arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.01400cond-mat.mtrl-sci
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用数值原子轨道基函数实现全电子周期$G_0W_0$:算法和基准

All-electron periodic $G_0W_0$ implementation with numerical atomic orbital basis functions: algorithm and benchmarks

Xinguo Ren, Florian Merz, Hong Jiang, Yi Yao, Markus Rampp, Hermann Lederer, Volker Blum, Matthias Scheffler

摘要:

我们提出了一个全电子,周期{ \GnWn }的数值原子轨道(NAO)的基础框架内实现。一个本地化的变体的分辨率的身份(RI)近似显着降低计算成本的评估和存储的两个电子库仑排斥积分。我们表明,本地化RI近似所产生的误差可以减少到一个微不足道的水平,通过提高一组辅助基函数,用于扩大两个单粒子NAO的产品。提出了一种适用于NAO框架的布里渊区采样中库仑奇异性的有效处理算法。我们进行了系统的收敛性测试,并确定了一组计算参数,这可以作为默认的选择,为大多数实际目的。基准计算进行了一组典型的半导体和绝缘体,并从一个独立的$G_0W_0$实施线性增广平面波(LAPW)加上高能量局域轨道(HLO)的基础上,以及实验结果的基础上获得的独立的参考值进行比较。使用中等(FHI-aims \textit{tier} 2)NAO基组,我们的$G_0W_0$计算产生的带隙通常位于标准LAPW和LAPW+HLO结果之间。补充\textit{tier} 2与高度本地化斯莱特型轨道(STO),我们发现,所获得的带隙显示出整体收敛到LAPW+HLO的结果。在这项工作中开发的算法和技术为NAO框架内的相关方法的有效实现铺平了道路。

英文摘要:

We present an all-electron, periodic {\GnWn} 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 $G_0W_0$ implementation based on linearized augmented plane waves (LAPW) plus high-energy localized orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims \textit{tier} 2) NAO basis set, our $G_0W_0$ calculations produce band gaps that typically lie in between the standard LAPW and the LAPW+HLO results. Complementing \textit{tier} 2 with highly localized Slater-type orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the LAPW+HLO results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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