2 2 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5
19 2 2 2 2 2 1 0 0 0 0 0 0 2A'⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕E'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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement