Results for Point Group D19d



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


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