Results for Point Group D19h



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



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