Abstract
This thesis aims to illustrate the limitations of quantum chemistry under the Born-Oppenheimer approx-imation, especially related to exited state systems and electronic transitions. Two of the most suitablemethods for excited state dynamics for photochemical processes, ab initio multiple spawning and tra-jectory surface hopping, are discussed as solutions to these problems in the context of applications.Further, possible future paths are discussed based on available literature including recent research basedon machine learning.