Results for Point Group D19d



Symmetric powers of degenerate representation E7u
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 i 2(S38)17 2(S38)15 2(S38)13 2(S38)11 2(S38)9 2(S38)7 2(S38)5 2(S38)3 2S38 19σd
1 2 -1.355 -0.165 1.578 -1.973 1.094 0.491 -1.759 1.892 -0.803 0 -2 1.355 0.165 -1.578 1.973 -1.094 -0.491 1.759 -1.892 0.803 0
2 3 0.835 -0.973 1.491 2.892 0.197 -0.759 2.094 2.578 -0.355 1 3 0.835 -0.973 1.491 2.892 0.197 -0.759 2.094 2.578 -0.355 1
3 4 0.224 0.326 0.775 -3.732 -0.879 -0.864 -1.924 2.986 1.088 0 -4 -0.224 -0.326 -0.775 3.732 0.879 0.864 1.924 -2.986 -1.088 0
4 5 -1.138 0.919 -0.268 4.470 -1.158 0.335 1.291 3.069 -0.520 1 5 -1.138 0.919 -0.268 4.470 -1.158 0.335 1.291 3.069 -0.520 1
5 6 1.318 -0.478 -1.198 -5.086 -0.388 1.028 -0.346 2.820 -0.671 0 -6 -1.318 0.478 1.198 5.086 0.388 -1.028 0.346 -2.820 0.671 0
6 7 -0.647 -0.840 -1.623 5.564 0.734 0.170 -0.682 2.266 1.059 1 7 -0.647 -0.840 -1.623 5.564 0.734 0.170 -0.682 2.266 1.059 1
7 8 -0.441 0.616 -1.363 -5.890 1.190 -0.945 1.546 1.466 -0.180 0 -8 0.441 -0.616 1.363 5.890 -1.190 0.945 -1.546 -1.466 0.180 0
8 9 1.245 0.738 -0.529 6.055 0.569 -0.634 -2.037 0.507 -0.914 1 9 1.245 0.738 -0.529 6.055 0.569 -0.634 -2.037 0.507 -0.914 1
9 10 -1.245 -0.738 0.529 -6.055 -0.569 0.634 2.037 -0.507 0.914 0 -10 1.245 0.738 -0.529 6.055 0.569 -0.634 -2.037 0.507 -0.914 0
10 11 0.441 -0.616 1.363 5.890 -1.190 0.945 -1.546 -1.466 0.180 1 11 0.441 -0.616 1.363 5.890 -1.190 0.945 -1.546 -1.466 0.180 1
11 12 0.647 0.840 1.623 -5.564 -0.734 -0.170 0.682 -2.266 -1.059 0 -12 -0.647 -0.840 -1.623 5.564 0.734 0.170 -0.682 2.266 1.059 0
12 13 -1.318 0.478 1.198 5.086 0.388 -1.028 0.346 -2.820 0.671 1 13 -1.318 0.478 1.198 5.086 0.388 -1.028 0.346 -2.820 0.671 1
13 14 1.138 -0.919 0.268 -4.470 1.158 -0.335 -1.291 -3.069 0.520 0 -14 -1.138 0.919 -0.268 4.470 -1.158 0.335 1.291 3.069 -0.520 0
14 15 -0.224 -0.326 -0.775 3.732 0.879 0.864 1.924 -2.986 -1.088 1 15 -0.224 -0.326 -0.775 3.732 0.879 0.864 1.924 -2.986 -1.088 1
15 16 -0.835 0.973 -1.491 -2.892 -0.197 0.759 -2.094 -2.578 0.355 0 -16 0.835 -0.973 1.491 2.892 0.197 -0.759 2.094 2.578 -0.355 0
16 17 1.355 0.165 -1.578 1.973 -1.094 -0.491 1.759 -1.892 0.803 1 17 1.355 0.165 -1.578 1.973 -1.094 -0.491 1.759 -1.892 0.803 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 -1.355 -0.165 1.578 -1.973 1.094 0.491 -1.759 1.892 -0.803 1 21 -1.355 -0.165 1.578 -1.973 1.094 0.491 -1.759 1.892 -0.803 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g E5g E6g E7g E8g E9g A1u A2u E1u E2u E3u E4u E5u E6u E7u E8u E9u
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 E7u
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E5g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 E2u⊕E7u
4 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E5g⊕E9g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 E2u⊕E3u⊕E7u
6 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E4g⊕E5g⊕E9g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 E2u⊕E3u⊕E7u⊕E8u
8 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g⊕E9g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 E2u⊕E3u⊕E6u⊕E7u⊕E8u
10 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g⊕E6g⊕E9g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 E1u⊕E2u⊕E3u⊕E6u⊕E7u⊕E8u
12 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E4g⊕E5g⊕E6g⊕E8g⊕E9g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 E1u⊕E2u⊕E3u⊕E4u⊕E6u⊕E7u⊕E8u
14 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E5g⊕E6g⊕E8g⊕E9g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E6u⊕E7u⊕E8u⊕E9u
16 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E8g⊕E9g
17 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u⊕E9u
18 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g
19 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 A1u⊕A2u⊕E1u⊕E2u⊕E3u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u⊕E9u
20 1 0 1 1 1 1 1 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕2E7g⊕E8g⊕E9g



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