First-principles calculations of surfaces or two-dimensional materials with a finite surface charge invariably include an implicit or explicit compensating countercharge. We show that an ideal constant-charge counterelectrode in the vacuum region can be introduced by means of a simple correction to the electrostatic potential in close analogy to the well-known dipole correction for charge-neutral asymmetric slabs. Our generalized dipole correction accounts simultaneously for the sheet-charge electrode and the huge voltage built up between the system of interest and the counterelectrode. We demonstrate its usefulness for two prototypical cases, namely, field evaporation in the presence of huge electric fields (20 V/nm) and the modeling of charged defects at an insulator surface. We also introduce algorithmic improvements to charge initialization and preconditioning in the density functional theory algorithm that proved crucial for ensuring rapid convergence in slab systems with high electric fields.

中文翻译：

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重复平板法中带电表面的广义偶极校正

具有有限表面电荷的表面或二维材料的第一性原理计算始终包括隐式或显式的补偿反电荷。我们表明，可以通过对静电势的简单校正来引入真空区域中的理想恒定电荷反电极，这与众所周知的电荷中性不对称平板的偶极校正非常相似。我们的广义偶极校正同时考虑了薄层电荷电极以及在目标系统和反电极之间建立的巨大电压。我们证明了它对于两种典型情况的有用性，即在存在巨大电场（20 V / nm）的情况下进行场蒸发以及在绝缘体表面进行带电缺陷建模。