Fast development of the x-ray facilities and experimental techniques allows studying the x-ray induced dynamics of complex molecules with ultra-high temporal and spatial resolution using advanced x-ray spectroscopy methods. Growing experimental interest requires already now theoretical simulations on a high accuracy level in order to model complex x-ray processes in free molecules and liquids. Theoretical background for various processes under x-ray excitation, including pump-probe spectroscopy techniques, was initially developed in our group and applied to studies of isolated molecules and condensed matter. In the present project we plan to use high performance computers at NAISS for accurate simulations of the electron-nuclear dynamics of quantum systems with application to various spectroscopic schemes. The numerical methods proposed in the project combine quantum and classical approaches, including fully quantum description of the nuclear motion and ab initio (RASPT2), TDDFT, ROCIS and DFT/ROCIS methods for the electronic structure simulations. Sufficient part of the project is devoted to modelling of the nuclear wave packet dynamics in multidimensional space. In the present project we plan to use a well optimised home-made codes eSPec, XRAMP and VCRAM developed for the solution of the complex dynamical problems on x-ray transitions. The software was tested on multi-core clusters and successfully applied for studies of isolated molecules and condensed matter (liquids). Recently we developed new protocols for using the developed software and numerical algorithm for computation of x-ray emission spectra (in both linear and nonlinear regimes), which were tested on NAISS supercomputers for isolated molecules (gas phase numerical experiment). In the present proposal, we plan to extend our simulations for much more complex object, namely real liquid targets, modelled as large molecular clusters. To attack this problem we plan to use the standard quantum chemical packages (ORCA, OpenMolcas, Gaussian, and VeloxChem) for multidimensional simulation of the potential energy surfaces, along with own software (XRAMP, eSPec, and VCRAM) for accurate quantum calculations of the nuclear dynamics for liquid water and methanol (linear case) and SF6 and H2O (nonlinear regime). For this large-scale calculation use of high performance multi-core computations are unavoidable. Due to this we apply for use of Darder and Tetralith (see details in the Resource Usage below). Our coming results are highly awaited to support present experimental activities of our collaborators from high-resolution X-ray spectroscopy VERITAS beamline @ MAX IV (Lund, Sweden) and SQS beamline @ The European XFEL and FLASH II (Hamburg, Germany).