Tutorial: theoretical methods for attosecond molecular ionization and dynamics

Ionization of molecules by ultrashort extreme ultraviolet and X-ray pulses triggers complex ultrafast electron-nuclear dynamics central to attochemistry. Unlike atoms, molecules feature multicentric potentials, reduced symmetry, and intrinsic vibrational motion, all of which complicate the theoretical description of continuum states and call for approaches that extend beyond standard atomic physics and quantum chemistry. Although atomic ionization is well understood, existing methods for molecular ionization are often specialized, fragmented across disciplines, and suited only to limited aspects of the problem. In this tutorial, we highlight the key physical features that set molecular ionization apart from its atomic counterpart, examine the challenges involved in modelling these processes, and present selected computational strategies applicable across weak and strong field regimes. Describing molecular photoionization in the XUV/X-ray range requires methods that approximate the complexity from nuclear motion, anisotropy, and continuum states, often creating a maze of specialised approaches. This tutorial reviews key concepts, highlights common modelling challenges, and guides the readers in selecting effective computational strategies.