DFTB Simulation of Charged Clusters Using Machine Learning Charge Inference

We present a modification to self-consistent charge density functional-based tight binding (SCC-DFTB), which allows computation based on approximate atomic charges. We obtain these charges by means of a machine learning (ML) process that combines a Coulomb model with a neural network. This allows us to avoid the SCC cycles in the SCC-DFTB calculation while maintaining its accuracy. The main input of the model is the atomic positions characterized by a set of atom-centered symmetry functions. The charge inference from our ML algorithm is as close as 10–2 units of charge from the exact SCC solution. Our ML-DFTB approach provides a good approximation of the density matrix and of the energy and forces with only a single diagonalization. This is a significant computational saving with respect to the complete SCC algorithm, which allows us to investigate a bigger ensemble of atoms. We show the quality of our approach in the case of charged silicon carbide (SiC) clusters. The ML-DFTB potential energy surface (PES) mimics the SCC-DFTB PES rather well, despite its simplicity. This allows us to obtain the same geometric structure ordering with respect to energy for small clusters. The dissociation barriers for ion emission are well-reproduced, which opens the way to investigating ion field emission and charged cluster stability. The ML-DFTB approach is obviously not limited to charged clusters or SiC materials. It opens a new route to investigate larger clusters than those investigated by standard SCC-DFTB, as well as surface and solid-state chemistry at the atomic level.

本工作提出了一种针对自洽电荷密度泛函紧束缚（self-consistent charge density functional-based tight binding, SCC-DFTB）方法的改进方案，该方案可基于近似原子电荷开展计算。我们通过结合库仑模型与神经网络的机器学习（machine learning, ML）流程获取此类近似电荷，能够在保留SCC-DFTB计算精度的同时，规避原方法中的自洽电荷循环步骤。本模型的核心输入为以一组原子中心对称函数表征的原子坐标，我们的ML算法所推断的电荷与精确SCC求解结果的偏差仅为10⁻²电荷量级。我们提出的ML-DFTB方法仅需一次对角化即可较好地近似密度矩阵、体系能量与原子受力，相较完整的SCC算法实现了显著的计算量缩减，从而得以研究更大尺度的原子集合。我们以带电碳化硅（silicon carbide, SiC）团簇体系验证了该方法的性能：尽管ML-DFTB势能面（potential energy surface, PES）构造较为简洁，但其仍能较好地复刻SCC-DFTB势能面的特征，可对小型团簇实现一致的能量排序几何结构预测；该方法还能准确复现离子发射的解离势垒，为开展离子场发射与带电团簇稳定性研究提供了可行路径。值得注意的是，ML-DFTB方法并不局限于带电团簇或碳化硅材料，它为研究超出标准SCC-DFTB计算规模的更大团簇，以及原子级别的表面与固态化学过程开辟了全新的研究途径。