Results for Point Group D9h



Symmetric powers of degenerate representation E'1
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 1.532 0.347 -1 -1.879 0 2 1.532 0.347 -1 -1.879 0
2 3 1.347 -0.879 0 2.532 1 3 1.347 -0.879 0 2.532 1
3 4 0.532 -0.653 1 -2.879 0 4 0.532 -0.653 1 -2.879 0
4 5 -0.532 0.653 -1 2.879 1 5 -0.532 0.653 -1 2.879 1
5 6 -1.347 0.879 0 -2.532 0 6 -1.347 0.879 0 -2.532 0
6 7 -1.532 -0.347 1 1.879 1 7 -1.532 -0.347 1 1.879 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 1.532 0.347 -1 -1.879 1 11 1.532 0.347 -1 -1.879 1
11 12 1.347 -0.879 0 2.532 0 12 1.347 -0.879 0 2.532 0
12 13 0.532 -0.653 1 -2.879 1 13 0.532 -0.653 1 -2.879 1
13 14 -0.532 0.653 -1 2.879 0 14 -0.532 0.653 -1 2.879 0
14 15 -1.347 0.879 0 -2.532 1 15 -1.347 0.879 0 -2.532 1
15 16 -1.532 -0.347 1 1.879 0 16 -1.532 -0.347 1 1.879 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 1.532 0.347 -1 -1.879 0 20 1.532 0.347 -1 -1.879 0
20 21 1.347 -0.879 0 2.532 1 21 1.347 -0.879 0 2.532 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 1 0 0 0 0 0 0 0 0 0 E'1
2 1 0 0 1 0 0 0 0 0 0 0 0 A'1⊕E'2
3 0 0 1 0 1 0 0 0 0 0 0 0 E'1⊕E'3
4 1 0 0 1 0 1 0 0 0 0 0 0 A'1⊕E'2⊕E'4
5 0 0 1 0 1 1 0 0 0 0 0 0 E'1⊕E'3⊕E'4
6 1 0 0 1 1 1 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'4
7 0 0 1 1 1 1 0 0 0 0 0 0 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 1 1 1 1 1 1 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4
10 1 0 2 1 1 1 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕E'3⊕E'4
11 1 1 1 2 1 1 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕2E'2⊕E'3⊕E'4
12 1 0 2 1 2 1 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕2E'3⊕E'4
13 1 1 1 2 1 2 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕2E'2⊕E'3⊕2E'4
14 1 0 2 1 2 2 0 0 0 0 0 0 A'1⊕2E'1⊕E'2⊕2E'3⊕2E'4
15 1 1 1 2 2 2 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕2E'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 1 1 2 2 2 2 0 0 0 0 0 0 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 1 1 3 2 2 2 0 0 0 0 0 0 A'1⊕A'2⊕3E'1⊕2E'2⊕2E'3⊕2E'4
20 2 1 2 3 2 2 0 0 0 0 0 0 2A'1⊕A'2⊕2E'1⊕3E'2⊕2E'3⊕2E'4


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