Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany.
J Chem Phys. 2023 Jul 7;159(1). doi: 10.1063/5.0154710.
We present a local and transferable machine-learning approach capable of predicting the real-space density response of both molecules and periodic systems to homogeneous electric fields. The new method, Symmetry-Adapted Learning of Three-dimensional Electron Responses (SALTER), builds on the symmetry-adapted Gaussian process regression symmetry-adapted learning of three-dimensional electron densities framework. SALTER requires only a small, but necessary, modification to the descriptors used to represent the atomic environments. We present the performance of the method on isolated water molecules, bulk water, and a naphthalene crystal. Root mean square errors of the predicted density response lie at or below 10% with barely more than 100 training structures. Derived polarizability tensors and even Raman spectra further derived from these tensors show good agreement with those calculated directly from quantum mechanical methods. Therefore, SALTER shows excellent performance when predicting derived quantities, while retaining all of the information contained in the full electronic response. Thus, this method is capable of predicting vector fields in a chemical context and serves as a landmark for further developments.
我们提出了一种局部且可转移的机器学习方法，能够预测分子和周期性系统对均匀电场的真实空间密度响应。新方法称为“三维电子响应的对称自适应学习（Symmetry-Adapted Learning of Three-dimensional Electron Responses，SALTER）”，它建立在对称自适应高斯过程回归和三维电子密度的对称自适应学习框架之上。SALTER 只需要对用于表示原子环境的描述符进行很小但必要的修改。我们在孤立水分子、体相水和萘晶体上展示了该方法的性能。预测密度响应的均方根误差在 10%以下，只需 100 多个训练结构。由此衍生的极化率张量，甚至进一步从这些张量推导出来的拉曼光谱，与直接从量子力学方法计算出的结果吻合得很好。因此，SALTER 在预测衍生量时表现出色，同时保留了全电子响应中包含的所有信息。因此，该方法能够在化学环境中预测向量场，并成为进一步发展的里程碑。
