Calculation of ¹H-NMR relaxation rates from a united-atom model of propane using reverse coarse-graining

The ¹H-NMR relaxation rates R₁ of molecular systems can be calculated from all-atom molecular dynamics simulations and serve as a critical support to experimental measurements. In previous work, we demonstrated that relaxation rates can also be accurately computed from coarse-grained simulations, provided that certain atomic details of the system are reconstructed. Specifically, the positions of the spin carriers, which are essential for NMR calculations, must be predicted. This reconstruction can be achieved using reverse coarse-graining methods applied to coarse-grained trajectories. However, these reconstructed trajectories often exhibit flaws, such as the omission of high-frequency motions and altered interatomic distances. In this study, we quantify the impact of reverse coarse-graining on the ¹H-NMR relaxation rate R₁ of a propane solution. We apply an analytical reverse coarse-graining method that is based on the equilibrium configuration of a single propane molecule to reconstruct the atomic details from a united-atom model. The NMR relaxation rates are then calculated from this reconstructed model and compared to a reference all-atom model. Furthermore, we decompose the NMR signal into intramolecular and intermolecular contributions to identify the effects of reverse coarse-graining on NMR measurements. We find that the error induced by reverse coarse-graining on R₁ is at most 6% in the case of the propane molecules under consideration, and that it mostly originates in the modified interatomic distances in reconstructed trajectory. The error introduced by the reverse coarse-graining is expected to increase for larger molecules where the reconstruction of atomic details could lead to greater inaccuracies in typical interatomic distances.