Results for Point Group D15d



Symmetric powers of degenerate representation E7g
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 i 2(S30)13 2(S30)11 2(S10)3 2(S30)7 2S6 2S10 2S30 15σd
1 2 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 0 2 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 0
2 3 2.827 2.338 1.618 0.791 0 -0.618 -0.956 1 3 2.827 2.338 1.618 0.791 0 -0.618 -0.956 1
3 4 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 0 4 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 0
4 5 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 1 5 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 1
5 6 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 0 6 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 0
6 7 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 1 7 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 1
7 8 -4.783 -0.511 1.618 0.547 -1 -0.618 0.747 0 8 -4.783 -0.511 1.618 0.547 -1 -0.618 0.747 0
8 9 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 1 9 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 1
9 10 -4.165 -2.129 -0.000 1.165 1 0.000 -0.871 0 10 -4.165 -2.129 -0.000 1.165 1 0.000 -0.871 0
10 11 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 1 11 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 1
11 12 -2.827 -2.338 -1.618 -0.791 0 0.618 0.956 0 12 -2.827 -2.338 -1.618 -0.791 0 0.618 0.956 0
12 13 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 1 13 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 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 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 1 17 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 1
17 18 2.827 2.338 1.618 0.791 0 -0.618 -0.956 0 18 2.827 2.338 1.618 0.791 0 -0.618 -0.956 0
18 19 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 1 19 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 1
19 20 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 0 20 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 0
20 21 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 1 21 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g E5g E6g E7g A1u A2u E1u E2u E3u E4u E5u E6u E7u
1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 E7g
2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g
3 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 E6g⊕E7g
4 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g
5 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 E5g⊕E6g⊕E7g
6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g
7 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 E4g⊕E5g⊕E6g⊕E7g
8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g
9 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 E3g⊕E4g⊕E5g⊕E6g⊕E7g
10 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g
11 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
12 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g
13 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
14 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
15 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
16 1 0 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕2E7g
17 1 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
18 1 0 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕2E6g⊕2E7g
19 1 1 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E1g⊕2E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g
20 1 0 1 1 1 1 2 2 2 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕2E5g⊕2E6g⊕2E7g



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