vdrotations
functions
functions
| C6v | E | 2C6 (z) | 2C3 (z) | C2 (z) | 3v |
3d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|
| A1 | +1 | +1 | +1 | +1 | +1 | +1 | z | x2+y2, z2 | z3, z(x2+y2) |
| A2 | +1 | +1 | +1 | +1 | -1 | -1 | Rz | - | - |
| B1 | +1 | -1 | +1 | -1 | +1 | -1 | - | - | x(x2-3y2) |
| B2 | +1 | -1 | +1 | -1 | -1 | +1 | - | - | y(3x2-y2) |
| E1 | +2 | +1 | -1 | -2 | 0 | 0 | (x, y) (Rx, Ry) | (xz, yz) | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| E2 | +2 | -1 | -1 | +2 | 0 | 0 | - | (x2-y2, xy) | [xyz, z(x2-y2)] |
| Number of symmetry elements | h = 12 |
| Number of irreducible representations | n = 6 |
| Abelian group | no |
| Number of subgroups | 8 |
| Number of distinct subgroups | 6 |
| Subgroups
(Number of different orientations) |
Cs (2) , C2 , C3 , C6 , C2v , C3v (2) |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | yes |
| dipole (p) | A1+E1 |
|---|---|
| quadrupole (d) | A1+E1+E2 |
| octopole (f) | A1+B1+B2+E1+E2 |
| hexadecapole (g) | A1+B1+B2+E1+2E2 |
| 32-pole (h) | A1+B1+B2+2E1+2E2 |
| 64-pole (i) | 2A1+A2+B1+B2+2E1+2E2 |
| 128-pole (j) | 2A1+A2+B1+B2+3E1+2E2 |
| 256-pole(k) | 2A1+A2+B1+B2+3E1+3E2 |
| 512-pole (l) | 2A1+A2+2B1+2B2+3E1+3E2 |
