Results for Point Group C9h



Symmetric powers of degenerate representation E''2
Vibrational overtones


Characters of symmetric powers
Power
To
E C9 (C9)2 C3 (C9)4 (C9)5 (C3)2 (C9)7 (C9)8 σh S9 (S9)11 S3 (S9)13 (S9)5 (S3)5 (S9)7 (S9)17
1 2 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 -2 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
2 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879
3 4 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 -4 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653
4 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653
5 6 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 -6 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879
6 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 -8 1.000 1.000 1 1.000 1.000 1 1.000 1.000
8 9 -0.000 -0.000 0 0.000 -0.000 0 0.000 0.000 9 -0.000 -0.000 0 0.000 -0.000 0 0.000 -0.000
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 -10 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
10 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347
11 12 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 -12 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879
12 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653
13 14 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 -14 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653
14 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879
15 16 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 -16 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
17 18 -0.000 -0.000 0 0.000 -0.000 0 0.000 0.000 -18 0.000 0.000 0 -0.000 0.000 0 -0.000 0.000
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000
19 20 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 -20 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
20 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879


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



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