hvdrotations
functions
functions
| D4h | E | 2C4 (z) | C2 | 2C'2 | 2C''2 | i | 2S4 | h |
2v |
2d |
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 | - | - |
| B1g | +1 | -1 | +1 | +1 | -1 | +1 | -1 | +1 | +1 | -1 | - | x2-y2 | - |
| B2g | +1 | -1 | +1 | -1 | +1 | +1 | -1 | +1 | -1 | +1 | - | xy | - |
| Eg | +2 | 0 | -2 | 0 | 0 | +2 | 0 | -2 | 0 | 0 | (Rx, Ry) | (xz, yz) | - |
| 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) |
| B1u | +1 | -1 | +1 | +1 | -1 | -1 | +1 | -1 | -1 | +1 | - | - | xyz |
| B2u | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | - | - | z(x2-y2) |
| Eu | +2 | 0 | -2 | 0 | 0 | -2 | 0 | +2 | 0 | 0 | (x, y) | - | (xz2, yz2) (xy2, x2y), (x3, y3) |
| Number of symmetry elements | h = 16 |
| Number of irreducible representations | n = 10 |
| Abelian group | no |
| Number of subgroups | 25 |
| Number of distinct subgroups | 13 |
| Subgroups
(Number of different orientations) |
Cs (3) , Ci , C2 (3) , C4 , D2 (2) , D4 , C2v (4) , C4v , C2h (3) , C4h , D2h (2) , D2d (2) , S4 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| [Al4]2--Ion | Xenontetrafluoride | Squaric Acid Dianion |
|---|
| dipole (p) | A2u+Eu |
|---|---|
| quadrupole (d) | A1g+B1g+B2g+Eg |
| octopole (f) | A2u+B1u+B2u+2Eu |
| hexadecapole (g) | 2A1g+A2g+B1g+B2g+2Eg |
| 32-pole (h) | A1u+2A2u+B1u+B2u+3Eu |
| 64-pole (i) | 2A1g+A2g+2B1g+2B2g+3Eg |
| 128-pole (j) | A1u+2A2u+2B1u+2B2u+4Eu |
| 256-pole(k) | 3A1g+2A2g+2B1g+2B2g+4Eg |
| 512-pole (l) | 2A1u+3A2u+2B1u+2B2u+5Eu |
