D_{2h} | E | C_{2} (z) | C_{2} (y) | C_{2} (x) | i | (xy) | (xz) | (yz) | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|---|---|
A_{g} | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x^{2}, y^{2}, z^{2} | - |
B_{1g} | +1 | +1 | -1 | -1 | +1 | +1 | -1 | -1 | R_{z} | xy | - |
B_{2g} | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | R_{y} | xz | - |
B_{3g} | +1 | -1 | -1 | +1 | +1 | -1 | -1 | +1 | R_{x} | yz | - |
A_{u} | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | - | - | xyz |
B_{1u} | +1 | +1 | -1 | -1 | -1 | -1 | +1 | +1 | z | - | z^{3}, y^{2}z, x^{2}z |
B_{2u} | +1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | y | - | yz^{2}, y^{3}, x^{2}y |
B_{3u} | +1 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | x | - | xz^{2}, xy^{2}, x^{3} |
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) |
C_{s} (3) , C_{i} , C_{2} (3) , D_{2} , C_{2v} (3) , C_{2h} (3) |
---|---|
Optical Isomerism (Chirality) | no |
Polar | no |
dipole (p) | B_{1u}+B_{2u}+B_{3u} |
---|---|
quadrupole (d) | 2A_{g}+B_{1g}+B_{2g}+B_{3g} |
octopole (f) | A_{u}+2B_{1u}+2B_{2u}+2B_{3u} |
hexadecapole (g) | 3A_{g}+2B_{1g}+2B_{2g}+2B_{3g} |
32-pole (h) | 2A_{u}+3B_{1u}+3B_{2u}+3B_{3u} |
64-pole (i) | 4A_{g}+3B_{1g}+3B_{2g}+3B_{3g} |
128-pole (j) | 3A_{u}+4B_{1u}+4B_{2u}+4B_{3u} |
256-pole(k) | 5A_{g}+4B_{1g}+4B_{2g}+4B_{3g} |
512-pole (l) | 4A_{u}+5B_{1u}+5B_{2u}+5B_{3u} |