具有数值原子轨道基函数的全电子周期G0W0实现:算法和基准

X. Ren, F. Merz, Hong Jiang, Yi Yao, M. Rampp, H. Lederer, V. Blum, M. Scheffler
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引用次数: 19

摘要

我们提出了一个全电子,周期{\GnWn}实现在数值原子轨道(NAO)的基础框架。采用了一种局域化的单位分辨率(RI)近似,大大降低了计算和存储两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积的辅助基函数集,可以将局域化RI近似引起的误差降低到微不足道的水平。介绍了一种适用于NAO框架的有效的布里渊区采样库仑奇点处理算法。我们进行了系统的收敛测试,并确定了一组计算参数,这些参数可以作为大多数实际目的的默认选择。对一组原型半导体和绝缘体进行了基准计算,并与基于线性化增广平面波(LAPW) +高能局域轨道(HLOs)基集的独立$G_0W_0$实现获得的独立参考值以及实验结果进行了比较。使用中等(FHI-aims \textit{tier} 2) NAO基础集,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。用高度局域化的slater型轨道(STOs)补充\textit{第2层},我们发现得到的带隙总体上收敛于LAPW+HLO的结果。在这项工作中开发的算法和技术为在NAO框架内有效实现相关方法铺平了道路。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
All-electron periodic G0W0 implementation with numerical atomic orbital basis functions: Algorithm and benchmarks
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.
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