Department of Chemistry, Fordham University, 441 East Fordham Road, The Bronx, New York 10458, United States.
J Chem Inf Model. 2020 Aug 24;60(8):3804-3811. doi: 10.1021/acs.jcim.0c00631. Epub 2020 Jul 29.
Coulomb matrix eigenvalues (CMEs) are global 3D representations of molecular structure, which have been previously used to predict atomization energies, prioritize geometry searches, and interpret rotational spectra. The properties of the CME representation and its relationship to molecular structure are established using the Gershgorin circle theorem. Numerical bounds are studied using a data set of 309 000 conformational samples of all constitutional isomers of acyclic alkanes, CH, from methane ( = 1) to undecane ( = 11), to establish the extent to which the CME preserves chemical intuitions about isomer and conformer similarity and its ability to distinguish constitutional isomers. Neither supervised nor unsupervised machine-learning algorithms can perfectly distinguish constitutional isomers as the molecular size increases, but the misclassification rate can be kept below 1%.
库仑矩阵本征值 (CME) 是分子结构的全局 3D 表示，它已被用于预测原子化能、优化几何搜索和解释旋转光谱。CME 表示的性质及其与分子结构的关系是使用 Gershgorin 圆定理来建立的。使用包含 309000 个非循环烷烃 CH 的所有构象异构体的构象样本的数据集研究了数值边界，从甲烷 ( = 1) 到十一烷 ( = 11)，以确定 CME 在多大程度上保留了关于异构体和构象相似性的化学直觉，以及它区分构象异构体的能力。无论是监督学习还是无监督学习算法都不能随着分子尺寸的增加而完美地区分构象异构体，但错误分类率可以保持在 1%以下。
