Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such fingerprints, also called structural descriptors, have been proposed. In this work, we compare the performance of fingerprints based on the overlap matrix, the smooth overlap of atomic positions, Behler–Parrinello atom-centered symmetry functions, modified Behler–Parrinello symmetry functions used in the ANI-1ccx potential and the Faber–Christensen–Huang–Lilienfeld fingerprint under various aspects. We study their ability to resolve differences in local environments and in particular examine whether there are certain atomic movements that leave the fingerprints exactly or nearly invariant. For this purpose, we introduce a sensitivity matrix whose eigenvalues quantify the effect of atomic displacement modes on the fingerprint. Further, we check whether these displacements correlate with the variation of localized physical quantities such as forces. Finally, we extend our examination to the correlation between molecular fingerprints obtained from the atomic fingerprints and global quantities of entire molecules.

原子环境指纹广泛用于计算材料科学，从机器学习潜力到原子配置之间相似性的量化。已经提出了许多构建这种指纹的方法，也称为结构描述符。在这项工作中，我们比较了基于重叠矩阵、原子位置的平滑重叠、Behler-Parrinello 原子中心对称函数、ANI-1ccx 势中使用的修正 Behler-Parrinello 对称函数和 Faber-Christensen 的指纹性能-Huang-Lilienfeld 指纹的各个方面。我们研究它们解决局部环境差异的能力，特别是检查是否存在某些使指纹完全或几乎不变的原子运动。以此目的，我们引入了一个灵敏度矩阵，其特征值量化了原子位移模式对指纹的影响。此外，我们检查这些位移是否与局部物理量（如力）的变化相关。最后，我们将研究扩展到从原子指纹获得的分子指纹与整个分子的全局数量之间的相关性。