C_{5v} | E | 2C_{5} (z) | 2(C_{5})^{2} | 5_{v} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|
A_{1} | +1 | +1 | +1 | +1 | z | x^{2}+y^{2}, z^{2} | z^{3}, z(x^{2}+y^{2}) |
A_{2} | +1 | +1 | +1 | -1 | R_{z} | - | - |
E_{1} | +2 | +2cos(2/5) | +2cos(4/5) | 0 | (x, y) (R_{x}, R_{y}) | (xz, yz) | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E_{2} | +2 | +2cos(4/5) | +2cos(2/5) | 0 | - | (x^{2}-y^{2}, xy) | [xyz, z(x^{2}-y^{2})] [y(3x^{2}-y^{2}), x(x^{2}-3y^{2})] |
Number of symmetry elements | h = 10 |
Number of irreducible representations | n = 4 |
Abelian group | no |
Subgroups | C_{s} , C_{5} |
---|---|
Optical Isomerism (Chirality) | no |
dipole (p) | A_{1}+E_{1} |
---|---|
quadrupole (d) | A_{1}+E_{1}+E_{2} |
octopole (f) | A_{1}+E_{1}+2E_{2} |
hexadecapole (g) | A_{1}+2E_{1}+2E_{2} |
32-pole (h) | 2A_{1}+A_{2}+2E_{1}+2E_{2} |
64-pole (i) | 2A_{1}+A_{2}+3E_{1}+2E_{2} |
128-pole (j) | 2A_{1}+A_{2}+3E_{1}+3E_{2} |
256-pole(k) | 2A_{1}+A_{2}+3E_{1}+4E_{2} |
512-pole (l) | 2A_{1}+A_{2}+4E_{1}+4E_{2} |