Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

中文翻译：

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连续对称性和手性测量：大分子结构的近似算法

量化分子的不完美对称性有助于探索结构扭曲的来源、作用和程度。基于连续对称性和手性测量的既定方法，我们开发了一组三维分子描述符来估计大型结构的扭曲。这些三维几何描述符量化了理想对称性（或手性）与实际对称性之间的差距。它们是分子几何形状的全局参数，直观地定义，并且能够检测整个化学（包括有机、无机和生化系统）中给定分子的微小结构变化。将这些方法应用于大型结构具有挑战性，因为对称运算涉及无数排列并且必须加以考虑。我们的方法侧重于迭代地找到三维空间中对称元素的近似方向以及相关的排列。描述了与以前版本相比的主要算法改进，显示出更高的准确性、可靠性和结构保留。新算法针对三组分子结构进行了测试，包括柱[5]芳烃与Li+的配合物、C100富勒烯和金属有机框架的大晶胞。这些进展补充了我们最近用于计算小分子和蛋白质同聚物的连续对称性和手性测量的算法，并简化了分子建模、QSAR 和化学信息学中各种研究目标的全套测量的使用。