Results for Point Group D19d



Symmetric powers of degenerate representation E8u
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 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0 -2 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 0
2 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 1 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 1
3 4 -1.924 -0.879 0.326 1.088 0.775 -3.732 2.986 0.224 -0.864 0 -4 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 0
4 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 1 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 1
5 6 -0.346 -0.388 -0.478 -0.671 -1.198 -5.086 2.820 1.318 1.028 0 -6 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 0
6 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 1 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 1
7 8 1.546 1.190 0.616 -0.180 -1.363 -5.890 1.466 -0.441 -0.945 0 -8 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 0
8 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 1 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 1
9 10 2.037 -0.569 -0.738 0.914 0.529 -6.055 -0.507 -1.245 0.634 0 -10 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 0
10 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 1 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 1
11 12 0.682 -0.734 0.840 -1.059 1.623 -5.564 -2.266 0.647 -0.170 0 -12 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 0
12 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 1 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 1
13 14 -1.291 1.158 -0.919 0.520 0.268 -4.470 -3.069 1.138 -0.335 0 -14 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 0
14 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 1 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 1
15 16 -2.094 -0.197 0.973 0.355 -1.491 -2.892 -2.578 -0.835 0.759 0 -16 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 0
16 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 1 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 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 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 1 21 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 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 0 1 0 E8u
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 E5u⊕E8u
4 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E6g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 E2u⊕E5u⊕E8u
6 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E6g⊕E9g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 E1u⊕E2u⊕E5u⊕E8u
8 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E6g⊕E7g⊕E9g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 E1u⊕E2u⊕E4u⊕E5u⊕E8u
10 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E4g⊕E6g⊕E7g⊕E9g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 E1u⊕E2u⊕E4u⊕E5u⊕E7u⊕E8u
12 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E3g⊕E4g⊕E6g⊕E7g⊕E9g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 E1u⊕E2u⊕E4u⊕E5u⊕E7u⊕E8u⊕E9u
14 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E6g⊕E7g⊕E9g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 E1u⊕E2u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u⊕E9u
16 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕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 1 2 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕2E8g⊕E9g



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