Advancing Computational Chemistry with Stochastic and Artificial Intelligence Approaches

Computational chemistry aims to simulate reactions and molecular properties at the atomic scale, advancing the design of novel compounds and materials with economic, environmental, and societal implications. However, the field relies on approximate quantum chemical methods that balance cost and accuracy. This trade-off hinders effective configuration sampling when combining ab initio methods with molecular dynamics (MD), limiting thermodynamic examination to systems with a few hundred atoms and temporal sampling of hundreds of picoseconds.This thesis focuses on leveraging unconventional approaches based on stochastic sampling and artificial intelligence (AI) to address the three-fold challenge of attaining high accuracy, accommodating large system sizes, and enhancing the efficiency of configurational sampling for specific problems.It starts with the implementation of second-order Møller-Plesset perturbation theory (MP2) in a plane wave (PW) basis set, that allows to systematically converge reference energies to the complete basis set (CBS) limit, devoid of basis set superposition errors, and enables the application of MP2 to periodic systems. A comparison of PW MP2 interaction energies with computationally more expedient correlation-consistent basis sets reveals the limitations of the latter in capturing full correlation energies at the CBS limit and for larger systems. Secondly, a PW Monte Carlo MP2 method is introduced, which stochastically samples virtual space contributions to the correlation energy, and reduces execution times up to a thousand-fold while maintaining low statistical errors. The PW MP2 implementation is not only valuable independently but also in the context of density functional theory (DFT), where it enables the development of the most accurate double-hybrid DFT functionals to date. Despite this, the accuracy of DFT results still depends on the specific system being studied. Thus, as a third step, the accuracy of popular Minnesota DFT functionals in describing the properties of liquid water is assessed, thanks to the acceleration and transferability of a machine learning (ML) multiple time step MD scheme. Comparisons with other DFT approximations and experimental data highlight the importance of a judicious amount of exact exchange for capturing hydrogen bonding. The M06-2X(-D3) functionals are identified as the top-performing candidates, demonstrating good performance for both structural and dynamical properties. This spotlights their potential for further validation when combined with an explicit treatment of nuclear quantum effects. The fourth topic of the thesis addresses configurational sampling using genetic algorithms (GAs) to sample low-energy configurations of peptides as observed in ultracold spectroscopy experiments. By utilizing a surrogate energy model and subsequent refinement with DFT, the GA approach enables efficient exploration of the potential energy surface (PES) in a matter of hours, significantly faster than traditional search methods that require weeks of trials. Remarkably, the newly developed GA approach successfully retrieves lowest-energy structures that align with experimentally-resolved infrared spectra. Finally, an alternative GA combined with unsupervised learning is introduced, improving PES coverage in low-energy regions. In summary, this thesis contributes to enhancing the PES accuracy and sampling by combining quantum chemical methods with stochastic and AI approaches.