Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression,Journal of Chemical Theory and Computation

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Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2020-03-10 , DOI: 10.1021/acs.jctc.9b00975
Chiara Panosetti ₁ , Artur Engelmann ₁ , Lydia Nemec ₁ , Karsten Reuter ₁ , Johannes T. Margraf ₁

Affiliation

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 V_rep poses a major challenge. In this paper, we propose a machine-learning (ML) approach to fitting V_rep, using Gaussian Process Regression (GPR) to reconstruct V_rep 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.

中文翻译：

学习使用力：将排斥势与高斯过程回归拟合在密度函数紧结合中

密度函数紧密绑定（DFTB）方法是对密度泛函理论（DFT）的一种流行的半经验近似方法。在许多情况下，DFTB可以以一小部分成本提供与DFT相当的精度，从而可以进行长度和时间尺度上的模拟，而这对于第一原理DFT是不可行的。同时（与经验性原子间电势和力场相反），DFTB仍然可以直接访问电子特性，例如能带结构。这些优点是以向该方法引入经验参数为代价的，与真正的第一原理方法相比，导致传递性降低。因此，如果可以针对给定项目例行调整参数集，那将非常有用。V _rep构成了重大挑战。在本文中，我们提出了一种机器学习（ML）来拟合V _rep的方法，该方法使用高斯过程回归（GPR）重建以DFT-DFTB力残差作为训练数据的V _rep。GPR的使用避免了对非线性或全局参数优化的需求，同时提供了功能形式上的任意灵活性。我们还表明，通过拟合包含碳，氢和氧的有机分子的排斥势，可以将所提出的方法一次应用于多个元素。总体而言，新方法将重点从功能形式和参数化程序的选择上移开了，转而采用了数据驱动的哲学。

更新日期：2020-04-24

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