Results for Point Group D14d



Symmetric powers of degenerate representation E13
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S28 2C14 2(S28)3 2C7 2(S28)5 2(C14)3 2S4 2(C7)2 2(S28)9 2(C14)5 2(S28)11 2(C7)3 2(S28)13 C2 14C'2 14σd
1 2 -1.950 1.802 -1.564 1.247 -0.868 0.445 0 -0.445 0.868 -1.247 1.564 -1.802 1.950 -2 0 0
2 3 2.802 2.247 1.445 0.555 -0.247 -0.802 -1 -0.802 -0.247 0.555 1.445 2.247 2.802 3 1 1
3 4 -3.514 2.247 -0.696 -0.555 1.082 -0.802 0 0.802 -1.082 0.555 0.696 -2.247 3.514 -4 0 0
4 5 4.049 1.802 -0.357 -1.247 -0.692 0.445 1 0.445 -0.692 -1.247 -0.357 1.802 4.049 5 1 1
5 6 -4.381 1.000 1.254 -1.000 -0.482 1.000 0 -1.000 0.482 1.000 -1.254 -1.000 4.381 -6 0 0
6 7 4.494 0.000 -1.604 -0.000 1.110 -0.000 -1 -0.000 1.110 0.000 -1.604 0.000 4.494 7 1 1
7 8 -4.381 -1.000 1.254 1.000 -0.482 -1.000 0 1.000 0.482 -1.000 -1.254 1.000 4.381 -8 0 0
8 9 4.049 -1.802 -0.357 1.247 -0.692 -0.445 1 -0.445 -0.692 1.247 -0.357 -1.802 4.049 9 1 1
9 10 -3.514 -2.247 -0.696 0.555 1.082 0.802 0 -0.802 -1.082 -0.555 0.696 2.247 3.514 -10 0 0
10 11 2.802 -2.247 1.445 -0.555 -0.247 0.802 -1 0.802 -0.247 -0.555 1.445 -2.247 2.802 11 1 1
11 12 -1.950 -1.802 -1.564 -1.247 -0.868 -0.445 0 0.445 0.868 1.247 1.564 1.802 1.950 -12 0 0
12 13 1.000 -1.000 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 -1.000 1.000 13 1 1
13 14 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0 -0.000 -0.000 -0.000 -0.000 0.000 0.000 -14 0 0
14 15 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 1.000 -1.000 15 1 1
15 16 1.950 1.802 1.564 1.247 0.868 0.445 0 -0.445 -0.868 -1.247 -1.564 -1.802 -1.950 -16 0 0
16 17 -2.802 2.247 -1.445 0.555 0.247 -0.802 1 -0.802 0.247 0.555 -1.445 2.247 -2.802 17 1 1
17 18 3.514 2.247 0.696 -0.555 -1.082 -0.802 0 0.802 1.082 0.555 -0.696 -2.247 -3.514 -18 0 0
18 19 -4.049 1.802 0.357 -1.247 0.692 0.445 -1 0.445 0.692 -1.247 0.357 1.802 -4.049 19 1 1
19 20 4.381 1.000 -1.254 -1.000 0.482 1.000 0 -1.000 -0.482 1.000 1.254 -1.000 -4.381 -20 0 0
20 21 -4.494 0.000 1.604 -0.000 -1.110 -0.000 1 -0.000 -1.110 0.000 1.604 0.000 -4.494 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E13
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1⊕E2
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 E11⊕E13
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 A1⊕E2⊕E4
5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 E9⊕E11⊕E13
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 A1⊕E2⊕E4⊕E6
7 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 E7⊕E9⊕E11⊕E13
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 A1⊕E2⊕E4⊕E6⊕E8
9 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 E5⊕E7⊕E9⊕E11⊕E13
10 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10
11 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 E3⊕E5⊕E7⊕E9⊕E11⊕E13
12 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12
13 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13
14 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10⊕E12
15 0 0 0 0 2 0 1 0 1 0 1 0 1 0 1 0 1 2E1⊕E3⊕E5⊕E7⊕E9⊕E11⊕E13
16 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10⊕2E12
17 0 0 0 0 2 0 2 0 1 0 1 0 1 0 1 0 1 2E1⊕2E3⊕E5⊕E7⊕E9⊕E11⊕E13
18 1 0 1 1 0 1 0 1 0 1 0 1 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕2E10⊕2E12
19 0 0 0 0 2 0 2 0 2 0 1 0 1 0 1 0 1 2E1⊕2E3⊕2E5⊕E7⊕E9⊕E11⊕E13
20 1 0 1 1 0 1 0 1 0 1 0 2 0 2 0 2 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕2E8⊕2E10⊕2E12



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