Results for Point Group D19h



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


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