D_{4} | E | 2C_{4} (z) | C_{2} (z) | 2C'_{2} | 2C''_{2} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|
A_{1} | +1 | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}, z^{2} | - |
A_{2} | +1 | +1 | +1 | -1 | -1 | z, R_{z} | - | z^{3}, z(x^{2}+y^{2}) |
B_{1} | +1 | -1 | +1 | +1 | -1 | - | x^{2}-y^{2} | xyz |
B_{2} | +1 | -1 | +1 | -1 | +1 | - | xy | z(x^{2}-y^{2}) |
E | +2 | 0 | -2 | 0 | 0 | (x, y) (R_{x}, R_{y}) | (xz, yz) | (xz^{2}, yz^{2}) (xy^{2}, x^{2}y) (x^{3}, y^{3}) |
Number of symmetry elements | h = 8 |
Number of irreducible representations | n = 5 |
Abelian group | no |
Number of subgroups | 6 |
Number of distinct subgroups | 3 |
Subgroups
(Number of different orientations) |
C_{2} (3) , C_{4} , D_{2} (2) |
---|---|
Optical Isomerism (Chirality) | yes |
dipole (p) | A_{2}+E |
---|---|
quadrupole (d) | A_{1}+B_{1}+B_{2}+E |
octopole (f) | A_{2}+B_{1}+B_{2}+2E |
hexadecapole (g) | 2A_{1}+A_{2}+B_{1}+B_{2}+2E |
32-pole (h) | A_{1}+2A_{2}+B_{1}+B_{2}+3E |
64-pole (i) | 2A_{1}+A_{2}+2B_{1}+2B_{2}+3E |
128-pole (j) | A_{1}+2A_{2}+2B_{1}+2B_{2}+4E |
256-pole(k) | 3A_{1}+2A_{2}+2B_{1}+2B_{2}+4E |
512-pole (l) | 2A_{1}+3A_{2}+2B_{1}+2B_{2}+5E |