The dynamics of carbon dioxide in third generation (i. e., flexible) Metal-Organic Frameworks (MOFs) can be experimentally observed by ¹³C NMR spectroscopy. The obtained line shapes directly correlate with the motion of the adsorbed CO₂, which in turn are readily available from classical molecular dynamics (MD) simulations. In this article, we present our publicly available implementation of an algorithm to calculate NMR line shapes from MD trajectories in a matter of minutes on any current personal computer. We apply the methodology to study an effect observed experimentally when adsorbing CO₂ in different samples of the pillared layer MOF Ni₂(ndc)₂(dabco) (ndc=2,6-naphthalene-dicarboxylate, dabco=1,4-diazabicyclo-[2.2.2]-octane), also known as DUT-8(Ni). In ¹³C NMR experiments of adsorbed CO₂ in this MOF, small (rigid) crystals result in narrower NMR line shapes than larger (flexible) crystals. The reasons for the higher mobility of CO₂ inside the smaller crystals is unknown. Our ligand field molecular mechanics simulations provide atomistic insight into the effects visible in NMR experiments with limited computational effort.