Development of machine learning enhanced density functional tight binding parametrization

Abstract

Density functional tight binding (DFTB) theory is an approximate method derived from density functional theory (DFT). Accurate and transferable parametrization is one of the key issues of DFTB development. Over the past two decades, machine learning (ML) has expanded significantly in physics, chemistry, and materials science, which also shows a potential application in the DFTB parametrization. This thesis concentrates on the parametrization of DFTB through both traditional and machine learning based methods.

First, we have focused on parametrizing a solid-state battery system consisting of lithium, phosphorus, sulfur, and chlorine elements, which shows great potential as a solid-state electrolyte. The resulting DFTB parametrization of the electronic and repulsive components yields reasonable accuracy of band structures and optimized geometries of DFTB calculations, comparable to the results of DFT calculations. Second, we have introduced the tight-binding machine learning toolkit (TBMaLT), an open source framework designed to incorporate physical insights into machine learning to predict quantum mechanical properties. The toolkit contains the DFTB layer with flexible interfaces that allow for the generations of Hamiltonian and overlap matrices. We have comprehensively described the DFTB layer and machine learning methodologies employed in TBMaLT, and a detailed analysis of the implementation features. Third, we have explored the applications of TBMaLT in molecular systems. The DFTB-ML workflow enables the optimization of electronic properties by generating two-centre integrals, either by training the basis function parameters (compression radii) or directly optimizing diatomic integrals. The onsite energies were also tuned. All machine learning approaches have successfully improved electronic property predictions, and multiple electronic properties can be optimized simultaneously for all approaches. Training on the basis functions yielded more consistent results of different electronic properties, with the obtained Hamiltonian and overlap matrices falling within physically reasonable ranges. Finally, we have extended the DFTB-ML framework to incorporate periodic boundary conditions, including bulk systems with different lattice types, defect systems, and slab systems consisting of silicon and carbon elements, as the training and testing systems. The reference property for the machine learning was based on band structures obtained through DFT calculations using a hybrid functional. The DFTB-ML model enables the improvement of band structure calculations across various chemical environments, showcasing the capacity of the DFTB-ML framework to predict band structures with high accuracy of the hybrid functional level at an approximate method computational cost. Besides, the DFTB-ML model also exhibits excellent scaling transferability, enabling training on small systems and prediction on larger ones.