Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised by the introduction of a uniform neutralising background, are very slow to converge with cell size. The periodicity introduces spurious electric fields which decay slowly with cell size and which also slow the convergence of other properties relating to the ground state charge density. This paper presents a simple self-consistent technique for producing rapid convergence of both energies and charge distribution in the particular geometry of 2D periodicity, as used for studying surfaces.

平面波密度泛函理论代码通常假定所有三个维度上的周期性。这在研究带电系统时会造成困难，例如每个晶胞的能量变得无限大，并且即使在通过引入均匀的中和背景重新归一化之后，与晶胞尺寸收敛的速度也很慢。周期性引入了随单元尺寸缓慢衰减的杂散电场，并且还减慢了与基态电荷密度相关的其他特性的收敛。本文提出了一种简单的自洽技术，用于在二维周期性的特定几何形状中产生能量和电荷分布的快速收敛，用于研究表面。