Results for Point Group D19h



Symmetric powers of degenerate representation E''6
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C19 2(C19)2 2(C19)3 2(C19)4 2(C19)5 2(C19)6 2(C19)7 2(C19)8 2(C19)9 19C'2 σh 2S19 2(S19)17 2(S19)3 2(S19)15 2(S19)5 2(S19)13 2(S19)7 2(S19)11 2(S19)9 19σv
1 2 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 0 -2 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 0
2 3 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 1 3 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 1
3 4 1.088 0.224 2.986 0.326 -1.924 0.775 -0.864 -3.732 -0.879 0 -4 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 0
4 5 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 1 5 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 1
5 6 -0.671 1.318 2.820 -0.478 -0.346 -1.198 1.028 -5.086 -0.388 0 -6 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 0
6 7 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 1 7 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 1
7 8 -0.180 -0.441 1.466 0.616 1.546 -1.363 -0.945 -5.890 1.190 0 -8 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 0
8 9 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 1 9 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 1
9 10 0.914 -1.245 -0.507 -0.738 2.037 0.529 0.634 -6.055 -0.569 0 -10 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 0
10 11 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 1 11 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 1
11 12 -1.059 0.647 -2.266 0.840 0.682 1.623 -0.170 -5.564 -0.734 0 -12 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 0
12 13 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 1 13 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 1
13 14 0.520 1.138 -3.069 -0.919 -1.291 0.268 -0.335 -4.470 1.158 0 -14 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 0
14 15 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 1 15 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 1
15 16 0.355 -0.835 -2.578 0.973 -2.094 -1.491 0.759 -2.892 -0.197 0 -16 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 0
16 17 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 1 17 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 1
17 18 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0 -18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0
18 19 -0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 1 19 -0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 1
19 20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0 -20 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0
20 21 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 1 21 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 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 E'8 E'9 A''1 A''2 E''1 E''2 E''3 E''4 E''5 E''6 E''7 E''8 E''9
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 E''6
2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'7
3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 E''1⊕E''6
4 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'5⊕E'7
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 E''1⊕E''6⊕E''8
6 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'5⊕E'7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 E''1⊕E''4⊕E''6⊕E''8
8 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'5⊕E'7⊕E'9
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 E''1⊕E''3⊕E''4⊕E''6⊕E''8
10 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'5⊕E'7⊕E'9
11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 E''1⊕E''3⊕E''4⊕E''6⊕E''8⊕E''9
12 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'7⊕E'9
13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''6⊕E''8⊕E''9
14 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'7⊕E'8⊕E'9
15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''8⊕E''9
16 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'7⊕E'8⊕E'9
17 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8⊕E''9
18 1 0 1 1 1 1 1 1 1 1 1 0 0 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⊕E'8⊕E'9
19 0 0 0 0 0 0 0 0 0 0 0 1 1 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⊕E''8⊕E''9
20 1 0 1 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'1⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕2E'6⊕E'7⊕E'8⊕E'9



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