We present an all-electron, periodic $G_{\text{0}}{W}_{\text{0}}$ implementation within the numerical atomic orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent $G_{\text{0}}{W}_{\text{0}}$ implementation based on linearized augmented plane waves (LAPWs) plus high-energy localized orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims tier 2) NAO basis set, our $G_{\text{0}}{W}_{\text{0}}$ calculations produce band gaps that typically lie in between the standard LAPW and the $\mathrm{LAPW}+\mathrm{HLO}$ results. Complementing tier 2 with highly localized Slater-type orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the $\mathrm{LAPW}+\mathrm{HLO}$ results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.

中文翻译：

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具有数字原子轨道基础函数的全电子周期G0W0实现：算法和基准

我们提出一种全电子的，周期性的 $G_{\text{0}}{\mathrm{w\; ^}}_{\text{0}}$ 在数字原子轨道（NAO）基础框架内实施。采用等位分辨率（RI）近似值的局部变量来显着降低评估和存储双电子库仑排斥积分的计算成本。我们证明，通过增强用于扩展两个单粒子NAO乘积的辅助基础函数集，可以将局部RI逼近所产生的误差降低到微不足道的水平。引入了一种有效的算法来处理适用于NAO框架的布里渊区采样中的库仑奇异性。我们执行系统的收敛性测试并确定一组计算参数，这些参数可以用作大多数实际目的的默认选择。$G_{\text{0}}{\mathrm{w\; ^}}_{\text{0}}$ 基于线性化增强平面波（LAPW）加上高能局域轨道（HLO）基础集的实现，以及实验结果。借助中等（FHI防御等级2）NAO基础设置，我们的$G_{\text{0}}{\mathrm{w\; ^}}_{\text{0}}$ 计算产生的带隙通常位于标准LAPW与 $\mathrm{拉普}+\mathrm{LO}$结果。与高度局部化的Slater型轨道（STO）互补的第2层，我们发现所获得的带隙显示出朝向$\mathrm{拉普}+\mathrm{LO}$结果。在这项工作中开发的算法和技术为在NAO框架内有效实施相关方法铺平了道路。