The electronic structures and optical properties of uniform ordered hexagonal Ge_0.5Si_0.5 alloys were investigated by the first-principle calculations. We first validated our approach for hexagonal Ge and Si, obtaining atomic geometries and band structures in excellent agreement with available experimental data. Then, the same approach was applied to predict electronic and optical properties of uniform ordered hexagonal Ge_0.5Si_0.5 alloys. The hex-Ge_0.5Si_0.5 alloy is a direct bandgap semiconductor. The dipole-forbidden or dipole-allowed transitions from the three highest valence bands (${\mathrm{\Gamma }}_{9\text{v}}^{+}$, ${\mathrm{\Gamma }}_{7\text{v}+}^{+}$, ${\mathrm{\Gamma }}_{7\text{v}-}^{+}$) to the first (${\mathrm{\Gamma }}_{8\text{c}}^{-}$) or second (${\mathrm{\Gamma }}_{7\text{c}}^{-}$) lowest conduction band at $\mathrm{\Gamma }$ point are obtained. The maximum absorption coefficient is close to 2 × 10⁶ cm⁻¹. The three small absorption peaks probably originates from the transition from the ${\mathrm{\Gamma }}_{9\text{v}}^{+}$, ${\mathrm{\Gamma }}_{7\text{v}+}^{+}$ or ${\mathrm{\Gamma }}_{7\text{v}-}^{+}$ to ${\mathrm{\Gamma }}_{7\text{c}}^{-}$ band around the $\mathrm{\Gamma }$ point, respectively.

_{采用第一性原理计算研究了均匀有序六方Ge 0.5} Si _0.5合金的电子结构和光学性质。我们首先验证了我们的六方锗和硅方法，获得了与可用实验数据非常一致的原子几何形状和能带结构。然后，同样的方法被应用于预测均匀有序六方Ge _0.5 Si _0.5合金的电子和光学性能。hex-Ge _0.5 Si _0.5合金是直接带隙半导体。三个最高价带的偶极禁止或偶极允许跃迁（${\mathrm{\Gamma }}_{9\text{v}}^{+}$,${\mathrm{\Gamma }}_{7\text{v}+}^{+}$,${\mathrm{\Gamma }}_{7\text{v}-}^{+}$) 到第一个 (${\mathrm{\Gamma }}_{8\text{C}}^{-}$) 或第二个 (${\mathrm{\Gamma }}_{7\text{C}}^{-}$) 最低导带在$\mathrm{\Gamma }$获得点。最大吸收系数接近2×10 ⁶ cm ^-1。三个小的吸收峰可能源于从${\mathrm{\Gamma }}_{9\text{v}}^{+}$,${\mathrm{\Gamma }}_{7\text{v}+}^{+}$或者${\mathrm{\Gamma }}_{7\text{v}-}^{+}$至${\mathrm{\Gamma }}_{7\text{C}}^{-}$乐队周围$\mathrm{\Gamma }$点，分别。