drotations
functions
functions
| D2d | E | 2S4 | C2 (z) | 2C'2 | 2d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|
| A1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | xyz |
| A2 | +1 | +1 | +1 | -1 | -1 | Rz | - | z(x2-y2) |
| B1 | +1 | -1 | +1 | +1 | -1 | - | x2-y2 | - |
| B2 | +1 | -1 | +1 | -1 | +1 | z | xy | z3, z(x2+y2) |
| E | +2 | 0 | -2 | 0 | 0 | (x, y) (Rx, Ry) | (xz, yz) | (xz2, yz2) (xy2, x2y) (x3, y3) |
| Number of symmetry elements | h = 8 |
| Number of irreducible representations | n = 5 |
| Abelian group | no |
| Number of subgroups | 6 |
| Number of distinct subgroups | 5 |
| Subgroups
(Number of different orientations) |
Cs , C2 (2) , D2 , C2v , S4 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Allene | Cyclobutane | Cyclooctatetraene |
|---|
| dipole (p) | B2+E |
|---|---|
| quadrupole (d) | A1+B1+B2+E |
| octopole (f) | A1+A2+B2+2E |
| hexadecapole (g) | 2A1+A2+B1+B2+2E |
| 32-pole (h) | A1+A2+B1+2B2+3E |
| 64-pole (i) | 2A1+A2+2B1+2B2+3E |
| 128-pole (j) | 2A1+2A2+B1+2B2+4E |
| 256-pole(k) | 3A1+2A2+2B1+2B2+4E |
| 512-pole (l) | 2A1+2A2+2B1+3B2+5E |
