Results for Point Group D3h



Symmetric powers of degenerate representation E''
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C3 3C'2 σh 2S3 3σv
1 2 -1 0 -2 1 0
2 3 0 1 3 0 1
3 4 1 0 -4 -1 0
4 5 -1 1 5 -1 1
5 6 0 0 -6 0 0
6 7 1 1 7 1 1
7 8 -1 0 -8 1 0
8 9 0 1 9 0 1
9 10 1 0 -10 -1 0
10 11 -1 1 11 -1 1
11 12 0 0 -12 0 0
12 13 1 1 13 1 1
13 14 -1 0 -14 1 0
14 15 0 1 15 0 1
15 16 1 0 -16 -1 0
16 17 -1 1 17 -1 1
17 18 0 0 -18 0 0
18 19 1 1 19 1 1
19 20 -1 0 -20 1 0
20 21 0 1 21 0 1


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


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