Machine Learning for the Acceleration of Quantum Chemical Simulations

Abstract

The development of quantum chemistry has long been shaped by a central tension: while the laws governing electronic structure are known, their exact application quickly becomes computationally prohibitive for realistic molecular systems. Over decades, this challenge has driven the design of increasingly sophisticated approximations that balance predictive accuracy with computational affordability. More recently, machine learning (ML) has emerged as a new addition to this methodological landscape, offering the possibility of reproducing high-level quantum chemical results at a fraction of the cost. This thesis explores how ML can contribute to this long-standing objective in a particularly resource-conscious way. Rather than treating ML purely as a black-box substitute for quantum chemistry, the work asks a broader methodological question: under finite budgets for data generation, training and inference, what is the most efficient way to use data-driven models to accelerate quantum chemical simulations? Across the different applications studied here, the guiding principle has been to identify the simplest effective strategy for the problem at hand while retaining as much physical structure and reusing as much existing data as possible. A first key result of this thesis is that substantial acceleration can, in some settings, be achieved with remarkably simple models. In the context of basis set extrapolation for GW quasiparticle energies, a linear regression model based on molecular orbital descriptors was shown to recover near-complete basis set accuracy from finite-basis calculations. This demonstrates that when the underlying quantum chemical representations already contain the essential physical information, even lightweight statistical models can provide acceleration while maintaining high-level quantum chemical accuracy. As many ML applications, especially neural networks, critically depend on sufficiently broad and reliable training data, part of this work focused on constructing a large-scale dataset of quasiparticle self-consistent GW (qsGW) quasiparticle energies, GW Bethe--Salpter equation (GW-BSE) neutral excitation energies, transition dipole moments and oscillator strengths across a chemically diverse space of organic molecules. Building on this foundation, a graph neural network was trained for the prediction of charged and neutral excitation energies. A central finding is that transfer learning from lower-fidelity but already widely available data sources, such as molecular orbital energies from density functional theory (DFT) and excitation energies from time-dependent DFT (TDDFT), can substantially improve the prediction of the high-fidelity qsGW and GW-BSE targets. In this way, previously generated computational data become a powerful resource for reducing the cost of expensive reference calculations. The question of how simple ML models can remain while still being effective was further investigated for solvation energies and geometry optimization in solution. Here, the results show that relatively simple graph neural network architectures can already yield accurate predictions of Gibbs solvation energies for highly charged molecules. At the same time, ML was also used to parametrize and correct established physically grounded solvation models. These results suggest that, in such settings, hybrid strategies that combine explicit physical models with learned components can be as effective as fully data-driven approaches while retaining the robustness and interpretability of the underlying physical description. Taken together, the work presented in this thesis shows that efficient ML for quantum chemistry does not rely on a single universally optimal model class. Instead, the most effective strategies arise from matching the complexity of the statistical model to the physical structure of the problem, reusing data across different levels of quantum chemical theory and retaining established physical models wherever they already provide reliable inductive bias. In this sense, ML serves not simply as a faster predictor but as a flexible methodological tool for extending the practical reach of quantum chemical simulations through resource-efficient acceleration.