(xy) (xz) (yz)rotations
functions
functions
| D2h | E | C2 (z) | C2 (y) | C2 (x) | i | (xy) |
(xz) |
(yz) |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ag | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2, y2, z2 | - |
| B1g | +1 | +1 | -1 | -1 | +1 | +1 | -1 | -1 | Rz | xy | - |
| B2g | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | Ry | xz | - |
| B3g | +1 | -1 | -1 | +1 | +1 | -1 | -1 | +1 | Rx | yz | - |
| Au | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | - | - | xyz |
| B1u | +1 | +1 | -1 | -1 | -1 | -1 | +1 | +1 | z | - | z3, y2z, x2z |
| B2u | +1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | y | - | yz2, y3, x2y |
| B3u | +1 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | x | - | xz2, xy2, x3 |
| Number of symmetry elements | h = 8 |
| Number of irreducible representations | n = 8 |
| Abelian group | yes |
| Number of subgroups | 14 |
| Number of distinct subgroups | 6 |
| Subgroups
(Number of different orientations) |
Cs (3) , Ci , C2 (3) , D2 , C2v (3) , C2h (3) |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| dipole (p) | B1u+B2u+B3u |
|---|---|
| quadrupole (d) | 2Ag+B1g+B2g+B3g |
| octopole (f) | Au+2B1u+2B2u+2B3u |
| hexadecapole (g) | 3Ag+2B1g+2B2g+2B3g |
| 32-pole (h) | 2Au+3B1u+3B2u+3B3u |
| 64-pole (i) | 4Ag+3B1g+3B2g+3B3g |
| 128-pole (j) | 3Au+4B1u+4B2u+4B3u |
| 256-pole(k) | 5Ag+4B1g+4B2g+4B3g |
| 512-pole (l) | 4Au+5B1u+5B2u+5B3u |
