"The spectral parameters of nuclear magnetic resonance (NMR) provide information on molecular structure and properties. Furthermore, NMR relaxation conveys information on molecular dynamics, rotation, chemical exchange and collisions. Paramagnetic NMR (pNMR) is gaining importance in chemistry, structural biology, magnetic resonance imaging (MRI) and materials science. Open-shell molecules experience the sc. paramagnetic relaxation enhancement (PRE) due to time-dependent interaction of the nuclear spin with the unpaired electron(s). Besides dynamics, the different contributions to PRE also encode structural information. Phenomenological theories describing PRE involve time correlation and spectral density functions of either the time-averaged or instantaneous hyperfine interaction, in the sc. Curie and electronic relaxation, respectively. These models rely on approximations such as single-exponential decay of the correlation functions, and simplified models of molecular dynamics. We will apply the full arsenal of state-of-the-art computational chemistry on PRE, by first performing ab initio molecular dynamics simulations, and then applying quantum-chemical calculations of the magnetic properties for instantaneous simulation snapshots. We apply the Redfield relaxation theory for the Curie mechanism, using the novel and general methodology for the pNMR shielding tensor developed by the host group, as well as the electron spin relaxation rate. The electronic relaxation of nuclear spins is then approached both by the semiclassical Redfield theory applied to the instantaneous dipolar interaction between the electronic and nuclear spins, as well as by fully quantum-mechanical, coupled time-evolution of the two systems. Methods are developed with the aqueous solution of the Ni(II) ion used as prototype system. Applications to Gd(aq) as well as endohedral Gd fullerenes are investigated, with impact on the development of novel, efficient and safe MRI contrast agents."