Niehaus, Thomas
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Item-typ:Veröffentlichung, Hybrid functionals for periodic systems in the density functional tight-binding method(2024-11-29); ; ; Over the last decades, hybrid exchange-correlation functionals have been established as a standard technique to address the delocalization problem of semi-local Kohn-Sham density functional theory (KS-DFT). The opposing delocalization in DFT and over-localization in Hartree-Fock (HF) theory gives rise to mutual error compensation when admixing exact HF-type exchange to the density functional approximation (DFA). Despite the ever-growing computational resources and algorithmic improvements, non-local HF-type exchange remains an expensive tool within first principles frameworks, particularly for periodic systems. Since its extension to purely long-range corrected hybrid functionals, the approximate density functional tight binding (DFTB) method, which is derived directly from KS-DFT, offers comparable quantum mechanical insights at a fraction of the computational cost. While the original formalism was restricted to molecules and long-range Fock exchange, this work generalizes the theoretical foundation and implementation to periodic boundary conditions beyond the Γ-point, covering the general class of range-separated hybrid functionals with Coulomb-attenuating method (CAM) type partitioning of the electron-electron interaction. Periodic boundary conditions are essential in broadening the applicability of hybrid DFTB, as most solid state systems cannot be adequately represented as cluster models. By implementing our work in the open-source software package DFTB+, a novel spectrum of methods allowing for an efficient treatment of problems beyond the reach of first principles schemes is made available to the materials science community. For the first time, we demonstrate optimally tuned screened range-separated hybrid DFTB to provide a qualitatively correct description of the polarization-induced fundamental gap renormalization in molecular crystals. Dielectric-dependent global hybrid DFTB accurately reproduces measured band gaps of simple bulk materials, that cover the entire range from narrow- to wide-gap semiconductors as well as insulators. At the same level of theory, we obtain the phonon-induced band gap renormalization of prototypical indirect semiconductors over a wide temperature range. To sample the nuclear wave function, we employ Williams-Lax theory, evaluated either by stochastic Monte-Carlo integration or a deterministic one-shot procedure, as well as classical Born-Oppenheimer molecular dynamics. Following the trend of higher-level many-body perturbation theory, such as Hedin's GW approximation, HF-type exchange admixed to the DFA systematically yields a slightly stronger electron-phonon renormalization, including zero-point corrections.Dissertation169 193 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Development of machine learning enhanced density functional tight binding parametrization(2023-11-06); ; ; ; 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.Dissertation481 230 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Integrating machine learning with density functional tight binding: method development and applications in material simulations(2025-12-12); ; Theoretical computational methods capable of predicting electronic properties have become increasingly important in materials research, providing fundamental insights and guiding material design. Among these, Density Functional Theory (DFT) is widely adopted for its accuracy and broad applicability. However, the high computational cost of ab initio methods limits their scalability to large systems. Density Functional Tight Binding (DFTB), an approximate method derived from DFT, offers a favorable balance between accuracy and efficiency, making it suitable for large-scale simulations. Achieving high performance with DFTB, however, depends on the quality of its parameterization. Recent developments in machine learning (ML) present opportunities to enhance DFTB, enabling more accurate and efficient simulations. This thesis explores two strategies for integrating ML into DFTB. The first approach involves optimizing the distance-dependent two-center integrals of DFTB parameterizations using ML within an automatic gradient-tracking framework. To support this, we have developed TBMaLT (PyTorch-based Tight-Binding Machine Learning Toolkit), an open-source framework that enables flexible construction and optimization of ML-enhanced tight-binding models. The framework is applied to defective periodic systems of silicon and silicon carbide, with the density of states (DOS) selected as the target property for optimization. The results demonstrate that the DFTB Hamiltonian and overlap matrices can be fine-tuned through backpropagation to achieve DOS predictions approaching DFT-level accuracy. Importantly, the integration of ML preserves access to additional electronic properties, such as projected DOS, Mulliken populations, and bandstructures. These properties are examined to ensure they remain physically meaningful and consistent following ML-based optimization. The model’s transferability and scalability are further validated on systems with varying sizes and defect types not included in the training data. The second approach employs Bayesian optimization to refine atomic parameters for generating electronic terms, aimed at applications in organic photovoltaics (OPVs). Two sets of parameters are constructed based on the B3LYP and CAM-B3LYP functionals, covering the elements H, C, N, O, F, S, and Cl, which are key components in OPV donor and acceptor molecules. Benchmarking against a dataset of 12 representative OPV systems demonstrates good agreement with DFT reference calculations for ground-state properties, including optimized geometries and frontier orbital energies. Additionally, excited-state properties of monomers and donor–acceptor dimers are investigated using real-time time-dependent DFTB. Charge-transfer excitations are observed in the dimer systems, and the influence of alkyl side chains on the photoinduced charge-transfer process is investigated. Together, these two approaches show the potential of integrating ML with physically grounded computational methods, offering new pathways for developing efficient and accurate simulation tools for complex materials systems.Dissertation47 68