Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany.
J Chem Theory Comput. 2020 Apr 14;16(4):2181-2191. doi: 10.1021/acs.jctc.9b00975. Epub 2020 Mar 19.
The Density-Functional Tight Binding (DFTB) method is a popular semiempirical approximation to Density Functional Theory (DFT). In many cases, DFTB can provide comparable accuracy to DFT at a fraction of the cost, enabling simulations on length and time scales that are unfeasible with first-principles DFT. At the same time (and in contrast to empirical interatomic potentials and force fields), DFTB still offers direct access to electronic properties such as the band structure. These advantages come at the cost of introducing empirical parameters to the method, leading to a reduced transferability compared to true first-principle approaches. Consequently, it would be very useful if the parameter sets could be routinely adjusted for a given project. While fairly robust and transferable parametrization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential poses a major challenge. In this paper, we propose a machine-learning (ML) approach to fitting , using Gaussian Process Regression (GPR) to reconstruct with DFT-DFTB force residues as training data. The use of GPR circumvents the need for nonlinear or global parameter optimization, while at the same time offering arbitrary flexibility in terms of the functional form. We also show that the proposed method can be applied to multiple elements at once, by fitting repulsive potentials for organic molecules containing carbon, hydrogen, and oxygen. Overall, the new approach removes focus from the choice of functional form and parametrization procedure, in favor of a data-driven philosophy.
密度泛函紧束缚（DFTB）方法是密度泛函理论（DFT）的一种流行的半经验近似方法。在许多情况下，DFTB 可以以较低的成本提供与 DFT 相当的准确性，从而能够在第一性原理 DFT 无法实现的长度和时间尺度上进行模拟。同时（与经验原子间势和力场相反），DFTB 仍然可以直接访问电子性质，如能带结构。这些优势是通过向方法中引入经验参数来实现的，与真正的第一性原理方法相比，其可转移性降低。因此，如果可以针对特定项目对参数集进行常规调整，那将非常有用。虽然 DFTB 的电子结构部分存在相当稳健且可转移的参数化工作流程，但所谓的排斥势仍然是一个主要挑战。在本文中，我们提出了一种机器学习（ML）方法来拟合 ，使用高斯过程回归（GPR）来使用 DFT-DFTB 力残差作为训练数据来重建 。使用 GPR 避免了对非线性或全局参数优化的需求，同时在功能形式方面提供了任意的灵活性。我们还表明，该方法可以同时应用于多个元素，通过拟合含有碳、氢和氧的有机分子的排斥势来实现。总的来说，新方法将重点从功能形式和参数化过程的选择上转移开，转而采用数据驱动的哲学。
