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 lengthand 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 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). 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 parameterization procedure, in favour of a data-driven philosophy.

Accessing Structural, Electronic, Transport and Mesoscale Properties of Li-GICs via a Complete DFTB Model with Machine-Learned Repulsion Potential

“…The electronic parameters (in [ 26 ], only the confinement potential) were optimized by means of particle swarm optimization (PSO) [ 27 ]. In our GPrep approach, the repulsion potential was then fitted using Gaussian process regression (GPR) [ 28 ] as described in [ 26 ]. The initial parametrization in [ 26 ] did not include the Li–Li repulsion.…”

Perspective on integrating machine learning into computational chemistry and materials science

“…A universal density functional provided by an ML model could potentially eliminate the need for exhaustively comparing different types of functionals for a given chemical problem. So far, ML has been used to generate new DFT functionals or to adjust the energy functional, bypassing the need to solve the iterative Kohn-Sham equations and accelerating simulations for the ground state 104,107,[129][130][131][132][133][134] and excited states 135 significantly. These models further promise better transferability for different types of molecular systems.…”

“…Beyond that, several groups have proposed to combine established DFTB Slater-Koster parametrizations with kernel ridge regression or NN representations of the repulsive energy contributions to improve the accuracy and transferability of DFTB. 149,150 On the example of the QM7-X data set 151 , a mean absolute error of 0.5 kcal/mol could be achieved on the atomization energies of the DFTB-ML model compared to hybrid DFT reference values. 149 Future directions: We expect a vivid development regarding the tight integration of ML within electronic structure software -an approach that some package developers already pursue (e.g., in the case of entos 152 and DFTB+ 153 ).…”

Benchmarks of the density functional tight-binding method for redox, protonation and electronic properties of quinones

“…Several recent methodological developments, like the development of the DFTB3 method 21 and its corresponding parameterization, 22 the use of long-range corrections, 23 improvement of the description of intermolecular 24 and dispersion interactions, 25–28 have significantly increased the accuracy of the method. For parameterization, several automated schemes and schemes which utilize machine learning have been developed, 29–37 increasing the applicability of the DFTB method to different systems and problems.…”