This document is provided by the Chemical Portal www.webqc.org D_{∞h} point group |
not Abelian, ∞ irreducible representations |
E | 2C_{∞} | ... | ∞σ_{v} | i | 2S_{∞} | ... | ∞C'_{2} | linear functions, rotations |
quadratic | |
---|---|---|---|---|---|---|---|---|---|---|
A_{1g}=Σ^{+}_{g} | 1 | 1 | ... | 1 | 1 | 1 | ... | 1 | x^{2}+y^{2}, z^{2} | |
A_{2g}=Σ^{-}_{g} | 1 | 1 | ... | -1 | 1 | 1 | ... | -1 | R_{z} | |
E_{1g}=Π_{g} | 2 | 2cos(φ) | ... | 0 | 2 | -2cos(φ) | ... | 0 | (R_{x}, R_{y}) | (xz, yz) |
E_{2g}=Δ_{g} | 2 | 2cos(2φ) | ... | 0 | 2 | 2cos(2φ) | ... | 0 | (x^{2}-y^{2}, xy) | |
E_{3g}=Φ_{g} | 2 | 2cos(3φ) | ... | 0 | 2 | -2cos(3φ) | ... | 0 | ||
... | ... | ... | ... | ... | ... | ... | ... | ... | ||
A_{1u}=Σ^{+}_{u} | 1 | 1 | ... | 1 | -1 | -1 | ... | -1 | z | |
A_{2u}=Σ^{-}_{u} | 1 | 1 | ... | -1 | -1 | -1 | ... | 1 | ||
E_{1u}=Π_{u} | 2 | 2cos(φ) | ... | 0 | -2 | 2cos(φ) | ... | 0 | (x, y) | |
E_{2u}=Δ_{u} | 2 | 2cos(2φ) | ... | 0 | -2 | -2cos(2φ) | ... | 0 | ||
E_{3u}=Φ_{u} | 2 | 2cos(3φ) | ... | 0 | -2 | 2cos(3φ) | ... | 0 | ||
... | ... | ... | ... | ... | ... | ... | ... | ... |