Results for Point Group D15h



Symmetric powers of degenerate representation E''3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7 15C'2 σh 2S15 2(S15)13 2S5 2(S15)11 2S3 2(S5)3 2(S15)7 15σv
1 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 0 -2 -0.618 1.618 1.618 -0.618 -2 -0.618 1.618 0
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 0 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 0
4 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 0 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 0
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1
7 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 0 -8 0.618 -1.618 -1.618 0.618 -8 0.618 -1.618 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1
9 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 0 -10 0.000 0.000 -0.000 -0.000 -10 0.000 0.000 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1
11 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 0 -12 -0.618 1.618 1.618 -0.618 -12 -0.618 1.618 0
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 0 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 0
14 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 0 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 0
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1
17 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 0 -18 0.618 -1.618 -1.618 0.618 -18 0.618 -1.618 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1
19 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 0 -20 0.000 0.000 -0.000 -0.000 -20 0.000 0.000 0
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1


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



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