This document is provided by the Chemical Portal www.webqc.org C_{5v} point group |
not Abelian, 4(6) irreducible representations |
Subgroups: C_{s}, C_{5} |
E | 2C_{5} (z) | 2(C_{5})^{2} | 5σ_{v} | linear, rotations |
quadratic | |
---|---|---|---|---|---|---|
A_{1} | 1 | 1 | 1 | 1 | z | x^{2}+y^{2}, z^{2} |
A_{2} | 1 | 1 | 1 | -1 | R_{z} | |
E_{1} | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | (x, y) (R_{x}, R_{y}) | (xz, yz) |
E_{2} | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | (x^{2}-y^{2}, xy) |
A_{1} | A_{2} | E_{1} | E_{2} | |
---|---|---|---|---|
A_{1} | A_{1} | A_{2} | E_{1} | E_{2} |
A_{2} | A_{2} | A_{1} | E_{2} | E_{1} |
E_{1} | E_{1} | E_{1} | A_{1}+A_{2}+E_{2} | E_{1}+E_{2} |
E_{2} | E_{2} | E_{2} | E_{1}+E_{2} | A_{1}+A_{2}+E_{2} |