Results for Point Group D9h



Symmetric powers of degenerate representation E''2
Vibrational overtones


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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement