机器学习分子相似性描述子的量子化学根
Quantum chemical roots of machine-learning molecular similarity descriptors
摘要：
在这项工作中，我们探讨了分子相似性描述符的量子化学基础。这些描述符是机器学习遍历化合物空间的关键。我们的重点是库仑矩阵和原子位置的平滑重叠（SOAP）。我们采用了一个基本的框架，使我们能够连接两个描述符的电子结构理论。这个框架使我们能够定义两个与电子结构理论更密切相关的新描述符，我们称之为库仑列表和电子密度平滑重叠（SOED）。通过研究它们作为分子相似性描述符的有用性，我们获得了库仑矩阵和SOAP如何以及为什么工作的新见解。此外，库仑列表避免了库仑矩阵的有点神秘的对角化步骤，并可能提供一种直接的方法来提取子系统信息，可以在不同维度的玻恩-奥本海默表面上进行比较。对于电子密度，我们推导出必要的形式主义，以创建SOED措施密切类似于SOAP。由于这种形式主义是更多的参与比SOAP，我们审查的基本理论，但也引入了一组近似，最终使我们能够与SOED在相同的实现可用于评估SOAP。我们把我们的分析集中在基元反应步骤上，其中过渡态结构与反应物或产物结构比后两者彼此更相似。然而，由于多构型效应的影响，过渡态结构的电子能量的预测可能比稳定中间体的电子能量的预测更困难。问题是在多大程度上植根于电子结构理论的分子相似性描述符可以解决这些复杂的影响。
英文摘要：
In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth overlap of atomic positions (SOAP). We adopt a basic framework that allows us to connect both descriptors to electronic structure theory. This framework enables us then to define two new descriptors that are more closely related to electronic structure theory, which we call Coulomb lists and smooth overlap of electron densities (SOED). By investigating their usefulness as molecular similarity descriptors, we gain new insights in how and why Coulomb matrix and SOAP work. Moreover, Coulomb lists avoid the somewhat mysterious diagonalization step of the Coulomb matrix and might provide a direct means to extract subsystem information that can be compared across Born-Oppenheimer surfaces of varying dimension. For the electron density we derive the necessary formalism to create the SOED measure in close analogy to SOAP. Since this formalism is more involved than that of SOAP, we review the essential theory, but also introduce a set of approximations that eventually allow us to work with SOED in terms of the same implementation available for the evaluation of SOAP. We focus our analysis on elementary reaction steps, where transition state structures are more similar to either reactant or product structures than the latter two are with respect to one another. The prediction of electronic energies of transition state structures can, however, be more difficult than that of stable intermediates due to multi-configurational effects. The question arises to what extent molecular similarity descriptors rooted in electronic structure theory can resolve these intricate effects.
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