The measurement of NMR relaxation quantities allow for detailed studies of molecular motions on time scales ranging from microseconds to minutes in systems as diverse as gases, liquids, gels, polymers, adsorbed liquids, or solids [8, 9], as well as proteins and other biological systems [10, 11].

The key ingredient needed for an accurate description of the nuclear spin relaxation of \(^1 \text{H}\) in soft matter systems is a realistic description of the random rotational and translational motions that molecules undergo, which makes classical molecular dynamics simulations (MDS) a natural choice. For instance, MDS have been used to characterize the NMR relaxation properties of Lennard-Jones fluid [1, 12], water and other small molecules [2, 4, 13, 14, 15, 16]. MDS are also used to study the NMR relaxation properties of molecules confined within nanoporous materials [17, 18], as well as large polymer molecules, lipid membranes, proteins, or glass transition phenomenon of glycerol [19].

In addition to classical MD, Ab initio MD has also been used to extract NMR relaxation time from water [13]. Ab initio and its variants are particularly useful in the case where the relaxation mechanisms involve quadrupolar interactions [20, 21], which is beyond the scope of the present contribution. Monte carlo simulations have also been used [22], although, in that case, some care must be taken to extract time-dependant quantities such as autocorrelation functions [23]. Recently, the possibility to calculate NMR relaxation rate from coarse grained models whose atomic details were reconstructed a posteriori was demonstrated [24].