Balancing Cost and Accuracy: Method Development, Assessment, and Application of Quantum Chemical Methods

Abstract

This thesis advances the field of computational chemistry through the development, systematic benchmarking, and targeted application of quantum chemical methods. A central methodological contribution is the extension of the r²SCAN-3c composite density functional approach to Slater-type orbitals, thereby demonstrating that composite schemes can be successfully transferred to alternative basis set types. Due to the application of an all-electron basis set and the implementation into the Amsterdam Modeling Suite, this development also enables, for the first time, the application of explicit relativistic treatments within the "3c" composite family, expanding the scope of such methods to heavier elements and more challenging systems. <br/> Further, comprehensive benchmark studies were conducted across diverse datasets, including ²⁰⁷Pb Nuclear Magnetic Resonance (NMR) chemical shifts (PbS50), inorganic heterocycle dimerizations (IHD302), and artificially generated "mindless" molecules (MB2061). These investigations provided a rigorous assessment of density functional approximations, semiempirical quantum mechanical methods, and machine-learning interatomic potentials. The results revealed systematic strengths and limitations across the different classes of methods, underscoring that accuracy is not universal but depends critically on both the targeted property and the underlying chemical environment. In this context, the recently developed semiempirical quantum mechanical g-xTB method and modern machine-learning potentials, such as UMA-sm, have emerged as particularly promising, offering hybrid DFT-level accuracy at a fraction of the computational cost. However, challenges regarding robustness and error distribution remain for machine-learning approaches. <br/> The practical relevance of the drawn insights was demonstrated through applications to silafullerane systems, where theoretical investigations complemented experimental studies by rationalizing unusual bonding motifs, predicting hydrogenation mechanisms, and accurately reproducing measured ³⁵Cl NMR shifts. These case studies highlight the dual explanatory and predictive role of theory in advancing chemical understanding. <br/> Taken together, the results of this thesis demonstrate that no single "best" method exists in quantum chemistry. Instead, reliability arises from carefully validated methodological choices tailored to the problem at hand, supported by systematic benchmarking and informed by practical applications. The findings emphasize the importance of composite methods, advanced semiempirical models, and machine learning potentials in balancing accuracy and computational efficiency, while also addressing the need for rigorous stress testing using challenging benchmark sets. Ultimately, this work establishes strategies for extending the reach, reliability, and robustness of computational chemistry, laying a foundation for future methodological advancements and for bridging the gap between theoretical predictions and experimental practice across an increasingly broad chemical space.