Results for Point Group D14d



Symmetric powers of degenerate representation E5
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 0.868 -1.247 -1.950 -0.445 1.564 1.802 0 -1.802 -1.564 0.445 1.950 1.247 -0.868 -2 0 0
2 3 -0.247 0.555 2.802 -0.802 1.445 2.247 -1 2.247 1.445 -0.802 2.802 0.555 -0.247 3 1 1
3 4 -1.082 0.555 -3.514 0.802 0.696 2.247 0 -2.247 -0.696 -0.802 3.514 -0.555 1.082 -4 0 0
4 5 -0.692 -1.247 4.049 0.445 -0.357 1.802 1 1.802 -0.357 0.445 4.049 -1.247 -0.692 5 1 1
5 6 0.482 1.000 -4.381 -1.000 -1.254 1.000 0 -1.000 1.254 1.000 4.381 -1.000 -0.482 -6 0 0
6 7 1.110 0.000 4.494 0.000 -1.604 0.000 -1 0.000 -1.604 -0.000 4.494 -0.000 1.110 7 1 1
7 8 0.482 -1.000 -4.381 1.000 -1.254 -1.000 0 1.000 1.254 -1.000 4.381 1.000 -0.482 -8 0 0
8 9 -0.692 1.247 4.049 -0.445 -0.357 -1.802 1 -1.802 -0.357 -0.445 4.049 1.247 -0.692 9 1 1
9 10 -1.082 -0.555 -3.514 -0.802 0.696 -2.247 0 2.247 -0.696 0.802 3.514 0.555 1.082 -10 0 0
10 11 -0.247 -0.555 2.802 0.802 1.445 -2.247 -1 -2.247 1.445 0.802 2.802 -0.555 -0.247 11 1 1
11 12 0.868 1.247 -1.950 0.445 1.564 -1.802 0 1.802 -1.564 -0.445 1.950 -1.247 -0.868 -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 -0.868 -1.247 1.950 -0.445 -1.564 1.802 0 -1.802 1.564 0.445 -1.950 1.247 0.868 -16 0 0
16 17 0.247 0.555 -2.802 -0.802 -1.445 2.247 1 2.247 -1.445 -0.802 -2.802 0.555 0.247 17 1 1
17 18 1.082 0.555 3.514 0.802 -0.696 2.247 0 -2.247 0.696 -0.802 -3.514 -0.555 -1.082 -18 0 0
18 19 0.692 -1.247 -4.049 0.445 0.357 1.802 -1 1.802 0.357 0.445 -4.049 -1.247 0.692 19 1 1
19 20 -0.482 1.000 4.381 -1.000 1.254 1.000 0 -1.000 -1.254 1.000 -4.381 -1.000 0.482 -20 0 0
20 21 -1.110 0.000 -4.494 0.000 1.604 0.000 1 0.000 1.604 -0.000 -4.494 -0.000 -1.110 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 1 0 0 0 0 0 0 0 0 E5
2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 A1⊕E10
3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 E5⊕E13
4 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 A1⊕E8⊕E10
5 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 E3⊕E5⊕E13
6 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 A1⊕E2⊕E8⊕E10
7 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 E3⊕E5⊕E7⊕E13
8 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 A1⊕E2⊕E8⊕E10⊕E12
9 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 E3⊕E5⊕E7⊕E11⊕E13
10 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E6⊕E8⊕E10⊕E12
11 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 E1⊕E3⊕E5⊕E7⊕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 1 0 1 0 1 0 1 0 2 0 1 0 1 E1⊕E3⊕E5⊕E7⊕2E9⊕E11⊕E13
16 1 0 1 1 0 1 0 2 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕2E4⊕E6⊕E8⊕E10⊕E12
17 0 0 0 0 2 0 1 0 1 0 1 0 2 0 1 0 1 2E1⊕E3⊕E5⊕E7⊕2E9⊕E11⊕E13
18 1 0 1 1 0 1 0 2 0 2 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕2E4⊕2E6⊕E8⊕E10⊕E12
19 0 0 0 0 2 0 1 0 1 0 1 0 2 0 2 0 1 2E1⊕E3⊕E5⊕E7⊕2E9⊕2E11⊕E13
20 1 0 1 1 0 1 0 2 0 2 0 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕2E4⊕2E6⊕E8⊕E10⊕2E12


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