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Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

机译:任意空间填充的Voronoi多面体上的有效等参积分,用于电子结构计算

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摘要

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab initio electronic-structure calculations. We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb singularity. We showcase the capability of our approach by first applying it to an analytic charge-density model achieving machine-precision accuracy with expected convergence properties in milliseconds. For contrast, we compare our results to those using shape-functions and show our approach is greater than 105 times faster and 107 times more accurate. A weighted Voronoi tessellation also allows for a physics-based partitioning of space that guarantees convex, space-filling VP while reflecting accurate atomic size and site charges, as we show within KKR methods applied to Fe-Pd alloys.
机译:提出了一种在凸Voronoi多面体(VP)上数值高效,准确且易于实现的集成方案,用于从头算电子结构计算。我们将加权Voronoi细分与通过Gauss-Legendre积分的等参积分相结合,以为各种被积物(包括具有库仑奇异性的被积物)提供快速收敛的VP积分。我们首先将其应用于分析电荷密度模型,以达到机器精度的精确度,并以毫秒为单位的预期收敛特性,从而展示了我们方法的功能。相比之下,我们将我们的结果与使用形状函数的结果进行比较,并表明我们的方法快105倍以上,准确度高107倍。加权Voronoi细分还允许对空间进行基于物理的划分,从而确保凸出的,充满空间的VP,同时反映准确的原子大小和位点电荷,正如我们在应用于Fe-Pd合金的KKR方法中所展示的那样。

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