| D4h | E | 2C4 | C2 | 2C2′ | 2C2″ | i | 2S4 | σh | 2σv | 2σd | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A2g | 1 | 1 | 1 | −1 | −1 | 1 | 1 | 1 | −1 | −1 | Rz | |
| B1g | 1 | −1 | 1 | 1 | −1 | 1 | −1 | 1 | 1 | −1 | x²−y² | |
| B2g | 1 | −1 | 1 | −1 | 1 | 1 | −1 | 1 | −1 | 1 | xy | |
| Eg | 2 | 0 | −2 | 0 | 0 | 2 | 0 | −2 | 0 | 0 | (Rx, Ry) | (xz, yz) |
| A1u | 1 | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | ||
| A2u | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | 1 | 1 | z | |
| B1u | 1 | −1 | 1 | 1 | −1 | −1 | 1 | −1 | −1 | 1 | ||
| B2u | 1 | −1 | 1 | −1 | 1 | −1 | 1 | −1 | 1 | −1 | ||
| Eu | 2 | 0 | −2 | 0 | 0 | −2 | 0 | 2 | 0 | 0 | (x, y) |
| 阶 hOrder h | 16 |
|---|---|
| 类数Classes | 10 |
| 所属族Family | Dnh |
| 代表分子Examples | XeF₄, [PtCl₄]²⁻, 反式-[CoCl₂(NH₃)₄]⁺, 环丁二烯XeF₄, [PtCl₄]²⁻, trans-[CoCl₂(NH₃)₄]⁺, cyclobutadiene |
在 3D 中查看并做对称操作Open in 3D and try the symmetry operationsXeF₄ →
约化可约表示Reduce a representation
输入可约表示在各类上的特征标，按约化公式 \(n_i = \frac{1}{h}\sum_R g_R\,\chi(R)\,\chi_i(R)^{*}\) 求出各不可约表示出现的次数。
Enter the characters of a reducible representation; the reduction formula gives how many times each irreducible representation occurs.