Department of Mathematics and Computer Science , University of Basel , Spiegelgasse 1 , 4051 Basel , Switzerland.
Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry , University of Basel , Klingelbergstrasse 80 , 4056 Basel , Switzerland.
J Chem Theory Comput. 2019 Mar 12;15(3):1546-1559. doi: 10.1021/acs.jctc.8b00832. Epub 2019 Feb 12.
Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multilevel combination (C) technique, to combine various levels of approximations made when molecular energies are calculated. When combined with quantum machine learning (QML) models, the resulting CQML model is a generalized unified recursive kernel ridge regression that exploits correlations implicitly encoded in training data composed of multiple levels in multiple dimensions. Here, we have investigated up to three dimensions: chemical space, basis set, and electron correlation treatment. Numerical results have been obtained for atomization energies of a set of ∼7000 organic molecules with up to 7 atoms (not counting hydrogens) containing CHONFClS, as well as for ∼6000 constitutional isomers of CHO. CQML learning curves for atomization energies suggest a dramatic reduction in necessary training samples calculated with the most accurate and costly method. In order to generate millisecond estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors reaching chemical accuracy (∼1 kcal/mol), the CQML model requires only ∼100 training instances at CCSD(T)/cc-pvdz level, rather than thousands within conventional QML, while more training molecules are required at lower levels. Our results suggest a possibly favorable trade-off between various hierarchical approximations whose computational cost scales differently with electron number.
受量子化学中流行的 Pople 图的启发，我们引入了一种基于多层次组合（C）技术的层次方案，以组合在计算分子能量时所做的各种近似层次。当与量子机器学习（QML）模型结合使用时，所得到的 CQML 模型是一种广义统一递归核岭回归，它利用了由多个维度的多个层次组成的训练数据中隐含编码的相关性。在这里，我们已经研究了高达三个维度：化学空间、基组和电子相关处理。我们获得了一组约 7000 个含有 CHONFClS 的有机分子的原子化能的数值结果，这些分子最多有 7 个原子（不包括氢原子），以及约 6000 个 CHO 的构象异构体。原子化能的 CQML 学习曲线表明，用最准确和最昂贵的方法计算所需的训练样本数量大幅减少。为了以达到化学精度（约 1 kcal/mol）的预测误差生成 CCSD(T)/cc-pvdz 原子化能的毫秒估计值，CQML 模型只需要在 CCSD(T)/cc-pvdz 级别上进行约 100 次训练实例，而不是在传统 QML 中需要数千次，而在较低级别则需要更多的训练分子。我们的结果表明，各种层次近似之间可能存在有利的权衡，其计算成本随电子数的不同而不同。
