Structure factors obtained from diffraction experiments are one of the most important quantities for characterizing the electronic and structural properties of materials. Methods for calculating this quantity from plane-wave density functional theory (DFT) codes are typically prohibitively expensive to perform, requiring the electron density to be constructed and evaluated on dense real-space grids. Making use of the projector functions found in both the Vanderbilt ultrasoft pseudopotential and projector augmented wave methods, we implement an approach to calculate structure factors which avoids the use of a dense grid by separating the rapidly changing contributions to the electron density and treating them on logarithmic radial grids. This approach is successfully validated against structure factors obtained from all-electron DFT and experiments for three prototype systems, allowing structure factors to be obtained at all-electron accuracy at a fraction of the cost of previous approaches for plane-wave DFT.

中文翻译：

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超软赝势和投影增广波DFT中准确高效的结构因子

从衍射实验中获得的结构因子是表征材料电子和结构特性的最重要的量之一。从平面波密度泛函理论 (DFT) 代码计算该数量的方法通常执行起来非常昂贵，需要在密集的实空间网格上构建和评估电子密度。利用范德比尔特超软赝势和投影增强波方法中的投影函数，我们实现了一种计算结构因子的方法，该方法通过分离对电子密度的快速变化贡献并将它们处理为对数，从而避免使用密集网格径向网格。