drotations
functions
functions
| D4d | E | 2S8 | 2C4 | 2(S8)3 | C2 | 4C'2 | 4d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|
| A1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | - |
| A2 | +1 | +1 | +1 | +1 | +1 | -1 | -1 | Rz | - | - |
| B1 | +1 | -1 | +1 | -1 | +1 | +1 | -1 | - | - | - |
| B2 | +1 | -1 | +1 | -1 | +1 | -1 | +1 | z | - | z3, z(x2+y2) |
| E1 | +2 | +(2)½ | 0 | -(2)½ | -2 | 0 | 0 | (x, y) | - | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| E2 | +2 | 0 | -2 | 0 | +2 | 0 | 0 | - | (x2-y2, xy) | [xyz, z(x2-y2)] |
| E3 | +2 | -(2)½ | 0 | +(2)½ | -2 | 0 | 0 | (Rx, Ry) | (xz, yz) | [y(3x2-y2), x(x2-3y2)] |
| Number of symmetry elements | h = 16 |
| Number of irreducible representations | n = 7 |
| Abelian group | no |
| Number of subgroups | 9 |
| Number of distinct subgroups | 8 |
| Subgroups
(Number of different orientations) |
Cs , C2 (2) , C4 , D2 , D4 , C2v , C4v , S8 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Sulfur S8 |
|---|
| dipole (p) | B2+E1 |
|---|---|
| quadrupole (d) | A1+E2+E3 |
| octopole (f) | B2+E1+E2+E3 |
| hexadecapole (g) | A1+B1+B2+E1+E2+E3 |
| 32-pole (h) | A1+A2+B2+E1+E2+2E3 |
| 64-pole (i) | A1+B1+B2+2E1+2E2+E3 |
| 128-pole (j) | A1+A2+B2+2E1+2E2+2E3 |
| 256-pole(k) | 2A1+A2+B1+B2+2E1+2E2+2E3 |
| 512-pole (l) | A1+A2+B1+2B2+3E1+2E2+2E3 |
