Results for Point Group D19d



Symmetric powers of degenerate representation E3g
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 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 0 2 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 0
2 3 0.197 -0.355 2.892 0.835 -0.759 2.578 1.491 -0.973 2.094 1 3 0.197 -0.355 2.892 0.835 -0.759 2.578 1.491 -0.973 2.094 1
3 4 -0.879 1.088 -3.732 0.224 -0.864 2.986 0.775 0.326 -1.924 0 4 -0.879 1.088 -3.732 0.224 -0.864 2.986 0.775 0.326 -1.924 0
4 5 -1.158 -0.520 4.470 -1.138 0.335 3.069 -0.268 0.919 1.291 1 5 -1.158 -0.520 4.470 -1.138 0.335 3.069 -0.268 0.919 1.291 1
5 6 -0.388 -0.671 -5.086 1.318 1.028 2.820 -1.198 -0.478 -0.346 0 6 -0.388 -0.671 -5.086 1.318 1.028 2.820 -1.198 -0.478 -0.346 0
6 7 0.734 1.059 5.564 -0.647 0.170 2.266 -1.623 -0.840 -0.682 1 7 0.734 1.059 5.564 -0.647 0.170 2.266 -1.623 -0.840 -0.682 1
7 8 1.190 -0.180 -5.890 -0.441 -0.945 1.466 -1.363 0.616 1.546 0 8 1.190 -0.180 -5.890 -0.441 -0.945 1.466 -1.363 0.616 1.546 0
8 9 0.569 -0.914 6.055 1.245 -0.634 0.507 -0.529 0.738 -2.037 1 9 0.569 -0.914 6.055 1.245 -0.634 0.507 -0.529 0.738 -2.037 1
9 10 -0.569 0.914 -6.055 -1.245 0.634 -0.507 0.529 -0.738 2.037 0 10 -0.569 0.914 -6.055 -1.245 0.634 -0.507 0.529 -0.738 2.037 0
10 11 -1.190 0.180 5.890 0.441 0.945 -1.466 1.363 -0.616 -1.546 1 11 -1.190 0.180 5.890 0.441 0.945 -1.466 1.363 -0.616 -1.546 1
11 12 -0.734 -1.059 -5.564 0.647 -0.170 -2.266 1.623 0.840 0.682 0 12 -0.734 -1.059 -5.564 0.647 -0.170 -2.266 1.623 0.840 0.682 0
12 13 0.388 0.671 5.086 -1.318 -1.028 -2.820 1.198 0.478 0.346 1 13 0.388 0.671 5.086 -1.318 -1.028 -2.820 1.198 0.478 0.346 1
13 14 1.158 0.520 -4.470 1.138 -0.335 -3.069 0.268 -0.919 -1.291 0 14 1.158 0.520 -4.470 1.138 -0.335 -3.069 0.268 -0.919 -1.291 0
14 15 0.879 -1.088 3.732 -0.224 0.864 -2.986 -0.775 -0.326 1.924 1 15 0.879 -1.088 3.732 -0.224 0.864 -2.986 -0.775 -0.326 1.924 1
15 16 -0.197 0.355 -2.892 -0.835 0.759 -2.578 -1.491 0.973 -2.094 0 16 -0.197 0.355 -2.892 -0.835 0.759 -2.578 -1.491 0.973 -2.094 0
16 17 -1.094 0.803 1.973 1.355 -0.491 -1.892 -1.578 0.165 1.759 1 17 -1.094 0.803 1.973 1.355 -0.491 -1.892 -1.578 0.165 1.759 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 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 1 21 1.094 -0.803 -1.973 -1.355 0.491 1.892 1.578 -0.165 -1.759 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E3g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E6g
3 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E3g⊕E9g
4 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E6g⊕E7g
5 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E3g⊕E4g⊕E9g
6 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E6g⊕E7g
7 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E9g
8 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g⊕E6g⊕E7g
9 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E8g⊕E9g
10 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E5g⊕E6g⊕E7g⊕E8g
11 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E3g⊕E4g⊕E5g⊕E8g⊕E9g
12 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E5g⊕E6g⊕E7g⊕E8g
13 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E8g⊕E9g
14 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g
15 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E7g⊕E8g⊕E9g
16 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g
17 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g
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 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g
20 1 0 1 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E1g⊕E2g⊕2E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g



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