hrotations
functions
functions
+1
-i
-1
+i
+1
-i
-1
+i
Rx-iRy
+1
-i
-1
+i
-1
+i
+1
-i
x-iy
| C4h | E | C4(z) | C2 | (C4)3 | i | (S4)3 | h |
S4 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ag | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | Rz | x2+y2, z2 | - |
| Bg | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | - | x2-y2, xy | - |
| Eg | +1 +1 |
+i -i |
-1 -1 |
-i +i |
+1 +1 |
+i -i |
-1 -1 |
-i +i |
Rx+iRy Rx-iRy |
(xz, yz) | - |
| Au | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | z | - | z3, z(x2+y2) |
| Bu | +1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | - | - | xyz, z(x2-y2) |
| Eu | +1 +1 |
+i -i |
-1 -1 |
-i +i |
-1 -1 |
-i +i |
+1 +1 |
+i -i |
x+iy x-iy |
- | (xz2, yz2) (xy2, x2y) (x3, y3) |
| Number of symmetry elements | h = 8 |
| Number of irreducible representations | n = 8 |
| Number of real irreducible representations | n = 6 |
| Abelian group | yes |
| Number of subgroups | 6 |
| Subgroups | Cs , Ci , C2 , C4 , C2h , S4 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| dipole (p) | Au+Eu |
|---|---|
| quadrupole (d) | Ag+2Bg+Eg |
| octopole (f) | Au+2Bu+2Eu |
| hexadecapole (g) | 3Ag+2Bg+2Eg |
| 32-pole (h) | 3Au+2Bu+3Eu |
| 64-pole (i) | 3Ag+4Bg+3Eg |
| 128-pole (j) | 3Au+4Bu+4Eu |
| 256-pole(k) | 5Ag+4Bg+4Eg |
| 512-pole (l) | 5Au+4Bu+5Eu |
