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