Ultrafast Quantum-Classical Dynamics: Applications in X-ray Spectroscopy and Method Development

Recent advances in laser technologies such as x-ray free-electron lasers and high harmonic generation have led to ever-shorter light pulses that enable us to probe ultrafastnuclear and electronic dynamics in atoms and molecules. Theoretical quantum dynamics simulations are indispensable in gaining deeper insights into these ultrafastprocesses. However, treating both electrons and nuclei fully quantum mechanically is computationally not feasible for large systems. Hence, due to their computationalefficiency, mixed quantum-classical dynamics methods such as Tully’s fewest switches surface hopping (FSSH) have become popular, in spite of their limitations. In thisthesis, I demonstrate how FSSH dynamics, combined with advanced statistical analysis techniques, can be used to understand ultrafast phenomena traced in experimentalspectra such as time-resolved x-ray absorption spectra (TRXAS). Furthermore, I introduce a new method developed to improve FSSH to provide a better description ofelectronic coherences relevant in attosecond science.With the aim of understanding the first steps of radiation damage in biomolecules, the first part of this thesis focuses on ab initio FSSH dynamics simulations of valenceionized urea monomer and dimer in vacuum as a prototypical example. Investigating the carbon, nitrogen, and oxygen K-edges in the simulated TRXAS reveals rich in-sights into the ultrafast processes. Further information is gained by applying machine learning techniques for statistical analysis which unravel uncorrelated collective mo-tions that most influence the spectra. Extending these simulations to urea in aqueous solution, I show in the second part of this thesis how the effect of proton transferbetween two hydrogen-bonded ureas and the subsequent electronic structure changes leave two distinct marks on the carbon K-edge of the TRXAS. This enables us to sep-arate the effect of nuclear and electronic motion on the spectra. These liquid phase results are in good agreement with recent pump-probe experiments on aqueous urea.In the last part, I present a new method, named ring polymer surface hopping - density matrix approach (RPSH-DM), developed to alleviate one of the shortcomingsof FSSH, namely the so-called overcoherence problem, which manifests as a poor description of electronic coherence and decoherence phenomena. RPSH-DM combinesFSSH with ring polymer molecular dynamics to incorporate decoherence effects by utilizing the spatial extent of the ring polymer, mimicking the width of the nuclearwave packet. By applying this method to a one-dimensional model system, I show how RPSH-DM can capture crucial decoherence mechanisms that are not present in FSSH.In future studies, employing RPSH-DM to investigate polyatomic systems can provide vital insights into ultrafast electronic processes occurring in attosecond experiments.