Results for Point Group C9h



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


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



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