"Proposal concentrates on applying and testing computational methodology for accurate calculations of magnetic resonance parameters with inclusion of the relevant physical effects, such as electron correlation, relativity, dynamics, temperature, and media effects, in the calculation. This will be done by combination of the electronic structure theory methods with the simulation approaches, such as molecular dynamics and Monte-Carlo methods in a multiscale fashion. We will try to overcome drawbacks of current density functional approaches using and testing the new family of local hybrid functionals. We will apply and test novel, recently developed approaches for treating the relativistic effects. The methods will be applied to and tested on endohedral fullerenes and confined Xe atom guest systems. These two classes of very dynamical systems represent very multidisciplinary fields crossing the chemistry, physics, medicine, materials science, biology, and other disciplines. We will concentrate on current experimental questions and problems. Our aim is to provide answers to current hot questions in the field of endohedral fullerenes and confined Xe systems via reliable computational modelling to gain new understanding and stimulate new experiment, while pushing the state-of-the-art computational methodology forward."