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