Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

Abstract

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 parameterization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential Vrep poses a major challenge. In this paper we propose a machine-learning (ML) approach to fitting Vrep, using Gaussian Process Regression (GPR). The use of GPR circumvents the need for non-linear 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 parameterization procedure, in favour of a data-driven philosophy.

Exchange Spin Coupling from Gaussian Process Regression

“…Experience so far shows that it is suitable for rather small training sets, which is a favorable property given that reference data for J are relatively costly to generate. GPR has been used in chemistry for, e.g., fitting repulsive potentials in tight-binding DFT 77 , for correcting empirical dispersion models 78 , for evaluating work functions 79 , for calculating vibrational Raman spectra 80 , for transition-state 81 and molecular-structure optimization 82-85 , for fitting potential-energy surfaces 86,87 , and for the error-controlled exploration of reaction networks 88,89 . We will employ GPR here for asking to what extent it is possible to machine-learn J, as compared with other molecular properties.…”

Machine learning for chemical discovery

“…Datasets such as QM9 13 , ANI-1x 14 , and QM7-X 15 contain QM properties for up to 10 7 molecular structures and enable essentially complete coverage of the chemical space of small drug-like molecules. These data has been used in many applications, for exampling to construct fast-to-evaluate neural network potentials for small molecules 11,16 , develop improved semiempirical quantum methods 17,18 , and obtain new insights into partitioning of molecular quantum properties into atomic and fragment-based contributions 11,12 .…”

Exchange Spin Coupling from Gaussian Process Regression

“…Experience so far shows that it is suitable for rather small training sets, which is a favorable property given that reference data for J are relatively costly to generate. GPR has been used in chemistry for, e.g., fitting repulsive potentials in tight-binding DFT 77 , for correcting empirical dispersion models 78 , for evaluating work functions 79 , for calculating vibrational Raman spectra 80 , for transition-state 81 and molecular-structure optimization [82][83][84][85] , for fitting potential-energy surfaces 86,87 , and for the error-controlled exploration of reaction networks 88,89 . We will employ GPR here for asking to what extent it is possible to machine-learn J, as compared with other molecular properties.…”