Assessment and Application of Quantum Mechanical Methods for the Calculation of Large and Condensed Systems

Quantum mechanical (QM) calculations of large and condensed matter require the availability of fast and reliable methods. This thesis assesses several QM methodologies with challenging systems pushing the boundaries of these approaches. First, the semi-empirical quantum mechanical methods GFN<em>n</em>-xTB (<em>n</em> = 1, 2) are tested for the geometry optimization of large (metallo-)proteins up to 5000 atoms using an all-atom single structure quantum mechanical (ASQM) ansatz. Thus, two benchmark sets are compiled for comparison against experimental data. In general, both extended tight binding models prove to efficiently yield accurate structures of various (metallo-)proteins with and without prosthetic groups. <br> Besides the ASQM workflow, two all-atom dynamic structure QM approaches are assessed for the calculation of one- and two-photon absorption (1PA, and 2PA) spectra of realistic systems. Additionally, the recently introduced dt-sTD-DFT-xTB method is evaluated, which has the potential to significantly reduce computational requirements. The ASQM workflow is tested on the two challenging proteins bR and iLOV. Analysis reveals the importance of including the chromophore's environment explicitly to properly describe chromophore-protein interactions, and transitions inside tryptophan units, impacting the spectra considerably. To furthermore resolve side-features (<em>e.g.</em>, broadening), ADQM schemes are evaluated for the computation of 1- and 2PA spectra of iLOV's chromophore, the flavin mononucleotide (FMN) in aqueous solution, either relying on Boltzmann-averaged spectra with implicit solvation (ADQM-B), or using uncorrelated snapshots from a MD simulation (ADQM-MD) of explicitly solvated FMN. While the ADQM-B workflow provides little improvement over the ASQM scheme, ADQM-MD reveals striking agreement with experimental data for FMN in aqueous solution, underlining the importance of considering all atoms in an explicit dynamic manner. Next, the ADQM-B scheme is applied to reveal structural features of two bistable rotaxanes, complementing experimental efforts to explain their photochemical properties. Based on a multilevel scheme, Gibbs energies for several conformations are calculated, revealing that strong folding in the molecular structure is responsible for the unexpected photochemical behavior. <br> Finally, the recently proposed TI-MD-<em>λ</em>DFT approach is assessed to explore relativistic effects on phase transition points of the coinage metals Cu, Ag, and Au. While the boiling points (BPs) show increasing relativistic effects with increasing nuclear charge, the melting points (MPs) defy this correlation, as the MP of Au in the spin-orbit relativistic (SOR) and the non-relativistic (NR) limits are very similar. An in-depth study considering thermodynamical quantities reveals a strong stabilization of the SOR Au liquid due to relativistic effects, rendering NR Au similar to SOR Ag, confirming a half-a-century old hypothesis by P. Pyykkö. <br>