Results for Point Group C19h



Symmetric powers of degenerate representation E''3
Vibrational overtones


Characters of symmetric powers
Power
To
E C19 (C19)2 (C19)3 (C19)4 (C19)5 (C19)6 (C19)7 (C19)8 (C19)9 (C19)10 (C19)11 (C19)12 (C19)13 (C19)14 (C19)15 (C19)16 (C19)17 (C19)18 σh S19 (S19)21 (S19)3 (S19)23 (S19)5 (S19)25 (S19)7 (S19)27 (S19)9 (S19)29 (S19)11 (S19)31 (S19)13 (S19)33 (S19)15 (S19)35 (S19)17 (S19)37
1 2 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 -1.759 -0.165 1.578 1.892 0.491 -1.355 -1.973 -0.803 1.094 -2 -1.094 0.803 1.973 1.355 -0.491 -1.892 -1.578 0.165 1.759 1.759 0.165 -1.578 -1.892 -0.491 1.355 1.973 0.803 -1.094
2 3 0.197 -0.355 2.892 0.835 -0.759 2.578 1.491 -0.973 2.094 2.094 -0.973 1.491 2.578 -0.759 0.835 2.892 -0.355 0.197 3 0.197 -0.355 2.892 0.835 -0.759 2.578 1.491 -0.973 2.094 2.094 -0.973 1.491 2.578 -0.759 0.835 2.892 -0.355 0.197
3 4 -0.879 1.088 -3.732 0.224 -0.864 2.986 0.775 0.326 -1.924 -1.924 0.326 0.775 2.986 -0.864 0.224 -3.732 1.088 -0.879 -4 0.879 -1.088 3.732 -0.224 0.864 -2.986 -0.775 -0.326 1.924 1.924 -0.326 -0.775 -2.986 0.864 -0.224 3.732 -1.088 0.879
4 5 -1.158 -0.520 4.470 -1.138 0.335 3.069 -0.268 0.919 1.291 1.291 0.919 -0.268 3.069 0.335 -1.138 4.470 -0.520 -1.158 5 -1.158 -0.520 4.470 -1.138 0.335 3.069 -0.268 0.919 1.291 1.291 0.919 -0.268 3.069 0.335 -1.138 4.470 -0.520 -1.158
5 6 -0.388 -0.671 -5.086 1.318 1.028 2.820 -1.198 -0.478 -0.346 -0.346 -0.478 -1.198 2.820 1.028 1.318 -5.086 -0.671 -0.388 -6 0.388 0.671 5.086 -1.318 -1.028 -2.820 1.198 0.478 0.346 0.346 0.478 1.198 -2.820 -1.028 -1.318 5.086 0.671 0.388
6 7 0.734 1.059 5.564 -0.647 0.170 2.266 -1.623 -0.840 -0.682 -0.682 -0.840 -1.623 2.266 0.170 -0.647 5.564 1.059 0.734 7 0.734 1.059 5.564 -0.647 0.170 2.266 -1.623 -0.840 -0.682 -0.682 -0.840 -1.623 2.266 0.170 -0.647 5.564 1.059 0.734
7 8 1.190 -0.180 -5.890 -0.441 -0.945 1.466 -1.363 0.616 1.546 1.546 0.616 -1.363 1.466 -0.945 -0.441 -5.890 -0.180 1.190 -8 -1.190 0.180 5.890 0.441 0.945 -1.466 1.363 -0.616 -1.546 -1.546 -0.616 1.363 -1.466 0.945 0.441 5.890 0.180 -1.190
8 9 0.569 -0.914 6.055 1.245 -0.634 0.507 -0.529 0.738 -2.037 -2.037 0.738 -0.529 0.507 -0.634 1.245 6.055 -0.914 0.569 9 0.569 -0.914 6.055 1.245 -0.634 0.507 -0.529 0.738 -2.037 -2.037 0.738 -0.529 0.507 -0.634 1.245 6.055 -0.914 0.569
9 10 -0.569 0.914 -6.055 -1.245 0.634 -0.507 0.529 -0.738 2.037 2.037 -0.738 0.529 -0.507 0.634 -1.245 -6.055 0.914 -0.569 -10 0.569 -0.914 6.055 1.245 -0.634 0.507 -0.529 0.738 -2.037 -2.037 0.738 -0.529 0.507 -0.634 1.245 6.055 -0.914 0.569
10 11 -1.190 0.180 5.890 0.441 0.945 -1.466 1.363 -0.616 -1.546 -1.546 -0.616 1.363 -1.466 0.945 0.441 5.890 0.180 -1.190 11 -1.190 0.180 5.890 0.441 0.945 -1.466 1.363 -0.616 -1.546 -1.546 -0.616 1.363 -1.466 0.945 0.441 5.890 0.180 -1.190
11 12 -0.734 -1.059 -5.564 0.647 -0.170 -2.266 1.623 0.840 0.682 0.682 0.840 1.623 -2.266 -0.170 0.647 -5.564 -1.059 -0.734 -12 0.734 1.059 5.564 -0.647 0.170 2.266 -1.623 -0.840 -0.682 -0.682 -0.840 -1.623 2.266 0.170 -0.647 5.564 1.059 0.734
12 13 0.388 0.671 5.086 -1.318 -1.028 -2.820 1.198 0.478 0.346 0.346 0.478 1.198 -2.820 -1.028 -1.318 5.086 0.671 0.388 13 0.388 0.671 5.086 -1.318 -1.028 -2.820 1.198 0.478 0.346 0.346 0.478 1.198 -2.820 -1.028 -1.318 5.086 0.671 0.388
13 14 1.158 0.520 -4.470 1.138 -0.335 -3.069 0.268 -0.919 -1.291 -1.291 -0.919 0.268 -3.069 -0.335 1.138 -4.470 0.520 1.158 -14 -1.158 -0.520 4.470 -1.138 0.335 3.069 -0.268 0.919 1.291 1.291 0.919 -0.268 3.069 0.335 -1.138 4.470 -0.520 -1.158
14 15 0.879 -1.088 3.732 -0.224 0.864 -2.986 -0.775 -0.326 1.924 1.924 -0.326 -0.775 -2.986 0.864 -0.224 3.732 -1.088 0.879 15 0.879 -1.088 3.732 -0.224 0.864 -2.986 -0.775 -0.326 1.924 1.924 -0.326 -0.775 -2.986 0.864 -0.224 3.732 -1.088 0.879
15 16 -0.197 0.355 -2.892 -0.835 0.759 -2.578 -1.491 0.973 -2.094 -2.094 0.973 -1.491 -2.578 0.759 -0.835 -2.892 0.355 -0.197 -16 0.197 -0.355 2.892 0.835 -0.759 2.578 1.491 -0.973 2.094 2.094 -0.973 1.491 2.578 -0.759 0.835 2.892 -0.355 0.197
16 17 -1.094 0.803 1.973 1.355 -0.491 -1.892 -1.578 0.165 1.759 1.759 0.165 -1.578 -1.892 -0.491 1.355 1.973 0.803 -1.094 17 -1.094 0.803 1.973 1.355 -0.491 -1.892 -1.578 0.165 1.759 1.759 0.165 -1.578 -1.892 -0.491 1.355 1.973 0.803 -1.094
17 18 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
18 19 -0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 19 -0.000 0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 0.000 0.000
19 20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 -20 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
20 21 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 -1.759 -0.165 1.578 1.892 0.491 -1.355 -1.973 -0.803 1.094 21 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 -1.759 -0.165 1.578 1.892 0.491 -1.355 -1.973 -0.803 1.094


Decomposition to irreducible representations
Power
To
A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* E'8* E'9* A'' 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 1 0 0 0 0 0 0 E''3
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'6
3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 E''3⊕E''9
4 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'6⊕E'7
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 E''3⊕E''4⊕E''9
6 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'6⊕E'7
7 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 E''2⊕E''3⊕E''4⊕E''9
8 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'5⊕E'6⊕E'7
9 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 E''2⊕E''3⊕E''4⊕E''8⊕E''9
10 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'5⊕E'6⊕E'7⊕E'8
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 E''2⊕E''3⊕E''4⊕E''5⊕E''8⊕E''9
12 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'5⊕E'6⊕E'7⊕E'8
13 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''8⊕E''9
14 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
15 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''7⊕E''8⊕E''9
16 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
17 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 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕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 2 1 1 1 1 1 1 1 1 1 2A''⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8⊕E''9
20 1 1 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9



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