This dissertation investigates the time-dependent quantum dynamics of molecules using wavefunction-based methods, focusing on two distinct, highly relevant phenomena: High Harmonic Generation (HHG) in strong laser fields and Exciton-Exciton Fusion (EEF) in molecular aggregates. The first part of the thesis addresses the challenge of accurately simulating strong-field HHG in H2+. A hybrid quantum dynamical approach is presented, which combines standard Gaussian-Type Orbitals (GTOs), augmented with Kaufmann functions, for the electronic structure with a numerical grid representation for the nuclear motion. Ionization is incorporated via a heuristic energy-dependent model. By performing benchmark comparisons against "exact" full-grid solutions, this work demonstrates that the hybrid GTO approach accurately reproduces the HHG spectra, validating it as a computationally efficient and scalable alternative. A key finding is that the explicit inclusion of nuclear motion is essential for a quantitative description of the harmonic intensities, whereas non-Born-Oppenheimer (NBO) coupling effects are found to be negligible for this system under the investigated conditions. The second part of the thesis explores multi-exciton dynamics by modeling the EEF process in perylene dimers. A tailored ab initio approach based on Time-Dependent double-Configuration Interaction Singles (TD-dCIS) is employed, utilizing molecular orbitals localized on the respective monomer fragments. To isolate and analyze the fusion process, a model system is constructed by slightly distorting the monomer geometry to achieve perfect energy resonance between the relevant excitonic states. The TD-dCIS simulations are compared to simpler, established models, such as the Molecular Exciton Hamiltonian (MEH). The results reveal that MEH models based on the point-dipole approximation significantly overestimate the inter-monomer coupling and fail to describe the dynamics at short distances. Finally, the study demonstrates that the requisite double-exciton (S1S1) state can be efficiently populated from the ground state using ultrashort laser pulses, providing a pathway for coherent control. Collectively, this work validates tailored TD-CI methods as a powerful framework for simulating complex, non-equilibrium quantum dynamics, providing fundamental insights into both strong-field interactions and multi-exciton processes in molecules.
Christoph Witzorky (Thu,) studied this question.