Results for Point Group C9h



Symmetric powers of degenerate representation E''1
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 -2 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532
2 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 3 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347
3 4 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 -4 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532
4 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 5 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532
5 6 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 -6 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347
6 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 7 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 11 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532
11 12 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 -12 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347
12 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532 13 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532
13 14 -0.532 0.653 -1 2.879 2.879 -1 0.653 -0.532 -14 0.532 -0.653 1 -2.879 -2.879 1 -0.653 0.532
14 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347 15 -1.347 0.879 0 -2.532 -2.532 0 0.879 -1.347
15 16 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532 -16 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532
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 1.532 0.347 -1 -1.879 -1.879 -1 0.347 1.532 -20 -1.532 -0.347 1 1.879 1.879 1 -0.347 -1.532
20 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347 21 1.347 -0.879 0 2.532 2.532 0 -0.879 1.347


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 1 0 0 0 E''1
2 1 0 1 0 0 0 0 0 0 0 A'⊕E'2
3 0 0 0 0 0 0 1 0 1 0 E''1⊕E''3
4 1 0 1 0 1 0 0 0 0 0 A'⊕E'2⊕E'4
5 0 0 0 0 0 0 1 0 1 1 E''1⊕E''3⊕E''4
6 1 0 1 1 1 0 0 0 0 0 A'⊕E'2⊕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 2 1 1 1 0 0 0 0 0 A'⊕2E'1⊕E'2⊕E'3⊕E'4
11 0 0 0 0 0 2 1 2 1 1 2A''⊕E''1⊕2E''2⊕E''3⊕E''4
12 1 2 1 2 1 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4
13 0 0 0 0 0 2 1 2 1 2 2A''⊕E''1⊕2E''2⊕E''3⊕2E''4
14 1 2 1 2 2 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕2E'4
15 0 0 0 0 0 2 1 2 2 2 2A''⊕E''1⊕2E''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 3 2 2 2 2A''⊕3E''1⊕2E''2⊕2E''3⊕2E''4
20 3 2 3 2 2 0 0 0 0 0 3A'⊕2E'1⊕3E'2⊕2E'3⊕2E'4



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