Results for Point Group D15h



Symmetric powers of degenerate representation E'4
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 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 0 2 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 0
2 3 -0.956 2.827 -0.618 2.338 0 1.618 0.791 1 3 -0.956 2.827 -0.618 2.338 0 1.618 0.791 1
3 4 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 0 4 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 0
4 5 0.871 4.165 0.000 2.129 -1 0.000 -1.165 1 5 0.871 4.165 0.000 2.129 -1 0.000 -1.165 1
5 6 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 0 6 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 0
6 7 -0.747 4.783 0.618 0.511 1 -1.618 -0.547 1 7 -0.747 4.783 0.618 0.511 1 -1.618 -0.547 1
7 8 0.747 -4.783 -0.618 -0.511 -1 1.618 0.547 0 8 0.747 -4.783 -0.618 -0.511 -1 1.618 0.547 0
8 9 0.591 4.574 -1.000 -1.445 0 -1.000 1.280 1 9 0.591 4.574 -1.000 -1.445 0 -1.000 1.280 1
9 10 -0.871 -4.165 0.000 -2.129 1 0.000 1.165 0 10 -0.871 -4.165 0.000 -2.129 1 0.000 1.165 0
10 11 -0.409 3.574 1.000 -2.445 -1 1.000 0.280 1 11 -0.409 3.574 1.000 -2.445 -1 1.000 0.280 1
11 12 0.956 -2.827 0.618 -2.338 0 -1.618 -0.791 0 12 0.956 -2.827 0.618 -2.338 0 -1.618 -0.791 0
12 13 0.209 1.956 -0.618 -1.827 1 1.618 -1.338 1 13 0.209 1.956 -0.618 -1.827 1 1.618 -1.338 1
13 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 0 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 0
14 15 -0.000 0.000 0.000 -0.000 0 0.000 -0.000 1 15 -0.000 0.000 0.000 -0.000 0 0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 1 1.000 1.000 0 16 1.000 1.000 1.000 1.000 1 1.000 1.000 0
16 17 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 1 17 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 1
17 18 -0.956 2.827 -0.618 2.338 0 1.618 0.791 0 18 -0.956 2.827 -0.618 2.338 0 1.618 0.791 0
18 19 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 1 19 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 1
19 20 0.871 4.165 0.000 2.129 -1 0.000 -1.165 0 20 0.871 4.165 0.000 2.129 -1 0.000 -1.165 0
20 21 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 1 21 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 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 1 0 0 0 0 0 0 0 0 0 0 0 0 E'4
2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A'1⊕E'7
3 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 E'3⊕E'4
4 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'7
5 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 E'3⊕E'4⊕E'5
6 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'6⊕E'7
7 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5
8 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'6⊕E'7
9 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5⊕E'6
10 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'5⊕E'6⊕E'7
11 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
12 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'5⊕E'6⊕E'7
13 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
14 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
15 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
16 1 0 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6⊕E'7
17 1 1 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕2E'7
18 1 0 1 1 2 2 1 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕2E'4⊕E'5⊕E'6⊕E'7
19 1 1 2 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕2E'7
20 1 0 1 1 2 2 2 1 1 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5⊕E'6⊕E'7



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