Results for Point Group C5h



Symmetric powers of degenerate representation E''2
Vibrational overtones


Characters of symmetric powers
Power
To
E C5 (C5)2 (C5)3 (C5)4 σh S5 (S5)7 (S5)3 (S5)9
1 2 -1.618 0.618 0.618 -1.618 -2 1.618 -0.618 -0.618 1.618
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 -4 1.000 1.000 1.000 1.000
4 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000
5 6 1.000 1.000 1.000 1.000 -6 -1.000 -1.000 -1.000 -1.000
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618
7 8 1.618 -0.618 -0.618 1.618 -8 -1.618 0.618 0.618 -1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 -0.000 0.000 -10 0.000 -0.000 0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -1.618 0.618 0.618 -1.618 -12 1.618 -0.618 -0.618 1.618
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 -14 1.000 1.000 1.000 1.000
14 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000
15 16 1.000 1.000 1.000 1.000 -16 -1.000 -1.000 -1.000 -1.000
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618
17 18 1.618 -0.618 -0.618 1.618 -18 -1.618 0.618 0.618 -1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 -0.000 0.000 -20 0.000 -0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000


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



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement