Results for Point Group D7h



Symmetric powers of degenerate representation E'3
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 7σv
1 2 -1.802 1.247 -0.445 0 2 -1.802 1.247 -0.445 0
2 3 2.247 0.555 -0.802 1 3 2.247 0.555 -0.802 1
3 4 -2.247 -0.555 0.802 0 4 -2.247 -0.555 0.802 0
4 5 1.802 -1.247 0.445 1 5 1.802 -1.247 0.445 1
5 6 -1.000 -1.000 -1.000 0 6 -1.000 -1.000 -1.000 0
6 7 -0.000 0.000 -0.000 1 7 -0.000 0.000 -0.000 1
7 8 1.000 1.000 1.000 0 8 1.000 1.000 1.000 0
8 9 -1.802 1.247 -0.445 1 9 -1.802 1.247 -0.445 1
9 10 2.247 0.555 -0.802 0 10 2.247 0.555 -0.802 0
10 11 -2.247 -0.555 0.802 1 11 -2.247 -0.555 0.802 1
11 12 1.802 -1.247 0.445 0 12 1.802 -1.247 0.445 0
12 13 -1.000 -1.000 -1.000 1 13 -1.000 -1.000 -1.000 1
13 14 -0.000 0.000 -0.000 0 14 -0.000 0.000 -0.000 0
14 15 1.000 1.000 1.000 1 15 1.000 1.000 1.000 1
15 16 -1.802 1.247 -0.445 0 16 -1.802 1.247 -0.445 0
16 17 2.247 0.555 -0.802 1 17 2.247 0.555 -0.802 1
17 18 -2.247 -0.555 0.802 0 18 -2.247 -0.555 0.802 0
18 19 1.802 -1.247 0.445 1 19 1.802 -1.247 0.445 1
19 20 -1.000 -1.000 -1.000 0 20 -1.000 -1.000 -1.000 0
20 21 -0.000 0.000 -0.000 1 21 -0.000 0.000 -0.000 1


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


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