This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the prediction of many target properties of crystal structures is computationally slow and is essentially repeated for many nearly identical simulated structures. The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations. The above properties make these distances ideal tools for clustering and visualizing large datasets of crystal structures. All the conclusions are rigorously proved and justified by experiments on real and simulated crystal structures reported in the Nature 2017 paper "Functional materials discovery using energy-structure-function maps".

中文翻译：

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任意晶格之间基于 Voronoi 的相似距离

本文开发了一种新的连续方法来解决理想晶体的周期性晶格之间的相似性。需要量化晶体结构之间的相似性以显着加快晶体结构预测，因为晶体结构的许多目标特性的预测在计算上很慢，并且对于许多几乎相同的模拟结构基本上是重复的。晶体结构的任意周期晶格之间的建议距离在所有刚性运动下都是不变的，满足原子微扰下的度量公理和连续性。上述特性使这些距离成为聚类和可视化大型晶体结构数据集的理想工具。