论文标题

通过顺序耗尽单粒子空间,最佳区域轨道定位的缩放降低

Reduced scaling of optimal regional orbital localization via sequential exhaustion of the single-particle space

论文作者

Weng, Guorong, Romanova, Mariya, Apelian, Arsineh, Song, Hanbin, Vlček, Vojtěch

论文摘要

Wannier功能已成为扩展系统的电子结构计算中的强大工具。与其他方案相比,广义的Pipek-Mezey Wannier功能具有吸引人的特征(例如,达到最佳定位和$σ$ - $π$轨道的分离)。但是,当应用于巨型纳米级系统时,当人们对系统的小片段中对局部状态感兴趣时,轨道定位会遭受巨大的计算成本。本文中,我们提出了一种快速,高效且可靠的方法,用于在广义Pipek-Mezey方案中获得子系统的区域局部轨道。提出的算法引入了一个减少的工作区,并依次耗尽整个轨道空间,直到定位功能的收敛性。它可以在0.5小时内使用$ \ sim $ 10000电子来处理系统,而与传统方法相比,本地化质量没有损失。通过明智地扩展子系统的大小,获得了更高范围的区域性轨道。在具有NV $^ - $中心的大体积和4 nm宽的钻石板上举例说明,我们演示了方法论,并讨论了定位区域的选择如何影响缺陷的激发能。此外,我们展示了如何轻松将顺序算法扩展到不提供单个单粒子本征态的随机方法。因此,它是一个有前途的工具,可以获取区域性的状态,以解决嵌入巨型冷凝系统中的子系统的电子结构问题。

Wannier functions have become a powerful tool in the electronic structure calculations of extended systems. The generalized Pipek-Mezey Wannier functions exhibit appealing characteristics (e.g., reaching an optimal localization and the separation of the $σ$-$π$ orbitals) when compared with other schemes. However, when applied to giant nanoscale systems, the orbital localization suffers from a large computational cost overhead when one is interested in localized states in a small fragment of the system. Herein we present a swift, efficient, and robust approach for obtaining regionally localized orbitals of a subsystem within the generalized Pipek-Mezey scheme. The proposed algorithm introduces a reduced workspace and sequentially exhausts the entire orbital space until the convergence of the localization functional. It tackles systems with $\sim$10000 electrons within 0.5 hours with no loss in localization quality compared to the traditional approach. Regionally localized orbitals with a higher extent of localization are obtained via judiciously extending the subsystem's size. Exemplifying on large bulk and a 4-nm wide slab of diamond with NV$^-$ center, we demonstrate the methodology and discuss how the choice of the localization region affects the excitation energy of the defect. Furthermore, we show how the sequential algorithm is easily extended to stochastic methodologies that do not provide individual single-particle eigenstates. It is thus a promising tool to obtain regionally localized states for solving the electronic structure problems of a subsystem embedded in giant condensed systems.

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