drotations
functions
functions
/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)/7)| D7d | E | 2C7 | 2(C7)2 | 2(C7)3 | 7C'2 | i | 2(S14)5 | 2(S14)3 | 2S14 | 7d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | - |
| A2g | +1 | +1 | +1 | +1 | -1 | +1 | +1 | +1 | +1 | -1 | Rz | - | - |
| E1g | +2 | +2cos(2/7) |
+2cos(4/7) |
+2cos(6/7) |
0 | +2 | +2cos(2/7) |
+2cos(4/7) |
+2cos(6/7) |
0 | (Rx, Ry) | (xz, yz) | - |
| E2g | +2 | +2cos(4/7) |
+2cos(6/7) |
+2cos(2/7) |
0 | +2 | +2cos(4/7) |
+2cos(6/7) |
+2cos(2/7) |
0 | - | (x2-y2, xy) | - |
| E3g | +2 | +2cos(6/7) |
+2cos(2/7) |
+2cos(4/7) |
0 | +2 | +2cos(6/7) |
+2cos(2/7) |
+2cos(4/7) |
0 | - | - | - |
| A1u | +1 | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | - | - | - |
| A2u | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | +1 | z | - | z3, z(x2+y2) |
| E1u | +2 | +2cos(2/7) |
+2cos(4/7) |
+2cos(6/7) |
0 | -2 | -2cos(2/7) |
-2cos(4/7) |
-2cos(6/7) |
0 | (x, y) | - | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| E2u | +2 | +2cos(4/7) |
+2cos(6/7) |
+2cos(2/7) |
0 | -2 | -2cos(4/7) |
-2cos(6/7) |
-2cos(2/7) |
0 | - | - | [xyz, z(x2-y2)] |
| E3u | +2 | +2cos(6/7) |
+2cos(2/7) |
+2cos(4/7) |
0 | -2 | -2cos(6/7) |
-2cos(2/7) |
-2cos(4/7) |
0 | - | - | [y(3x2-y2), x(x2-3y2)] |
| Number of symmetry elements | h = 28 |
| Number of irreducible representations | n = 10 |
| Abelian group | no |
| Number of subgroups | 8 |
| Subgroups | Cs , Ci , C2 , C7 , D7 , C7v , C2h , S14 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| dipole (p) | A2u+E1u |
|---|---|
| quadrupole (d) | A1g+E1g+E2g |
| octopole (f) | A2u+E1u+E2u+E3u |
| hexadecapole (g) | A1g+E1g+E2g+2E3g |
| 32-pole (h) | A2u+E1u+2E2u+2E3u |
| 64-pole (i) | A1g+2E1g+2E2g+2E3g |
| 128-pole (j) | A1u+2A2u+2E1u+2E2u+2E3u |
| 256-pole(k) | 2A1g+A2g+3E1g+2E2g+2E3g |
| 512-pole (l) | A1u+2A2u+3E1u+3E2u+2E3u |
