Results for Point Group C7h



Symmetric powers of degenerate representation E''3
Vibrational overtones


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


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


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