Results for Point Group D15h



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


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