Results for Point Group D19d



Symmetric powers of degenerate representation E1u
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 1.892 1.578 1.094 0.491 -0.165 -0.803 -1.355 -1.759 -1.973 0 -2 -1.892 -1.578 -1.094 -0.491 0.165 0.803 1.355 1.759 1.973 0
2 3 2.578 1.491 0.197 -0.759 -0.973 -0.355 0.835 2.094 2.892 1 3 2.578 1.491 0.197 -0.759 -0.973 -0.355 0.835 2.094 2.892 1
3 4 2.986 0.775 -0.879 -0.864 0.326 1.088 0.224 -1.924 -3.732 0 -4 -2.986 -0.775 0.879 0.864 -0.326 -1.088 -0.224 1.924 3.732 0
4 5 3.069 -0.268 -1.158 0.335 0.919 -0.520 -1.138 1.291 4.470 1 5 3.069 -0.268 -1.158 0.335 0.919 -0.520 -1.138 1.291 4.470 1
5 6 2.820 -1.198 -0.388 1.028 -0.478 -0.671 1.318 -0.346 -5.086 0 -6 -2.820 1.198 0.388 -1.028 0.478 0.671 -1.318 0.346 5.086 0
6 7 2.266 -1.623 0.734 0.170 -0.840 1.059 -0.647 -0.682 5.564 1 7 2.266 -1.623 0.734 0.170 -0.840 1.059 -0.647 -0.682 5.564 1
7 8 1.466 -1.363 1.190 -0.945 0.616 -0.180 -0.441 1.546 -5.890 0 -8 -1.466 1.363 -1.190 0.945 -0.616 0.180 0.441 -1.546 5.890 0
8 9 0.507 -0.529 0.569 -0.634 0.738 -0.914 1.245 -2.037 6.055 1 9 0.507 -0.529 0.569 -0.634 0.738 -0.914 1.245 -2.037 6.055 1
9 10 -0.507 0.529 -0.569 0.634 -0.738 0.914 -1.245 2.037 -6.055 0 -10 0.507 -0.529 0.569 -0.634 0.738 -0.914 1.245 -2.037 6.055 0
10 11 -1.466 1.363 -1.190 0.945 -0.616 0.180 0.441 -1.546 5.890 1 11 -1.466 1.363 -1.190 0.945 -0.616 0.180 0.441 -1.546 5.890 1
11 12 -2.266 1.623 -0.734 -0.170 0.840 -1.059 0.647 0.682 -5.564 0 -12 2.266 -1.623 0.734 0.170 -0.840 1.059 -0.647 -0.682 5.564 0
12 13 -2.820 1.198 0.388 -1.028 0.478 0.671 -1.318 0.346 5.086 1 13 -2.820 1.198 0.388 -1.028 0.478 0.671 -1.318 0.346 5.086 1
13 14 -3.069 0.268 1.158 -0.335 -0.919 0.520 1.138 -1.291 -4.470 0 -14 3.069 -0.268 -1.158 0.335 0.919 -0.520 -1.138 1.291 4.470 0
14 15 -2.986 -0.775 0.879 0.864 -0.326 -1.088 -0.224 1.924 3.732 1 15 -2.986 -0.775 0.879 0.864 -0.326 -1.088 -0.224 1.924 3.732 1
15 16 -2.578 -1.491 -0.197 0.759 0.973 0.355 -0.835 -2.094 -2.892 0 -16 2.578 1.491 0.197 -0.759 -0.973 -0.355 0.835 2.094 2.892 0
16 17 -1.892 -1.578 -1.094 -0.491 0.165 0.803 1.355 1.759 1.973 1 17 -1.892 -1.578 -1.094 -0.491 0.165 0.803 1.355 1.759 1.973 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 1.892 1.578 1.094 0.491 -0.165 -0.803 -1.355 -1.759 -1.973 1 21 1.892 1.578 1.094 0.491 -0.165 -0.803 -1.355 -1.759 -1.973 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 1 0 0 0 0 0 0 0 0 E1u
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 E1u⊕E3u
4 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g
5 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 E1u⊕E3u⊕E5u
6 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 E1u⊕E3u⊕E5u⊕E7u
8 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E8g
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 E1u⊕E3u⊕E5u⊕E7u⊕E9u
10 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E8g⊕E9g
11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 E1u⊕E3u⊕E5u⊕E7u⊕E8u⊕E9u
12 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E7g⊕E8g⊕E9g
13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 E1u⊕E3u⊕E5u⊕E6u⊕E7u⊕E8u⊕E9u
14 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g
15 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 E1u⊕E3u⊕E4u⊕E5u⊕E6u⊕E7u⊕E8u⊕E9u
16 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕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 2 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E1g⊕E2g⊕E3g⊕E4g⊕E5g⊕E6g⊕E7g⊕E8g⊕E9g


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