Charged defects are often studied within the periodic density functional theory (DFT), but this introduces strong finite-size artifacts. In this work, we develop an electrostatic image interaction correction (IIC) method based on the direct solution of the Poisson equation for charge models constructed directly from DFT calculations. These IICs are found to be detail-insensitive, depending almost entirely on bulk dielectric properties. As these IICs are not able to fully explain the observed finite-size scaling, we explore potential alignment in detail and introduce a novel decomposition to separate out different contributions. We find that the two main sources of potential alignment are defect image interactions and changes in the number of atoms present in the supercell. This first effect is accurately predicted by the periodic part of our IIC. The second contribution is unrelated to the IIC and justifies the common observation that the magnitude of finite-size dependence can strongly vary between vacancy and interstitial defects. It can be approximately predicted using atomic radius, but is strongly sensitive to the pseudopotential employed. Combined, these developments provide a new justification for known finite-size scaling rules. Our results suggest that for cubic supercells, the Lany-Zunger IIC, combined with simplified potential alignment between neutral systems, can yield accurate corrections in spite of the simplicity of the approach.

中文翻译：

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周期性边界条件下图像电荷与带电缺陷的电势对准校正之间的关系

带电缺陷通常在周期性密度泛函理论（DFT）中进行研究，但这会引入强大的有限大小伪像。在这项工作中，我们针对直接由DFT计算构建的电荷模型，基于泊松方程的直接解，开发了静电图像相互作用校正（IIC）方法。发现这些IIC对细节不敏感，几乎完全取决于体介电特性。由于这些IIC无法完全解释所观察到的有限大小缩放，因此我们将详细探讨潜在的对齐方式，并引入新颖的分解方法以分离出不同的贡献。我们发现，电位对准的两个主要来源是缺陷图像相互作用和超级电池中存在的原子数的变化。IIC的定期部分可以准确地预测出第一个效果。第二个贡献与IIC无关，它证明了普遍的看法，即有限尺寸依赖性的大小在空位和间隙缺陷之间可能会发生很大变化。可以使用原子半径近似地预测它，但对所使用的伪势非常敏感。这些发展相结合，为已知的有限大小缩放规则提供了新的依据。我们的结果表明，对于立方超级电池，尽管方法简单，但Lany-Zunger IIC与中性系统之间简化的电势对准相结合，仍可产生准确的校正。但对所使用的伪电位非常敏感。这些发展相结合，为已知的有限大小缩放规则提供了新的依据。我们的结果表明，对于立方超级电池，尽管方法简单，但Lany-Zunger IIC与中性系统之间简化的电势对准相结合，仍可产生准确的校正。但对所使用的伪电位非常敏感。这些发展相结合，为已知的有限大小缩放规则提供了新的依据。我们的结果表明，对于立方超级电池，尽管方法简单，但Lany-Zunger IIC与中性系统之间简化的电势对准相结合，仍可产生准确的校正。